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Mental Arithmetic and Evaluative Pressure: The Role of Distributed Cognition

by

Anna-Stiina Wallinheimo

Submitted for the Degree of Doctor of Philosophy

School of PsychologyFaculty of Health and Medical Sciences

University of Surrey

Supervisors: Dr Harriet Tenenbaum and Dr Adrian Banks

©Anna-Stiina Wallinheimo 2019

Declaration

This thesis and the work to which it refers are the results of my own efforts. Any

ideas, data, images or text resulting from the work of others (whether published or

unpublished) are fully identified as such within the work and attributed to their originator in

the text, bibliography or in footnotes. This thesis has not been submitted in whole or in part

for any other academic degree or professional qualification. I agree that the University has

the right to submit my work to the plagiarism detection service TurnitinUK for originality

checks. Whether or not drafts have been so-assessed, the University reserves the right to

require an electronic version of the final document (as submitted) for assessment as above.

Signature: Anna-Stiina Wallinheimo

Date: July 2nd, 2019

Abstract

The purpose of this thesis was to further our understanding of the role of distributed

cognition (with the use of pen and paper) in defusing the impact of evaluative pressure

caused by priming gender-related stereotypes about girls’ maths performance and

performance-approach goals on mental arithmetic performance. Interactivity is the

transferring of internal cognitive process (e.g., computing simple maths tasks) to the outside

world by using different tools (e.g., pen and paper). Some members of social groups (e.g.,

women) may not perform well in mathematics after negative stereotypes about their academic

performance in the mathematical domain, which is known as stereotype threat. Stereotype

threat is the risk of confirming a negative stereotype expectation about one’s group. Another

decrement to performance may be caused by achievement goals, such as performance-

approach goals. Performance-approach goals are linked to normative behaviour where the

individual is motivated by outperforming others in academic performance. Negative

stereotyping and performance-approach goals can generate anxiety that deplete existing

working memory resources. However, some of these working memory limitations can be

compensated by off-loading the internal cognitive process to the external environment. We

tested whether off-loading could buffer the effects of stereotype threat and performance-

approach goals in four experiments.

In Studies 1 (16-year-old girls) and 2 (female university students), participants carried

out mental arithmetic tasks in the stereotype threat condition or control, crossed with

interactivity or no interactivity. There was increased maths performance (accuracies) with

interactivity, confirming existing literature. Additionally, the solution latencies were

improved when the mental arithmetic tasks were in a known format. However, when the

maths tasks were in a novel format, the participants of the second study became slower

because of speed-accuracy trade-off. The first two studies found no statistically significant

i

effects of stereotype threat on maths performance. Nevertheless, working memory in

participants in Study 1 was depleted in the stereotype threat condition, but it did not affect

mental arithmetic performance. Finally, the participants in the interactive conditions in Study

2 had a reduction of their state maths anxiety levels measured at the end of the experiment.

Studies 3 (Pilot Study) and 4 focused on achievement goals and their differing effects on

working memory. Female university students carried out modular arithmetic tasks in a

performance-approach goal or mastery-approach goal condition crossed with interactivity or

no interactivity. Performance-approach goal endorsement hampered cognitive performance,

as measured by maths accuracy in Study 3, but not in Study 4. These findings were extended

in Study 4 where these negative effects were reduced with the help of interactivity. Across

both studies, individuals in the mastery-approach goal condition had a performance drop in

the interactive condition (Study 3 and 4). Thus, interactivity did not benefit the cognitive

performance of these participants. Finally, Study 4 reported higher maths anxiety levels for

the individuals in the performance-approach condition. However, the increased maths anxiety

levels were not reduced with the help of distributed cognition. Reasons for the findings and

future implications will be discussed.

ii

Publications

Conference Presentations:

Wallinheimo, A., Tenenbaum, H., & Banks, A. (2019, July). Achievement goals and mental

arithmetic: The role of distributed cognition. A 6-page submission has been accepted to be

presented at the 41st Annual Conference of the Cognitive Science Society. Montreal, Canada.

Wallinheimo, A., Banks, A., & Tenenbaum, H. (2018, August). Modular arithmetic tasks

and phonological loop: The role of distributed cognition. Paper presented at the British

Psychological Society Cognitive Section Annual Conference, Liverpool, UK.

Wallinheimo, A., Tenenbaum, H., & Banks, A. (2017, September). Interactivity reduces the

effects of stereotype threat on maths performance, and maths anxiety. Poster presented at the

European Society of Cognitive Psychology, Potsdam, Germany.

Wallinheimo, A., Tenenbaum, H., & Banks, A. (2017, July). Interactivity, stereotype threat,

and working memory. Poster presented at the 39th Annual Conference of the Cognitive

Science Society. London, England, UK.

Wallinheimo, A. (2016, April). Interactivity, maths anxiety, and mental arithmetic. Poster

session presented at the Annual Conference of British Psychological Society, Nottingham,

UK.

iii

Acknowledgements

I would like to express my sincere gratitude to my supervisors, Dr Harriet Tenenbaum

and Dr Adrian Banks, for their continuous support of my PhD study and related research, for

their patience, motivation, and immense knowledge. Their guidance helped me in all the time

of research and writing of this thesis. I could not have imagined having better supervisors and

mentors for my PhD study.

I would also like to thank my family, my husband and my children, without whom I

would not have been able to complete the PhD journey.

iv

Table of Contents

Abstract.......................................................................................................................................i

Publications...............................................................................................................................iii

Acknowledgements...................................................................................................................iv

Table of Contents.......................................................................................................................v

List of Tables..........................................................................................................................xiii

List of Figures..........................................................................................................................xv

Preface........................................................................................................................................1

A Summary of the Thesis.......................................................................................................1

Chapter 1: Introduction..............................................................................................................6

1.1 The Extended Mind and the History of Distributed Cognition............................................7

1.2 Complementary Strategies...................................................................................................9

1.2.1 Primary Areas of Distributed Cognition.....................................................................10

1.2.2 The Concept of Interactivity.......................................................................................11

1.2.3 Interactivity and Problem Solving..............................................................................12

1.2.4 Critical Evaluation of Kirsh's Work…………………………………………………14

1.3 Stereotype Threat...............................................................................................................16

1.3.1 Women and Maths Performance.................................................................................20

1.3.2 Non-Academic Domains of Stereotype Threat...........................................................21

1.3.3 An Integrated Process Model of Stereotype Threat Effects on Performance.............23

1.3.4 Stereotype Threat and Working Memory...................................................................29

1.4 Introduction to Achievement Goals...................................................................................31

1.4.1 Academic Consequences of Performance-Approach Goals.......................................33

1.4.2 Maladaptive Behaviours of Performance-Approach Goals........................................34

v

1.4.3 Components of Performance-Approach Goals...........................................................35

1.4.4 Performance-Approach Goals and Distraction...........................................................37

1.4.5 Negative Affect...........................................................................................................38

1.4.6 Achievement Goals and Theories about Intelligence..................................................38

1.4.7 Motivation and Task Values.......................................................................................39

1.4.8 Choking under Pressure..............................................................................................40

1.4.9 Evaluative Pressure.....................................................................................................42

1.4.10 The Effects of Performance-Approach Goals on Working Memory Capacity.........44

1.4.11 Achievement Goals and Cognition...........................................................................45

1.5 Working Memory...............................................................................................................46

1.5.1 Working Memory and Intrusive Thoughts..................................................................48

1.5.2 Working Memory and Mental Arithmetic..................................................................49

1.6 Maths Anxiety....................................................................................................................50

1.6.1 Onset of Maths Anxiety..............................................................................................51

1.6.2 Maths Anxiety and Mathematical Problem Solving...................................................52

1.6.3 Mathematics Anxiety and Working Memory.............................................................53

1.6.4 Emotional Processing and Maths Anxiety..................................................................54

1.6.5 Maths Anxiety and Individuals with High Working Memory....................................55

1.6.6 Physiological Factors Linked to Maths Anxiety.........................................................56

1.6.7 Maths Anxiety and Stereotype Threat.........................................................................57

1.7 Conclusion..........................................................................................................................57

vi

Chapter 2: The Effects of Stereotype threat on Girls’ Mathematics Performance: The Role of

Distributed Cognition...............................................................................................................57

2.1.1 Stereotype Threat and Working Memory...................................................................58

2.1.2 Maths Anxiety.............................................................................................................59

2.1.3 Mental Arithmetic and Working Memory..................................................................60

2.1.4 External Representations.............................................................................................61

2.1.5 Mental Arithmetic and Interactivity............................................................................64

2.2 The Present Experiment.....................................................................................................65

2.3 Method...............................................................................................................................67

2.3.1 Participants..................................................................................................................67

2.3.2 Materials......................................................................................................................67

2.3.3 Procedure.....................................................................................................................69

2.4 Results................................................................................................................................70

2.4.1 Data Analysis Plan......................................................................................................70

2.4.2 Percentage Correct (Solution Accuracy).....................................................................71

2.4.3 Latency to Solution.....................................................................................................73

2.4.4 Working Memory........................................................................................................73

2.4.5 Mathematics Anxiety (State).......................................................................................74

2.4.6 Correlational Analysis.................................................................................................74

2.5 Discussion..........................................................................................................................77

2.6 Limitations.........................................................................................................................80

2.7 Future Studies.....................................................................................................................80

Chapter 3: The Effects of Stereotype threat on Female University Students’ Maths

Performance: The Role of Distributed Cognition....................................................................81

vii

3.1.1 Maths Anxiety and Interactivity..................................................................................83

3.2 Pilot Study..........................................................................................................................84

3.3 Method...............................................................................................................................84

3.3.1 Participants..................................................................................................................84

3.3.2 Material and Measures................................................................................................85

3.3.3 Procedure.....................................................................................................................87

3.4 Pilot Study Findings...........................................................................................................87

3.5 The Current Study..............................................................................................................89

3.6 Method...............................................................................................................................90

3.6.1 Participants..................................................................................................................90

3.6.2 Material and Measures................................................................................................90

3.6.3 Procedure.....................................................................................................................92

3.7 Results................................................................................................................................94

3.7.1 Data Analysis Plan......................................................................................................94

3.7.2 Group Differences.......................................................................................................95

3.7.3 Percentage Correct (Mental Arithmetic Tasks)...........................................................95

3.7.4 Percentage Correct (Modular Arithmetic Tasks, Low WM Load).............................98

3.7.5 Percentage Correct (Modular Arithmetic Tasks, High WM Load).............................98

3.7.6 Latencies (Mental Arithmetic Tasks)..........................................................................99

3.7.7 Latencies (Modular Arithmetic Tasks, Low WM Load)............................................99

3.7.8 Latencies (Modular Arithmetic Tasks, High WM Load)..........................................100

3.7.9 Working Memory......................................................................................................101

3.7.10 Maths Anxiety (State).............................................................................................101

viii

3.7.11 Individual Differences.............................................................................................102

3.8 Discussion........................................................................................................................103

3.9 Limitations.......................................................................................................................106

3.10 Future Studies.................................................................................................................107

Chapter 4: Achievement Goals and Mental Arithmetic: The Role of Interactivity...............107

4.1.1 Achievement Goals...................................................................................................108

4.1.2 Mastery-Approach Goals and Performance-Approach Goals...................................109

4.1.3 Achievement Goals and Modular Arithmetic Tasks.................................................110

4.1.4 Achievement Goals and Working Memory..............................................................110

4.1.5 The Benefits of Interactivity.....................................................................................111

4.2 Present Study (Pilot Study to Study 4).............................................................................113

4.2.1 Hypotheses of the Study............................................................................................113

4.3 Method.............................................................................................................................115

4.3.1 Participants................................................................................................................115

4.3.2 Material and Measures..............................................................................................115

4.3.3 Procedure...................................................................................................................118

4.4 Results..............................................................................................................................119

4.4.1 Data Analysis Plan....................................................................................................119

4.4.2 Group Differences.....................................................................................................119

4.4.3 Accuracy...................................................................................................................122

4.4.4 Latencies...................................................................................................................124

4.5 Discussion........................................................................................................................125

4.6 Limitations of the Study...................................................................................................128

ix

4.7 Future Studies...................................................................................................................129

Chapter 5: Achievement Goals, Maths Performance, and Interactivity.................................130

5.1.1 Maths Anxiety...........................................................................................................130

5.1.2 Maths Anxiety and Working memory.......................................................................131

5.1.3 Achievement Goals and Maths Anxiety...................................................................132

5.1.4 Positive Affect and Working Memory......................................................................133

5.1.5 The Current Study.....................................................................................................133

5.2 Method.............................................................................................................................135

5.2.1 Participants................................................................................................................135

5.2.2 Material and Measures..............................................................................................136

5.2.3 Procedure...................................................................................................................140

5.3 Results..............................................................................................................................141

5.3.1 Data Analysis Plan....................................................................................................141

5.3.2 Group Differences.....................................................................................................141

5.3.3 Accuracy...................................................................................................................143

5.3.4 PANAS......................................................................................................................145

5.3.5 Maths Anxiety (State)...............................................................................................146

5.3.6 Mediation..................................................................................................................147

5.3.7 Correlations...............................................................................................................148

6 Discussion...........................................................................................................................149

7 Limitations..........................................................................................................................155

8 Future Studies......................................................................................................................155

Chapter 6: Discussion............................................................................................................156

x

1.1 Summary of the Findings.............................................................................................156

1.2 The Effects of Interactivity on Maths Performance.....................................................159

1.3 The Impact of Stereotype Threat on Mental Arithmetic Performance........................160

1.4 Stereotype Threat and State Maths Anxiety.................................................................163

1.5 Stereotype Threat and Working Memory....................................................................166

1.6 Achievement Goals......................................................................................................170

1.7 The Impact of Interactivity on Maths Performance.....................................................171

1.8 Interactivity and the Impaired Maths Performance of the Participants in the Mastery-

Approach Goal Condition..................................................................................................172

1.9 The Maths Performance of the Performance-Approach Goal Participants..................174

1.10 The Endorsement of Performance-approach Goals and Interactivity........................178

1.11 State Maths Anxiety...................................................................................................179

1.12 State Maths Anxiety and Distributed Cognition........................................................180

2 Limitations and Future Studies...........................................................................................182

3 Contributions of the Findings..............................................................................................182

References..............................................................................................................................186

Appendix A: Ethical Approval for Study 1.......................................................................203

Appendix B: SAFE for Study 2...........................................................................................205

Appendix C: SAFE for Study 3...........................................................................................208

Appendix D: SAFE for Study 4...........................................................................................211

Appendix E: Basic Arithmetic Skills Test (BAS), Study 1, 2, and 4................................215

Appendix F: Mathematics Self-Efficacy and Anxiety Questionnaire, Study 1 and 2....216

Appendix G: Maths Anxiety Scale (Trait), Study 2 and 4................................................217

Appendix H: Computation Span (Working Memory), Study 1, 2, and 4.......................219

xi

Appendix I: Mental Arithmetic Tasks (Known Format), Study 1 and 2........................234

Appendix J: Modular Arithmetic Tasks, Study 2.............................................................235

Appendix K: Modular Arithmetic Tasks, Study 3 and 4.................................................237

Appendix L: Positive and Negative Affect Scale (PANAS), Study 4...............................240

Appendix M: Maths Anxiety Scale (State), Study 1, 2, and 4..........................................241

xii

List of Tables

Table 1: Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data) 71

Table 2: Descriptive Statistics: Means and Standard Errors (Post-Testing Data) 72

Table 3: Correlation Matrix for the Performance Measures (Percentage Correct, Latencies,

Working Memory, and Mathematics Anxiety) in the Stereotype Threat, Interactive Condition

75


Working Memory, and Mathematics Anxiety) in the Stereotype Threat, Non-Interactive

Condition 76


Working Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Interactive

Condition 76


Working Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Non-Interactive

Condition 77


Table 8: Descriptive Statistics: Means and Standard Errors (Post-Testing Data) 97

Table 9: Descriptive Statistics: Means and Standard Errors of Modular Arithmetic

Performance (Accuracy and Latency to Solution) in Block 1 120

Table 10: Descriptive Statistics: Means and Standard Errors of Modular Arithmetic

Performance (Accuracy and Latency to Solution) in Block 2 (Interactive Condition) 120

Table 11: Descriptive Statistics and Standard Errors of Modular Arithmetic Performance

(Accuracies and Latencies to Solution) in Block 2 121


Difference (B2 - B1) across the Experimental Conditions 123



(Accuracy and Latencies to Solution) in Block 1 142

xiii


(Accuracy and Latencies to Solution) in Block 2 143

Table 16: Descriptive Statistics and Standard Errors of the Primary Dependent Variables

(Based on a Performance Difference Score, B2 – B1) 145

Table 17: Summary of Correlations in the Performance-approach Goal and Non-Interactive

Condition only 149

Table 18: Summary of Correlations in the Performance-approach Goal and Interactive

Condition only 149

xiv

List of Figures

Figure 1: Examples of low-load and high-load modular arithmetic tasks 116

Figure 2: Examples of vertical and horizontal modular arithmetic tasks 117

Figure 3: Mean difference in modular arithmetic performance (%) as a function of

experimental condition (performance-approach goal or mastery-approach goal crossed with

interactivity or control) 123


experimental condition (performance-approach goal or mastery approach goal) 124

Figure 5: Examples of low-load and high-load modular arithmetic tasks 138

Figure 6: Examples of vertical and horizontal modular arithmetic problems 138



interactivity or control) 144

Figure 8: Mean difference in state maths anxiety levels as a function of experimental

condition (performance-approach goal or mastery-approach goal) 147

xv

Preface

A Summary of the Thesis

The aim of this thesis is to further the understanding of the role of distributed cognition in

mental arithmetic performance, in evaluative pressure situations. When people are in a high-

stakes testing situation (e.g., caused by a standardised maths test), the stressful situation can

adversely affect people’s ability to solve maths problems. Individuals might be fully

motivated to perform well in these stress-laden situations, but the circumstances can have

detrimental consequences and cause people to perform at their worst (i.e., choke under

pressure), (Beilock, 2008). The additional pressure (caused by for example stereotype threat

or performance-approach goal) can fill working memory with thoughts about the stressful

situation (Eysenck & Calvo, 1992). This thesis focuses on whether interactivity can overcome

negative consequences of distraction in situations activated by stereotype threat and goal

theory. The first focus, stereotype threat, occurs when awareness of a negative stereotype

about how one’s social group is expected to perform (e.g., girls are not good at maths tasks)

can produce less than optimal academic performance (Steele, 1997). Past research has

suggested that this might be due to additional taxation of the working memory (due to

additional worries) and therefore the individual has less capacity available to deal with the

task (Schmader & Johns, 2003). The second focus is on achievement goals, which can be

associated with increased worry of succeeding in achieving optimal performance. The

achievement goals construct refers to the way individuals represent and pursue competence in

challenging settings (Elliot & Dweck, 2005). Due to the nature of the performance-approach

goals (dominated by normative structure and social comparison to peers), there can be

worries about succeeding, similar to stereotype threat, consequently leading to reduced

working memory resources (Crouzevialle & Butera, 2013)

1

The negative thoughts caused by these stress-laden situations compete with the resources

that are normally allocated to the execution of the required task. This additional pressure

serves to create a dual-task environment where the additional pressure and the task in hand

compete for the same limited working memory resources (Beilock, Holt, Kulp, & Carr,

2004). Explicit monitoring (self-focus) theories, on the other hand, claim that when there is

increased performance pressure (e.g., caused by a normative performance-approach goal

where a social comparison is made), this can elevate anxiety levels and self-consciousness

about performing correctly and to a high standard. The individual is conscious about the

required steps to the solution and therefore is being careful of every step and hoping that by

being careful, the overall performance is improved. However, attention to performance at

such a component specific level is thought to disrupt the proceduralized processes that are not

normally completed with the help of working memory (Beilock & Carr, 2001). When an

individual is concerned of not reaching academic standards or goals (e.g., when faced with a

stereotype threat), there are ruminative thoughts that can consume attentional resources of the

working memory. This concern about not reaching the goals, is called self-evaluation threat

and it can induce attentional focusing leading to reduced working memory capacity (Koole &

Dijksterhuis, 1999).

The overall structure of this thesis takes the form of six chapters, including this

introductory chapter (Summary of the Thesis). In Chapter 1, we begin by introducing the

literature on distributed cognition and its associations with working memory off-loading and

enhanced problem solving and mental arithmetic performance in particular (Guthrie &

Vallée-Tourangeau, 2015; Kirsh, 2010; Maglio, Matlock, Raphaely, Chernicky, & Kirsh,

1999). The focus is then moved to the stereotype threat literature followed by a review of the

literature on achievement goals.

2

The first experiment is presented in Chapter 2. The purpose of the first study was to

investigate the role of interactivity in defusing the impact of gender stereotype threat on

difficult mental arithmetic tasks, having 16-year-old girls as participants. The effects of

negative stereotyping on working memory and maths anxiety were also investigated as part

of the study. The study found statistically significant effects of stereotype threat on working

memory capacity but failed to find a causal effect of working memory on mental arithmetic

performance. One inference was that the maths tasks were in an easily recognisable format

and therefore the participants used well-rehearsed patterns, almost automatic processes that

were less working memory resource demanding.

Chapter 3 summarises the background and findings of Experiment 2. Similar to the

first study, the purpose of the second study was to look at the negative effects of stereotype

threat on female university students’ maths performance and working memory. Two different

types of maths tasks (with varying levels of working memory taxation) were utilised: mental

arithmetic tasks (known format) and modular arithmetic tasks that were in a novel format

(low WM load and high WM load). As before, we further explored whether distributed

cognition could be employed to mitigate the negative effects of stereotype threat on the maths

performance. Additionally, the study investigated whether there were any carry-over effects

of stereotype threat and interactivity on state maths anxiety that was measured at the

completion of the experiment. Finally, there were no statistically significant effects of

stereotype threat on the mental arithmetic performance, modular arithmetic performance, and

on working memory. However, the participants in the interactive condition were less maths

anxious after the experiment.

We then move to Chapter 4 where the third experiment is presented. The aim of the

Study 3 was to further examine the influence of achievement goal states on working memory.

As before, we also investigated whether interactivity could be used to mitigate any of the

3

possible negative effects of achievement goals on maths performance. It was argued that if

working memory is loaded due to outcome related worry then there is additional taxation on

the working memory (Crouzevialle & Butera, 2013). Together with the horizontally

presented maths problems (modular arithmetic tasks) there can be maths performance

decrements when in the performance-approach goal condition (Beilock, 2008). We reasoned

that, if worries of outperforming others lead to poor maths performance, then giving students

the opportunity to externalize the internal cognitive process would reduce the internal

working memory demands and enhance the maths performance. As expected, it was reported

that the maths performance of the individuals in the performance-approach goal condition

was lower than the participants in the mastery-approach goal when there was no interaction

with external artefacts. In addition, mastery-focused individuals’ maths performance

deteriorated from the use of interactivity confirming existing findings. If the agent has the

internal cognitive abilities to complete the task, then there is limited need to make use of

external artefacts. The coupling of internal and external resources is an exercise relative the

degree of tasks difficulty and the cognitive resources of the agent (Kirsh, 2010; Vallée-

Tourangeau & Wrightman, 2010; Webb & Vallée-Tourangeau, 2009). These findings lend

their support to the theory by Crouzevialle and Butera (2013) who stated that mastery-

focused individuals are not as distracted as their performance-approach goal counterparts, and

therefore their internal cognitive resources (working memory in particular) are not affected.

Chapter 5 presents the findings for the Study 4. This study expands on the findings of

the earlier study (Study 3). Additionally, we argued that it would be the performance-focused

individuals who would show higher levels of maths anxiety (due to outcome related concerns,

in a mathematical domain). Experiment 4 therefore measured maths anxiety of the

participants both before the experiment (trait maths anxiety) and after (state maths anxiety).

Additionally, it was argued that if there is increased state maths anxiety when performance-

4

approach goal is made salient, then clearly there should be more benefits of externalizing the

internal cognitive process to the outside world for the performance-focused individual. As

predicted, the performance-focused participants benefited from coupling the internal and

external resources and their maths performance was enhanced. As before, the benefits of

distributed cognition were not experienced by the mastery-focused participants; their maths

performance was depleted when interactivity was employed. These results match those

observed in previous studies (Kirsh, 2010; Vallée-Tourangeau & Wrightman, 2010; Webb &

Vallée-Tourangeau, 2009). Finally, the study confirmed that it was the performance-approach

goal individuals who experienced increased maths anxiety levels after the experiment.

However, these increased maths anxiety levels were not reduced with the help of

interactivity.

The final chapter (Chapter 6) draws upon the entire thesis, tying up the various

theoretical and empirical strands in order to conclude on the empirical findings of the entire

thesis. Additionally, a discussion of the implication of the findings to future research into this

area is included.

5

Chapter 1: Introduction

According to the classical view of cognitive psychology to solve a problem, internal

representations of a problem’s structure are created (the problem space) to complete a

required task. The traditional cognitive view suggests that there are core set of processes for a

variety of different problems. Additionally, if two agents have different capacities (i.e.,

expertise and intellectual ability) they face different task environments (Newell & Simon,

1972). However, the classical view has been heavily criticized by the school of situated

cognition (also called embodied and interactive cognition) where problems are not believed

to follow a formal structure that maybe the same across different activities. The situated view

claims that each problem is directly linked to a concrete setting and is only resolved by

reasoning in situation-specific ways. The agent makes use of the material and cultural

resources locally available in order to solve the required problem (Kirsh, 2009). Clearly,

problem-solving is a form of reasoning that is connected with the activities and context in

which it takes place. However, according to the traditionalists, putting a finger on an object,

utilising pen and paper, and talking to one-self are not part of the actual problem-solving

activity. This is in complete contrast with the situationalist view where these actions are

regularly observed and further linked to the successful performance of the agent (Kirsh,

2009).

Kirsh (1995a) claimed that individuals use the external world to support their thinking

and problem solving. Complementary strategies (external representations) are any organizing

activities which recruit external elements to reduce cognitive loads (e.g., pointing, arranging

the position and orientation of objects, writing things down, and manipulating artefacts that

can encode the state of a process or simplify perception), (Kirsh, 1995a). Hutchins (1995)

stated that cognition was a socially distributed phenomenon. Based on his observations on the

navigation bridge of a US navy ship, Hutchins (1995) defined navigation as it was performed

6

by a team on the bridge as the unit of cognitive analysis. It was concluded that human

cognition (naturally situated cognition) was not just influenced by culture and society, it was

a cultural and social process in itself. Clearly, as human cognition is situated in a relatively

complex sociocultural world, it cannot be unaffected by its surroundings (Hutchins, 1995).

The purpose of this programme of research is to investigate ways of reducing the

additional taxation of working memory caused by evaluative pressure. There are various

situations that are linked to evaluative pressure but the research reported here concentrates on

stereotype threat about females’ maths performance and achievement goals (performance-

approach goals and mastery-approach goals, in particular). These two situation-inducing

stress situations have been chosen due to their similar taxing effects of existing working

memory resources. It has been suggested that one creative way of off-loading the increased

working memory load caused by stereotype threat or achievement goals (and performance-

approach goals in particular) is interactivity (i.e., the use of pen and paper).

1.1 The Extended Mind and the History of Distributed Cognition

Research in cognitive science and philosophy of mind called for rethinking of the

historical concepts of cognition because of evidence that cognition is distributed across brain,

body, and the world (Clark & Chalmers, 1998). According to Clark and Chalmers (1998), the

objects within the environment around us function as part of the mind and therefore it would

be arbitrary to say that the mind is contained only within the head alone (traditional cognitive

view). As external objects have an important role in assisting with the cognitive processes,

there is a coupled system between the mind and the environment which functions as a

complete cognitive system of its own (Clark & Chalmers, 1998). However, the notion of

utilising tools to navigate through the world is not new. People have always utilised external

7

artefacts and objects in assisting with tasks that require internal cognitive resources. For

example, small children use their fingers to help with a simple maths task.

As mentioned earlier, there is a close coupling in how navy crew members use external

artefacts to bring a ship into a port. This distributed cognitive system comprises of sailors,

procedures, and instruments. These cognitive systems are composed of multiple agents and

external artefacts (Hutchins, 1995). Distributed cognition accentuates the ways that cognition

is off-loaded into the environment through both technological and social means. It is a way

for studying and understanding cognition rather than a type of cognition. The distributed

cognition framework involves the co-ordination between individuals, artefacts, and the

environment. Additionally, distributed cognition is a framework that aims to understand how

the cognitive properties emerge from the interactions of the different component parts (across

the members of the social group, between people and environment, and over time),

(Hutchins, 2001).

Additionally, the theory of distributed cognition is focused on comprehending the

organisation of cognitive systems. It does this by extending beyond the individual to

encompass interactions between people, resources, and materials in the environment. Firstly,

it differs with the traditional views of cognition in the way that it looks for cognitive

processes wherever they might take place. This is based on the functional relationships of

elements that are part of the process. Secondly, distributed cognition looks for a broader class

of cognitive events and it does not expect these events to take place internally in people’s

heads. Cognitive processes can be distributed across the members of a group. There can be

coordination between internal and external structure and cognitive processes can be

distributed through time so that the earlier events can change the nature of the later events

(Hollan, Hutchins, & Kirsh, 2000).

8

Finally, there is no single definition of interactivity. Interactivity has links to Human-

Computer Interaction (HCI). It can be viewed as dialogue, transmission, optimal behaviour,

embodiment, and tool use (Hornbaek & Oulasvirta, 2017). According to Cowley and Vallée-

Tourangeau (2017), human-computer interaction (HCI), language, problem solving, and other

cognitive skills are based in sense-saturated coordination or interactivity (Cowley & Vallée-

Tourangeau, 2017). Additionally, cognitive interactivity is defined as “the meshed network of

reciprocal causations between an agent’s mental processing and the transformative actions

she applies to her immediate environment to achieve a cognitive result” (Vallée-Tourangeau

& Vallée-Tourangeau, 2017, p. 133). The research reported here uses the term interactivity

when pen and paper are used to come to the solution of the mathematical tasks. Distributed

cognition refers to the actual framework of externalising the internal cognitive process to the

outside world. Distributed cognition as a descriptive framework explains human work

systems in informational and computational terms. Distributed cognition is particularly useful

for analysing situations that require problem solving (e.g., mathematical problem solving)

and as such it was chosen as the framework for this thesis.

1.2 Complementary Strategies

One of the most common complementary strategies is the use of pen and paper to assist

the individual in adding multi-digit numbers. This programme of research has employed pen

and paper as a form of complementary strategy. By doing this, individuals off-load the

portion of working memory that is needed to store intermediate results. These actions

complement the internal cognitive processes while adding up the numbers. There are several

factors involved in the choice of a complementary strategy: speed, reduction of probable error

rate, to cope with larger problems, and to deal with interference more successfully (measures

9

of performance). Complementary strategies allow agents to compensate for processing power

and working memory resource limitations.

There are several reasons to enhance cognitive power, thinking, and comprehension.

External representations are used to save internal memory but this is not the only reason.

Interactivity changes the cost structure of the cognitive process. People go where ever it is

easier to perform the required task. If it is simpler to draw a picture of a process rather than

only thinking internally, then people externalize the process and draw a picture (Kirsh, 2010).

Additionally, interaction allows the agent to process more efficiently and more effectively

than by working inside the head alone. Interactive cognition can enhance efficiency due to

fewer errors and greater speed. Finally, effectiveness allows individuals to deal with harder

problems and it can assist people to compute more deeply and more precisely (Kirsh, 2010).

1.2.1 Primary Areas of Distributed Cognition

It has been reported that there are four primary areas of distributed cognition. The first

one relates to the use of tools that can change the way we think and perceive. The second idea

is that people generally think with their bodies and not just with the brains. Thirdly, people

know more about doing than by seeing. And finally, there can be situations when people do

their thinking with things. Kirsh (2013) explored these ideas in an experiment that tested the

effectiveness of three diverse ways of practicing a new dance phrase. Partially modelling a

dance phrase by marking the phrase (a form of practicing a dance phrase aspect-by-aspect in

a less than complete manner) was a better method of practising than working on the complete

phrase. It was also concluded that marking and full-out practice were better than repeated

mental stimulation. In other words, it is better to practise physically rather than in one’s head

only. In conclusion, by externalizing one’s thought process, the inner processes can be

improved and reshaped (Kirsh, 2013).

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When the cognitive process is externalized, the entire cognitive process becomes more

visible to the outside world and people around the agent. This process of sharing the internal

thought makes the thoughts more identifiable and clearer to everybody. The thoughts can

now be manipulated and probed by the environment too. Additionally, the act of

materializing can function as a stepping-stone for the next set of thoughts. The power of

physical re-arrangement is that it gives one the opportunity to visually compare items. This

re-arrangement makes it possible to examine relations that can feel distant or visually

complex (a good example of this is a when completing a puzzle). One would not complete a

puzzle without trying whether the pieces fit together both physically and visually. With the

help of interaction, the world can be converted from a place where only internal computation

is required to solve a problem to one where the relevant property can be physically

discovered. Unlike the internal representations, external representations offer physical

persistence and stability over time and the external representations allow us to reinstate our

thoughts. We cannot be sure that the mental image that we have today is the same as next

week. Additionally, there is normally a better idea of the effect of for example, rotation,

translation, and lighting when interacting with external representations than with the internal,

mental representations (Kirsh, 2010).

1.2.2 The Concept of Interactivity

Kirsh (1997) has explored the concept of interactivity by critiquing the decision cycle

model by Norman (1986). In this model, interaction is seen to be corresponding to a model

driven feedback system; the user would have a mental model of the environment and then

formulate a plan internally. There would then be a direct instruction to the environment and at

the end, feedback would be observed. What this model ignores is the fact that goals are not

fully formed in an agent’s head only. People use the possibilities of the surrounding

environment to help shape the thoughts and goals to see that what is possible (e.g., when

11

writing an essay). Additionally, the decision cycle model fails to recognize the dynamics that

emerge due to long term contact with the process and with the environment. Agents do

somewhat shape their environments by action as they go along. An example of this would be

when an agent writes an essay and has papers on the desk, marks books, and makes lists that

are used later on to assist with the writing process. These activities might be considered

trivial but would make it easier to write the essay next time by assisting with the writing

process (Kirsh, 1997).

1.2.3 Interactivity and Problem Solving

There are various ways that people interact with environments when they try to make

decisions and solve problems. Interactivity has been linked to better performance in problem

solving due to better allocation of attentional resources (attention available to perform

cognitive tasks) and better distribution of the cognitive load, caused by the task in hand. Most

importantly the performance increments have been achieved by allowing the agent to shape

and reshape the physical problem presentation by gestures, pointing and the use of external

artefacts (e.g., use of pen and paper or use of tokens). In one study, four levels of interactivity

(no interactivity, pointing, use of pen and paper, and use of wooden tokens) were used to

complete mental arithmetic tasks. Participants completed 5 sums that consisted of 11 single-

digit numbers in all 4 conditions. Mental arithmetic performance was enhanced with

increasing levels of interactivity. Additionally, the participants felt happier and more engaged

with the task when they were allowed to reconfigure the problem through interactivity

(Guthrie & Vallée-Tourangeau, 2015). Furthermore, interactivity can be used to mitigate the

impact of depleted working memory resources (e.g., caused by articulatory suppression) and

mathematics anxiety on maths performance (Vallée-Tourangeau, Sirota, & Vallée-

Tourangeau, 2016). Finally, in a simple coin counting experiment (seen as a simple mental

12

arithmetic task), the participants in the no hands condition were slower and less accurate than

the participants who were allowed to point and count the coins (Kirsh, 1995b).

Additionally, interactivity defuses the impact of maths anxiety in primary school

children’s maths performance. Allen and Vallée-Tourangeau (2016) explored whether

interactivity could be used to reduce the impact of primary school children’s maths anxiety

on simple addition problems. There were two independent variables: the length of the sums

(either 7 or 11 number tokens) and the level of interactivity (low or high). As expected,

longer sums led to poorer performance. The performance was increased in the high

interactivity condition (accuracy, absolute calculation error, and efficiency). In the low

interactivity condition, maths anxiety levels predicted the children’s maths performance but

not in the high interactivity condition. Finally, these results suggested that elevated

interactivity can be used to defuse the impact of maths anxiety on maths performance and

working memory resources can be augmented (Allen & Vallée-Tourangeau, 2016). However,

the study failed to show a reduction of state maths anxiety levels. Only the trait maths anxiety

of the participants was measured in the beginning of the experiment. Based on the level of

maths anxiety, the participants were either high or low in maths anxiety. The study concluded

that there were more benefits of interactivity for the more maths anxious individual.

Another innovative way to lighten the cognitive load is gesturing while a person talks.

Children and adults were asked to remember a list of words or letters while explaining how

they had solved a maths problem. Gesturing improved the performance of both groups; both

of the groups remembered more words and letters when they were allowed to gesture. It was

found that gesturing saved the speakers’ cognitive resources on the explanation task allowing

the participants to allocate more resources on the memory task (Goldin-Meadow et al., 2001).

Gesturing can take different forms; when a gesture is produced on its own and it is the main

form of communication, it takes on a language like form. However, when gesture is produced

13

in conjunction with speech and it takes an imagistic form and can convey information not

normally found in a speech. Additionally, gesture sheds light on how people think and it can

change those thoughts. In other words, gesture can be part of language or it can itself be the

language, by changing its form to fit the function (Goldin-Meadow, 2006).

1.2.4 Critical Evaluation of Kirsh’s Work

Whilst there is ample evidence of the benefits of applying complementary strategies to

complete problem solving tasks and to support people with reduction of their cognitive load

to complete tasks (Kirsh, 1995a; Kirsh 1995b; Kirsh, 2009; Kirsh, 2010), there are a number

of methodological and theoretical problems with the work of Kirsh. First, in the simple coin

counting experiment (Kirsh, 1995a) where complementary strategies were utilised to enhance

cognitive performance, participants were shown images, each depicting a different

arrangement of quarters, dimes, and nickels (functioning as a simple counting exercise based

on an everyday activity). The participants needed to determine the dollar value of represented

images. The speed of completing the task was improved by allowing the participants to point

or count when using fingers or hands compared to when the participants were not allowed to

touch the images. Additionally, there were fewer mistakes made in the hands condition

compared to the no-hands condition. However, these findings were based on a very small

sample size (n = 5) and as such they lack statistical power. Another limitation of Kirsh

(1995a) was the use of images rather than actual coins when computing the task. The

experiment utilised an everyday activity (coin counting) to illustrate the concept of

complementary strategies but did not allow the participants to actually physically interact

with coins not making the task representative of real life and as such, the actual effects of

complementary strategies on the dollar counting performance cannot be measured.

Kirsh (1995b) explains that people intelligently use space around them by

investigating and observing workplace for particular everyday tasks and how this workplace

14

was managed throughout the activity. The study found that spatial arrangements were mainly

made to simplify choice for the participants (e.g., by organising a kitchen in a way that only

certain subtasks were performed in a certain area and therefore reducing the range of possible

actions that could be done in that station) and that internal computation was assisted by

utilising different spatial activities. Finally, spatial adjustments allowed for simplified human

perception (e.g., an obvious way of making perception simpler is to arrange objects in a way

that they form classes that reflect properties that are useful to notice). The data for the study

were drawn from various videos of cooking and everyday observations in supermarkets,

workshops, and playrooms and is heavily influenced by the author’s own views rather than

experimental manipulations. Although Kirsh argues that environments are arranged in a

logical fashion, there are many arguments to the contrary. Moreover, Kirsh did not test

whether arranging environments differently would have had a negative impact on

performance. Clearly, the findings of the Kirsh 1995b study have highlighted the importance

of managing the spatial arrangement of items and how there are clear benefits of utilising

spatial adjustments. Clearly, there is a gap in the research to experimentally investigate the

effects in of interactivity on maths performance by using experimental manipulations.

Kirsh (2010) claimed that interactivity allows enhanced efficiency because it leads to

fewer errors and greater speed. Effectiveness, on the other hand, translates to deeper and

more accurate performance. However, the examples that have been used to demonstrate this

behaviour are simplistic and as before, not based on experimental manipulations. Kirsh

(2010) talks about drawing a diagram to further our understanding of complex information. It

is clearly easier to draw a right angle triangle and median when faced with the claim ‘in a

right-angled triangle, the median of the hypotenuse is equal in length to half the hypotenuse’.

Whilst it is evident that it is easier to understand the properties of the right angle diagram

with the help of drawing, there are no measurements taken to measure possible errors or

15

speed when completing the task. Another limitation of the findings is that the concept of

speed-accuracy trade-off is ignored. According to the speed-accuracy trade-off, decisions can

be made slowly with high accuracy or fast with reduced performance (Chittka, Skorupski, &

Raine, 2009). Kirsh (2010) claims that efficiency is enhanced with interactivity but ignores

the fact that there can be a speed-accuracy trade-off. By responding quicker to the task, there

might be a decline in accuracy or by responding slower, there might be improved accuracy.

This is clearly something that would require further attention.

1.3 Stereotype Threat

As mentioned in the introduction, the research reported here is focused on two different

types of situation-induced stress caused by stereotype threat or achievement goals. This

section focuses on the literature of stereotype threat. Stereotype threat is one of the most

widely researched areas of Social Psychology. In the classic Steele and Aronson (1995)

paper, stereotype threat is defined as being at risk of confirming a negative stereotype about

one’s group (Steele & Aronson, 1995). The stereotype threat concept has been widely used to

explain differences of academic performance mainly between African-Americans and

European-Americans and between men and women. However, there are multitude of factors

that shape academic performance and not just stereotype threat and therefore it could be

argued that the stereotype threat predicament is an elementary way of explaining academic

performance differences. A large meta-analysis of stereotype threat effects was conducted

and an overall mean effect size of .26 was found (Nguyen, 2008). The analysis confirmed that

a number of studies have been able to replicate the original findings of Steele and Aronson

(1995) but it was also found that some researchers were unable to replicate these findings.

The finding of the stereotype threat effect suggests that there are a number of moderating

effects for stereotype threat (stereotype threat relevance, domain identification, and test

difficulty), (Nguyen, 2008). However, the effects of stereotype threat on performance have

16

been tested in various circumstances and therefore it is possible that the tasks may have

varied in relation to the degree difficulty and challenge that the participants have

encountered. Hence, it can be difficult to draw comparable conclusions of the stereotype

threat effects. Consequently, it is important to focus on understanding the underlying

mechanisms of stereotype threat instead. Hence, the research reported here is focusing on

these mechanisms, and particularly on the effects of stereotype threat on working memory.

There are certain preconditions for the stereotype threat phenomenon to occur. Stereotype

threat happens in situations that bring to mind negative stereotypes about one’s group identity

(e.g., women are not good at mathematics). The occurrence of these effects requires

knowledge of these negative stereotypes, desire to be successful in the domain (e.g.,

mathematics), and a test (e.g., maths test) that tests the upper boundaries of the person’s skill

level (Steele, 1997). Stereotype threat is closely linked to the domain identification that

assumes that in order to succeed in an educational setting, the individual has to identify with

school and its subdomains (Osborne & Jones, 2011). However, there are certain groups (e.g.,

women in the mathematics domain and African-Americans in an educational setting) that

face achievement barriers. In other words, there are pressures on these groups that can disrupt

this identification (e.g., economic disadvantage, segregation, and gender roles). There can be

further achievement barriers due to stereotype threat. This can cause dis-identification with

school in general, and academic performance (Steele, 1997).

Steele and Aronson (1995) gave African-American and European-American university

students a test that comprised of difficult items from the verbal Graduate Record Examination

(GRE). The participants in the stereotype threat condition were told that the test was

diagnostic of their intellectual ability. The participants in the non-stereotype threat condition

were advised that the test was a laboratory problem-solving task (i.e., non-diagnostic test).

African-Americans performed worse than European-Americans when in the ability-

17

diagnostic condition but not in the non-diagnostic condition compared to their previous

performance (Studies 1 and 2). In Study 3, participants in the stereotype threat condition felt

more self-doubt and wanted to distance themselves from African-American stereotypes. The

participants were requested to complete word fragments that included words that were

symbolic of African-American stereotypes. African-American participants showed more

stereotype and self-doubt related words and they had fewer preferences for things that were

related to African-American culture (e.g., basketball and hip-hop music). Additionally, in

Study 4, African-American students’ performance was impaired when stereotype threat was

made salient by asking the participants to record their race (an example of priming racial

identity). This performance impairment happened even when the test was not described as

diagnostic of intellectual ability (Steele & Aronson, 1995). However, whilst the study made

strong findings about the effects of stereotype threat on academic performance, this study

utilised standardised verbal tests (the verbal Graduate Record Examination, GRE) and as

such it can be difficult to generalise these findings to other domains. Additionally, the study

concluded that stereotype threat caused an inefficiency of processing which is similar to the

effects of evaluative pressure. Consequently, the stereotype-threatened participants seemed to

spend more time doing fewer items more inaccurately. However, the inefficiency of

processing was not measured as part of the investigation, no working memory processing

measure was taken as part of the study. The conclusions were solely based on the task

performance, number of items that the participants answered, and on the fact that the African-

American participants reread the items more than the European-American participants. It was

concluded that the African-American participants were alternating attention between

answering the required questions and assessing the self-significance of their frustration of the

task, causing the inefficiency of processing. Finally, the study also failed to confirm that

whether the stereotype-threatened participants were more anxious than the control

18

participants which could have explained the behaviour of the participants in the stereotype

threat condition. Increased anxiety can reduce the working memory capacity available to

compute the task (Eysenck & Calvo, 1992). In another study, African-American participants

performed better on an IQ test when it was introduced as a test of eye-hand co-ordination

rather than a diagnostic test of their academic ability (manipulation of stereotype threat),

(Katz, Roberts, & Robinson, 1965).

Schmader and Johns (2003) hold the view that stereotype threat can affect any

individual’s academic performance (assuming that the situation evokes a stereotype-based

expectation of poor performance). When a working memory test (Operation Span Test) was

described as a measure of general intelligence, the working memory capacity of Latinx

participants was negatively affected and they remembered fewer words than Latinx

participants in the control condition and the European-American participants. The Latinx

individuals also reported feeling more anxious than their European-American counterparts

(Schmader & Johns, 2003). However, when the actual maths tasks (used to trigger a level of

brain processing) were further analysed, it was concluded that priming of stereotype threat

did not reduce the maths performance of the African-American participants. It was only the

recall of words (as part of the Operations Span Task) that was affected by stereotype threat.

Additionally, it has been confirmed that students from poorer backgrounds perform worse on

intellectual tasks. One of the explanations for this performance difference is stereotype threat.

When participants from low socioeconomic statuses were told that a test was diagnostic of

their intellectual ability, they performed worse than participants from high economic statuses.

However, when the test was presented to participants as non-diagnostic of intellectual ability,

the performance of the low socioeconomic participants did not deplete (Croizet & Claire,

1998).

19

It should be noted here that stereotype threat does not always require history of

stigmatization or feelings of inferiority; it can arise as a result of situational pressures alone.

Two experiments were conducted to test this notion. The participants were European-

American math-proficient men from Stanford University who were chosen for their high

ability in the domain (mathematics). In Study 1, stereotype threat was induced by a

comparison with a minority group, stereotyped to excel in mathematics (Asians). It was

confirmed that the European-American men in the stereotype threat group performed worse

in the difficult maths (at the upper limit of the student’s abilities) tasks than the control group.

The second study confirmed the results of the first study. However, it also concluded that

stereotype threat is partly mediated by domain identification and therefore it is most likely to

affect the participants who are highly identified with the domain being tested (Aronson,

Quinn, & Spencer, 1998).

1.3.1 Women and Maths Performance

Women risk being judged by the negative stereotype that females perform worse in

mathematics than males do. There is evidence to suggest that this form of stereotype threat

can disrupt women’s maths performance. Previous research has shown that women

underperform on the difficult maths tests but not on the easy ones when stereotype threat has

been made salient. There were equal numbers of women and men in this study and the

participants had strong maths background. The second study concluded that if stereotype

threat was lowered (by telling the participants that the test does not produce gender

differences) the performance issues could be eliminated. However, when the stereotype threat

was high and the female participants were made aware of the gender differences, the maths

performance of the females was worse than the males (Spencer, Steele, & Quinn, 1999).

Whilst this study was conducted in a laboratory setting it has strong external validity as the

20

participants were tested in mixed male and female groups of 3 to 6 attempting to create a

more realistic educational setting.

Recent research has suggested that negative stereotypes can also carry a strong message

that a certain group (e.g., women in mathematics) is less valued than men in the domain.

When a negative stereotype about women in mathematics is made salient, women might feel

less accepted in the maths community as a whole. Thus, women would have lower sense of

belonging to maths. Students who believe that maths skills can be acquired rather than

something that you are born with, can maintain a high sense of belonging to the maths

domain which in turn can reduce the power of stereotype threat (Good, Rattan, & Dweck,

2012). Investigation on women who majored in maths-related fields found that the women

who believe that there are gender differences in maths performance, are more likely to

endorse gender stereotypes about women’s maths abilities. This predicted more negative self-

perceptions of maths competence and also reduced interest in continuing to study maths at a

higher level. Additionally, these women were also found to be more susceptible to negative

stereotypes which in turn affected their maths performance (Schmader, Johns, & Barquissau,

2004).

1.3.2 Non-Academic Domains of Stereotype Threat

Since the Steele and Aronson classic experiment (1995), stereotype threat research has

broadened its scope to other areas; stereotype threat extends beyond underachievement on

academic performance. There are a number of non-academic domains where stigmatized

individuals’ performance is affected by negative stereotypes. The literature reported here as

part of the thesis is not an exhaustive literature review but rather a summary of the main non-

academic domains of stereotype threat. There are various findings made in this field but as

with the stereotype threat literature, various domains and different methods have been used

and therefore the findings are not easily generalizable. When European-American

21

participants were told that a laboratory golf task was about natural athletic ability, they felt

threatened about confirming the negative stereotype about poor white athleticism. Poor

natural athletic ability, can been seen as a widely held negative stereotype about European-

American athletes. When the participants were made aware of this negative stereotype, the

participants felt worried about confirming this stereotype. This resulted in European-

American athletes avoiding sports practice, using a behavioural self-handicapping strategy.

This kind of strategy is used to explain poor performance. The poor performance is explained

by lack of effort and that more practice would have achieved better results (Stone, 2002). As

the golf task was completed in a laboratory setting, it is possible that these findings are not

transferable to the real world. It is possible that the White-American participants felt

threatened about the negative stereotype about white athleticism only when a laboratory golf

task was used.

Similar findings have been made about racial stereotypes about African-American or

European-American athletes and how these stereotypes affect performance in sports. When a

golf task was framed as diagnostic of sports intelligence, the African-American participants

performed significantly worse than their European-American counterparts. When the task

was framed as diagnostic of natural athletic ability the European-American participants

performed worse than the control participants (Stone, Lynch, Sjomeling, & Darley, 1999). In

another experiment, women were told that females are poor drivers to see if this particular

stereotype disrupts control of an automobile. These women were twice more likely to collide

with jaywalking pedestrians than the control group who were not told about the negative

stereotype (Chi, Yeung, & Von Hippel, 2008).

Additionally, when gay men were reminded of their stigmatized identity (before

interacting with young children in a nursery school) their childcare abilities were poorer than

the participants in the control group. This effect was driven by the men’s non-verbal anxiety,

22

in the presence of children. Non-verbal anxiety was defined as any behaviours that

communicate discomfort, anxiety, awkwardness or a similar emotion (e.g., fidgeting,

chewing on lip, playing with hair, nervous smiling, biting nails, stiff posture, and averting

eyes), (Bosson, Haymovitz, & Pinel, 2004). In another study, when stereotypically feminine

traits were linked to successful negotiating skills, women performed better in a mixed-gender

negotiation scenario. However, this was not the case when gender-neutral traits were

associated with negotiation success. Women outperformed men in a mixed-gender

negotiation scenario when masculine traits were linked to poor negotiating performance.

However, men outperformed women when poor negotiation skills were linked to feminine

traits (Kray, Galinsky, & Thompson, 2002).

1.3.3 An Integrated Process Model of Stereotype Threat Effects on Performance

There are three distinct mechanisms that can disrupt performance (performance on

both cognitive and social interaction tasks) under stereotype threat (Schmader, Johns, &

Forbes, 2008): physiological stress, monitoring of performance, and suppression. The

integrated process model of stereotype threat contributes to the stereotype threat literature in

a way that it allows further our understanding of the biological and behavioural aspects of

stereotype threat, to build a complete view of the effects of stereotype threat on performance

of cognitive and interaction tasks. To start with, there is a physiological stress that directly

impairs prefrontal processing. Working memory is situated in the prefrontal cortex which is

responsible for deploying inhibitory processes, and controlling attention (Kane & Engle,

2002). There are vast amounts of empirical studies that have investigated physiological stress

response of stereotype threat. The physiological stress response studies give strong evidence

of the existence of stereotype threat. To start with, greater sympathetic nervous system (SNS)

activation (the area responsible for the fight and flight response) was measured when female

participants were watching a group of students (a group of unbalanced ratio of men to women

23

or a balanced group) conversing about a math, science, and engineering conference.

Furthermore, the women who watched the gender-imbalanced video reported a lower sense

of belonging and less desire to participate in the conference, compared with the women who

saw a gender-balanced video (Murphy, Steele, & Gross, 2007).

In another study, the effect of stereotype threat on blood pressure reactivity was

investigated. African-Americans under stereotype threat (compared with European-

Americans, and African-Americans under little or no stereotype threat) exhibited larger

increases in mean arterial blood pressure during an academic test that was described as

diagnostic of intellectual ability than one that was not (Blascovich, Spencer, Quinn, & Steele,

2001). The extent to which ethnic minority group members or a devalued group caused threat

reactions from interaction partners was measured in a study. When European-Americans

were interacting with African-Americans or disadvantaged confederates, participants

exhibited cardiovascular threat responses, whereas participants collaborating with European-

American or advantaged confederates primarily showed cardiovascular challenge responses.

In line with cardiovascular responses, participants who were paired with European-

Americans performed better (during a cooperative task) than participants who were paired

with African-American participants (Mendes, Blascovich, Lickel, & Hunter, 2002). Another

study supporting this relationship was conducted by Klein and Boals (2001). Participants

with more life event stress performed more poorly on Turner and Engle's (1989) operation

word span task (working memory task), and particularly on the longer operations of the task.

The participants tried to remember sequentially presented words in the correct order while

simultaneously solving simple maths equations. The maths equations consist of between 2

and 6 successively presented equation–word pairs (e.g., 8 ÷ 4 + 3 = ? moon). The stressful

life events competed with the task demands for attentional resources of the working memory

(Klein & Boals, 2001).

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Various empirical studies have looked at the relationship between elevated cortisol

levels caused by stress and cognitive performance. In one study, the association between

cortisol levels and memory performance in healthy adults was investigated. In the first study,

the participants were exposed to a brief psychosocial laboratory stress with the help of Trier

Social Stress Test (TSST). Induced stress was created with the help of socially evaluative

situations (divided into 5-minute components). During the first 5 minutes, the participants

were asked to plan a presentation, this presentation was then given to the judges during the

next 5 minutes. The test was concluded with a mental arithmetic task where participants were

asked to count backwards from 1022 in steps of 13. The TSST was followed by a test of

declarative memory performance. The first study concluded that there was a significant

negative relationship between stress-induced cortisol levels and performance in the

declarative memory task. The participants (with high cortisol response to the stressor)

showed poorer memory performance. In the second study, the authors investigated that if

cortisol alone (without any psychological stress) would impair performance of the

participants. The participants received either 10 mg of cortisol or placebo (orally). They were

then tested one hour later for procedural memory, declarative memory and spatial thinking.

The participants who received cortisol showed impaired performance in the declarative

memory and spatial thinking tasks but not in the procedural memory task. Thus, elevated

cortisol levels were associated with impaired memory function of healthy adults

(Kirschbaum, Wolf, May, Wippich, & Hellhammer, 1996).

Another study was conducted to investigate whether the effects of cortisol on working

memory depended on the level of adrenergic activity (as measured by sympathetic activation)

during memory performance. Participants were (after exposure to a psychosocial stress task),

divided into cortisol responders and cortisol non-responders. There were working memory

impairments for the cortisol responders during the psychosocial stress phase, when cortisol

25

and adrenergic activity were enhanced. This same pattern could not be found for the cortisol

non-responders. Working memory of cortisol responders did not differ from that of non-

responders during recovery when cortisol levels were elevated but adrenergic activity was

normalized. There were several stress measures but cortisol was the only significant predictor

for working memory performance during stress. Thus, adrenergic activation is essential for

the impairing effects of stress-induced cortisol on working memory (Elzinga & Roelofs,

2005).

In regards to the second mechanism that is associated with disrupted performance,

there is a tendency for individuals to actively monitor the self-relevance of performance.

Individuals become more conscious of the self and one’s performance. Schmader et al.,

(2008) stated that when individuals try to avoid failure when stereotype threat has been made

salient, they switch from a more automated state of functioning into a more controlled state of

monitoring the self within the situation. The more conscious approach is employed to assist

in managing the new situation caused by the primed conditions (Schmader et al., 2008). This

paradigm was investigated further in another study by looking at the effects of high-pressure

performance situations (caused by offering performance-contingent rewards) on golf putting

performance. The authors investigated whether choking under pressure was caused by

distraction (cognitive load) where the high-pressure performance situation distracts the

attention away from the task in hand or self-focus, whereby the individual completing the

task shifts the attention to oneself which in turn interferes with the putting performance.

Cognitive load was elevated by asking the male participants to count backwards from 100.

Furthermore, self-awareness was manipulated by videotaping half of the participants (during

the practice trials). As expected, golf putting performance dropped dramatically in the high-

pressure performance condition. Additionally, in the high-pressure condition (without

distraction treatment), there was increased performance for the self-awareness adopted

26

participants. This pattern could not be found in the low-pressure condition. In other words,

self-awareness adaptation treatment allowed the participants in the high-performance

condition to elevate the effects of high pressure on putting performance. These results

confirmed the self-focus account of the choking under pressure phenomenon (Lewis &

Linder, 1997). In line with the previous study, Seibt and Forster (2004) found that the

individuals who had been primed to stereotype threat became more conscious of avoiding

failure on the task in hand. This is in turn, helped the participants to have a more careful and

systematic performance as opposed to a more creative and eager performance that the

positively stereotyped individuals endorsed (Seibt & Förster, 2004). There can also be

increased vigilance to threat- and failure-related cues. This vigilance occurs when individuals

become more vigilant to external feedback that might confirm that one is not performing well

enough and up to the required academic standard and therefore there is a risk of confirming

the stereotype (e.g., the negative stereotype of girls and maths). This was investigated further

in another study by looking at the effects of stereotype threat effects on minority students’

(African-American and Latinx participants, in particular) tendency to be more vigilant to task

errors in an academic setting. The two groups of ability-stigmatized participants completed a

basic response-conflict task (a flanker task). The task was described either as a measure of

intellectual ability (stereotype threat condition) or a neutral pattern task (control). Event-

related potential (ERP) methodology was employed while the participants completed the

response-conflict task. ERPs were recorded from scalp regions that were located above the

dorsal anterior cingulate cortex. This is the region of the brain that is involved in monitoring

behaviour that conflicts with goals. The authors confirmed that the (academic) minority

students showed larger ERP amplitudes when the task was completed in the intellectually

threatening condition compared with the neutral condition. It was concluded that this elevated

27

neural activity was caused by the increased vigilance to the errors on the response-conflict

task (Forbes, Schmader, & Allen, 2008).

And finally, according to Schmader et al., (2008) the third mechanism that can

contribute to cognitive inefficiency is linked to individuals’ efforts to suppress negative

thoughts and emotions while in the stereotype threat condition. The individuals who bear the

burden of negative stereotypes might experience self-doubt in relation to their performance

on the task. For example, Steele and Aronson (1995) Study 4 showed that African-American

students’ performance could be impaired by the mere salience of the stereotype threat even

when informed that the test was not diagnostic of ability (Steele & Aronson, 1995).

Negative stereotypes can also make the stigmatized individuals feel that there is

generally a negative expectancy in relation to their academic performance. When the

participants were told that they had high ability on a task this predicted future performance on

similar tasks compared with the other group where they were given ambiguous feedback

about their academic abilities to complete the task. However, when the negative stereotype

was made salient, the positive performance expectations of the performance deteriorated

(Stangor, Carr, & Kiang, 1998).

The role of negative thinking was investigated and whether it was a possible mediator

of maths performance decrements when stereotype threat had been made salient. Sixty female

participants were asked to complete a difficult maths task after being assigned to a stereotype

threat condition or control. The women who were primed into the stereotype threat condition,

reported a larger number of negative thoughts compared with the women in the control

condition. The increased negative thoughts were particularly related to the task in hand and to

mathematics in general. Additionally, there was a large performance drop for the women in

the stereotype threat condition, particularly during the second half of the test which was

28

mediated by the elevated negative thoughts of completing the task (Cadinu, Maass,

Rosabianca, & Kiesner, 2005).

The suppression process regulating negative thoughts consumes the internal cognitive

resources, and working memory in particular. Muravan and Baumeister (2000) reported that

self-control that is part of the inhibitory control (the ability to regulate one’s emotions,

thoughts, and behaviour in the face of temptations) is a limited resource. Self-control efforts

are required when coping with a stressful situation, resisting temptations, and regulating

negative affect. Unfortunately, after multitude of self-control efforts, subsequent attempts of

self-control might fail, confirming the fact that self-control can been seen as a limited

resource. The authors concluded that these self-control decrements were not caused by

negative moods or learned helplessness. These decrements were specific to behaviours that

involved self-control (Muraven & Baumeister, 2000). To sum up, it is evident that all of the

three mechanisms consume the existing working memory resources, and as a consequence

negatively affect task performance.

1.3.4 Stereotype Threat and Working Memory

Stereotype threat can increase the levels of situation-induced feelings of pressure and this

in turn can create anxiety about the situation. These increased worries can compete for

working memory resources that would normally be available for maths performance. The

maths performance of individuals who rely heavily on working memory resources (higher-

WM individuals) can deplete when there is pressure caused by the stress-laden environment.

This type of situation causes the individual to complete the maths tasks in a dual-task setting.

The maths task execution and the worries of the stressful situation tax working memory

capacity simultaneously (Beilock, 2008). It has been suggested that verbal processes (e.g.,

thinking) are more compromised in a stressful situation. In the Beilock (2008) study,

participants who completed horizontal modular arithmetic tasks (these tasks rely heavily on

29

phonological aspects of working memory) under stereotype threat, performed worse than the

participants who completed vertical modular arithmetic tasks. The vertical MA tasks use the

column subtraction format and therefore the participant does not need to rely on the working

memory resources as much as with the horizontal MA tasks. When the vertical format is

used, the participant can use the layout of the maths task to their own benefit. Unlike with the

horizontal tasks, all the required steps need to be stored in the working memory. The Beilock

(2008) study utilised high WM load and low WM load tasks but the difficulty level of the low

WM load tasks was too low to see any taxation of the working memory resources. The tasks

were single-digit numbers up to 10 and as such they might not have taxed the working

memory in a way that was anticipated.

There are a large number of empirical studies on the effects of stereotype threat on task

performance but far less is known that how these effects are realized. Beilock, Rydell, &

McConnell (2007) used mathematical problems (modular arithmetic tasks) that relied heavily

on working memory as a test bed to see any performance decrements in simple maths tasks

when stereotype threat was made salient. The authors examined the types of modular

arithmetic tasks that were most susceptible to stereotype threat (vertical or horizontal

problems). The purpose of these type of modular arithmetic tasks is to judge the validity of

maths problems like 61 ≡ 18 (mod 4). The middle number is subtracted from the first number

(i.e., 61-18) and then the difference is divided by 4. If the answer is a whole number, the

maths problem is true. The horizontally presented maths problems were more reliant on

phonological resources. Therefore, it was concluded that stereotype threat taxed the verbal

working memory resources and consequently harmed women’s maths performance. The

worries of stereotype threat put extra burden on the working memory (phonological loop, in

particular), and together with the horizontally presented maths problems there were maths

performance decrements under stereotype threat (Beilock, Rydell, & McConnell, 2007).

30

In similar vein, Schmader and Johns (2003) confirmed that negative stereotypes reduced

working memory capacity by putting extra burden on cognitive resources, and working

memory in particular. The authors tested this hypothesis with three experiments. Women

completed the working memory assessment as a test that was related to their mathematical

ability (stereotype threat condition), (Study 1). In the second study, Latinx participants in the

stereotype threat condition were advised that the working memory test was a measurement of

general intelligence. Working memory capacity of both women and Latinx participants was

reduced by priming these self-relevant negative stereotypes. Finally, the Study 3 found that

working memory capacity mediates the negative effects of stereotype threat (Schmader &

Johns, 2003). However, when these findings were further analysed it was found that the

performance of the actual maths tasks of the working memory task (Operation Span Task)

that was a dual-task (comprising of simple mental arithmetic tasks and recall of words) did

not deteriorate. It was only the word recall of the task that was affected in the stereotype

threat condition.

1.4 Introduction to Achievement Goals

Another area in which interactivity may support people in situations of evaluative

pressure is when they endorse performance-approach goals. This programme of research

focused on two different situations linked to evaluative pressure (stereotype threat and

achievement goals). The purpose of the following section is to focus on the latter. There are

a multitude of empirical studies on achievement goals and their effects on academic

outcomes. Over the past 25 years, achievement goals have inspired over 1000 published

papers. Nevertheless, much less is known about the effects on working memory and whether

interactivity supports elevated mental arithmetic performance for participant with normative

strivings (performance-approach goal participants). The achievement goals construct refers to

the way individuals represent and pursue competence in challenging settings (Elliot &

31

Dweck, 2005). According to Poortvliet and Darnon (2010) achievement goals are said to

reflect the aim of an individual’s achievement pursuits. Additionally, achievement goals

function as frameworks that can help to understand how individuals react to various

achievement situations (e.g., in academic setting), (Poortvliet & Darnon, 2010).

Achievement goal theory (Harackiewicz & Barron, 2002) distinguishes between

mastery-approach goals (i.e., task mastery and knowledge acquisition), mastery-avoidance

goals (i.e., avoiding the failures of not learning the required task), performance-approach

goals (i.e., aiming for outperforming others and demonstrating competence in the subject

field), and performance avoidance goals (i.e., avoiding to do worse than others). However,

this theory assumes that there are 4 distinct achievement goals and that they function in

isolation. The theory ignores the fact that there can be situations where a mixture of goals can

be experienced. Current educational practices strongly promote the endorsement of

performance-approach goals (the notion of normative success and dominance over others).

For example, students’ knowledge acquisition is measured via exams and tests that allow the

examiners to give grades based on the students’ academic performance. Striving for academic

success over others can cause elevated feelings of pressure. Hence, the programme of

research reported here focuses on performance-approach goals only (with mastery approach-

goals functioning as a comparison group), (Crouzevialle & Butera, 2013).

Individuals pursuing performance-approach goals are good at knowing the material

that is essential for the task in hand (Elliott, Shell, Henry, & Maier, 2005). They listen to the

cues about the future assignments and tests and then adjust their individual learning based on

these cues. Students perform better when they focus on topics that the teacher deems

important and that are tested as part of the curriculum (Broekkamp, Hout-Wolters, & Van

Hout-Wolters, 2007). Students with performance-approach goals concentrate on memorising

rather than elaboration and knowledge construction (Entwistle, 1988). This approach can lead

32

to surface learning and rote learning (Harackiewicz & Linnenbrink, 2005). Performance-

focused students tend not to not earn the same high marks in the more advanced classes that

require deeper understanding because of the surface learning strategies of performance-

approach goals (Senko, Hulleman, & Harackiewicz, 2011). On the contrary, students with

mastery-focused goals are freer to pursue their own agenda which is guided by their own

personal interests and their curiosity of the current topic. Hence, mastery-approach goals

predict the use of adaptive cognitive strategies that lead to deeper processing. This kind of

approach might benefit the students in the long run because it promotes deeper learning but

might not help in gaining the highest grades because it is based on personal interests rather

than the areas that might be tested. When people endorse performance-approach goals, their

focus is on the outcome of the task and therefore the individuals might not be fully engaged

with the process and the activity to complete the task. Mastery-approach goals allow the

individual to focus on the learning process rather than the activity of outperforming others.

Mastery-focused individuals focus on learning and their personal improvement, and therefore

have a focus on the task that allows them to explore both intrinsic and utility value. Finally, it

is this task focus that allows the individual to experience both intrinsic and utility value

(Hulleman, Durik, Schweigert, & Harackiewicz, 2008).

1.4.1 Academic Consequences of Performance-Approach Goals

There are mixed empirical findings regarding the academic consequences of

performance-approach goal pursuits. On the one hand, performance-approach goal adaption

has been seen as a positive predictor of exam performance and academic achievement in a

multitude of studies (Church, Elliot, & Gable, 2001; Elliot & Church, 1997; Harackiewicz,

Barron, Tauer, Carter, & Elliot, 2000; Skaalvik, 1997; Wolters, Yu, & Pintrich, 1996).

However, most of these investigations have been longitudinal studies based on self-reported

questionnaires rather than studies that measure the current academic performance.

33

Additionally, some of the current academic exam performance is assessed using multiple

choice questionnaires (MCQs) which generally only measure surface level understanding of

the material. These types of exams do not allow the student to exhibit deeper understanding

of the material and therefore allows the student to be efficient and only to learn that what is

required for the exam. The superficial way to prepare for an exam is a successful way of

preparing for a multiple-choice type of assessment but this same approach would not work

for an assessment that requires deeper understanding of the topic (Harackiewicz, Barron,

Carter, Lehto, & Elliot, 1997). The link between performance goals (both approach and

avoidance goals) and academic performance is mediated by the perceived difficulty of the

academic task. Achievement goal endorsement leads to perceiving the task either as

something within reach (in the case of performance-approach goals) or as too difficult and

impossible to complete for the avoidance goal participants. As a consequence, the perceptions

of difficulty then influence the task performance and in the case of performance-approach

goals, provides a buffer against the harmful effects of fear of failure (Darnon, Butera, Mugny,

Quiamzade, & Hulleman, 2009).

1.4.2 Maladaptive Behaviours of Performance-Approach Goals

Additionally, performance-approach goal pursuits can be linked to various

maladaptive behaviours and outcomes in an educational setting. Performance-focused

students are generally less inclined to cooperate and share information with their peers

(Poortvliet, Janssen, Van Yperen, & Van De Vliert, 2007). Additionally, when there is a

disagreement, individuals with performance-goal reject other people’s opinion and, just

impose their own views and ideas (Darnon, Muller, Schrager, Pannuzzo, & Butera, 2006).

This kind of behaviour can have detrimental consequences for the performance-driven

students and it can hinder learning. Finally, performance-approach goals have also been

associated with cheating. It was reported that individuals who intended to cheat in the areas

34

of education, sport and work, did it as a function of their achievement goals in that particular

environment. Additionally, by imposing achievement goals on participants affects their actual

cheating behaviour during the required task performance. The normative goal endorsement

encourages individuals to achieve their performance-approach goal for any price. The

performance-focused individuals do not seem to care how this goal is attained. Hence,

cheating might help them to achieve their normative goal (Van Yperen, Hamstra, & Van Der

Klauw, 2011).

1.4.3 Components of Performance-Approach Goals

Grant and Dweck (2003) hold the view that there are four different components of

performance-approach goals that help individuals to perform and reach their academic goals.

To begin with, validation of ability is where the individual concentrates on appearance and

wanting to look good in front of peers. Normative comparisons allow the individual to

compete with peers. Normative ability is where the individual aims to outperform others

doing similar tasks (combined ability validation and normative comparisons) and finally,

outcome goals that are focused on attaining a positive outcome in the form of good grades

(Grant & Dweck, 2003). However, the general study of achievement goals (including

performance-approach goals) has clearly found basic motivational processes but there still

remains controversy surrounding their nature and impact on performance. First, the effects of

achievement goals on academic performance and on motivation have been tested on a

number of circumstances by using e.g., puzzles, concept-formation tasks, and solving

difficult maths problems (Elliott & Harackiewicz, 1998; Elliott & Dweck, 1998; Barron &

Harackiewicz, 2001) and it is possible that the tasks have varied in relation to the actual

degree of difficulty and the challenge that the participants have faced. The different ways of

operationalising achievement goals might explain some of the inconsistent findings by

various researchers of the achievement goal effects on academic performance. Grant and

35

Dweck (2003) attempted to investigate some of these issues further with the help of five

studies and found that the impact of the various achievement goals depended on how they

were operationalised. Active learning predicted active coping, sustained motivation, and

higher achievement (in the face of a challenge). Ability goals predicted withdrawal and lower

performance (when challenged). However, there was a performance boost when students

were met with success. Additionally, there were no performance or motivation decrements

with normative goals.

However, the achievement goal inventory items that were utilised as part of the

investigation, comprised of three items only for each achievement goal (outcome goal, ability

goal, normative outcome goal, normative ability goal, learning goal, and challenge-mastery

goal), which therefore reduced the validity and reliability of the inventory. Originally, there

were 10 items for each goal. These were clearly tested and the most reliable items were kept.

Whilst it has been shown that the remaining achievement goal items employed have high

Cronbach alpha values, it is possible that the 3-item scale might not have accurately reflected

the behaviour of the participants and therefore reducing the validity and reliability of the

scale and its findings. The authors justified the use of three items to make it simpler for the

participants to respond to a multitude of achievement goal items and to avoid any form of

confusion by using a multitude of similarly worded items. Additionally, the Confirmatory

Factor Analysis (CFA) that was used as part of the Study 1 found that there were two models

that provided a good fit to the data. Although Model B (a 6-factor model, based on all of the

achievement goals that were measured) was a slightly better fit, Model A with only 4 primary

factors (an ability goal factor, an outcome goal factor, a normative factor comprising of

normative ability and normative outcome factors, and a learning factor that included learning

and challenge-mastery factors) was used as the basis of analysis as it was consistent with the

earlier results of the Exploratory Factor Analysis (EFA). In the 4-factor model, there is no

36

further specification of the normative goal items (i.e., outcome and ability) and of the

learning goal items (i.e., learning and challenge-mastery). The 6-factor model included these

specifications. It can therefore be argued that the additional information provided by the 6-

factor model was not taken into consideration as part of the Grant and Dweck (2003)

investigation and therefore not allowing the authors to develop these thoughts further.

Additionally, this theory assumes that the different achievement goals function in isolation. It

could be argued that people have more than one goal and as such the use of categorical

measurements (as part of the achievement goal inventory) can mask these effects.

1.4.4 Performance-Approach Goals and Distraction

Performance-approach goals are also linked to distraction and diminished task focus.

Distraction theory suggests that the additional pressure creates an environment that draws

attention away from the primary task. In other words, the execution-irrelevant activity in

working memory caused by the pressure situation causing skill failure (Beilock et al., 2004).

Concerns of outperforming peers distract students from the task (Brophy, 2005).

Additionally, individuals are less likely to become fully immersed and absorbed in the

academic task when they are mainly concerned with their self-worth in comparison to others.

On the other hand, mastery-approach goals are linked to various positive processes (e.g.,

challenge appraisals and absorption during preparation), (McGregor & Elliot, 2002).

According to the processing efficiency theory, anxiety can reduce the storage (mainly

phonological loop) and processing capacity (central executive) of the working memory

system available for the task in hand. Additionally, anxiety can make individuals increase

task effort and activities to improve performance (e.g., maths performance), (Eysenck &

Calvo, 1992).

37

1.4.5 Negative Affect

Performance-approach goals are related to increased negative affect. On the contrary,

mastery-approach goals are associated with reduced negative affect, which in turn is related

to increased working memory functioning. These results indicated a clear difference between

the two achievement goal endorsements, and their relation with negative affect. Performance-

approach goal endorsement together with a challenging task may not allow the individual to

meet their goal of outperforming peers and as a consequence levels of negative affect might

become elevated. Mastery-approach goal adoption, on the other hand, allows the individual to

experience the difficult task as a challenge and therefore the individual is not worried about

failure, and as a consequence the levels of negative affect are reduced (Linnenbrink, Ryan, &

Pintrich, 1999). Negative affect leads to increased task-irrelevant thoughts which in turn taxes

working memory and as a consequence, the overall cognitive capacity is depleted. As a

result, the phonological loop is filled with task-irrelevant thoughts and central executive

processing is affected by additional processing of this information that is not related to the

task (Elliman, Green, Rogers, & Finch, 1997). Achievement goals are directly linked to task-

irrelevant thoughts. As mentioned earlier, performance-focused students focus on their

academic performance and how it relates to others (normative behaviour). Mastery-oriented

students, in contrast, stay focused on the task in hand. Thus, these two approaches have

different effects on the thoughts that do not support the task in hand (Elliott & Dweck, 1988).

1.4.6 Achievement Goals and Theories about Intelligence

Previous developmental research has shown that children’s theories about intelligence

may guide them towards different achievement goals (Dweck, 1986). When children believe

that intelligence is a fixed trait, they tend to orient towards performance-approach goals to

gain favourable judgements about their competence from their peers. The goal is to gain

positive judgements, and to avoid negative judgements of competence. When the child’s

38

confidence in ability is high, the child seeks challenge, and is persistent in achieving the goal.

But when the confidence is low, the child feels helpless and avoids the challenge, and is low

in persisting in the goal. On the contrary, the children who believe that intelligence is a

malleable quality tend to orient towards developing competence. And in both high and low

confidence, the child seeks challenge that fosters learning and remains persistent with this

approach (Dweck, 1986).

Mastery-achievement goals involve the aim for improving one’s own performance. In

contrast, performance-approach goals reflect the pursuit of outperforming others. People who

strive for mastery-approach goal, mainly compare their present performance with their own

previous performance. By doing this, they develop a self-referenced focus in different

achievement situations. Individuals who pursue performance-approach goals tend to compare

their performance to others and they therefore develop an other-referenced focus (Dweck,

1986).

1.4.7 Motivation and Task Values

Interest in the activity is one of the most important components of motivation, and

motivated behaviour (Schiefele, 1991). One way to develop this interest is to find value (task

values that individuals perceive when engaging in tasks), and meaning in the activities that

people do. Achievement goals help individuals to find value in the tasks that they do

(Pintrich, 2003). Two of these values are intrinsic and utility value. When it comes to tasks

with utility value, they are seen important by the individual because they are relevant beyond

the immediate situation. These are tasks that are also useful for other future tasks, and other

aspects of an individual’s life. Tasks of intrinsic value are important to the individual because

they are seen as enjoyable and fun. There are studies that show a clear relationship between

how the utility of a task is perceived and how the subsequent performance is. For example,

persistence and performance in a physical education class was elevated by informing the

39

participants of the usefulness of the activity (Simons, Dewitte, & Lens, 2003). In another

study, it was concluded that students’ classroom performance was predicted by the relevance

of school work to students’ future goals. There are experimental studies that have

documented a correlation between mastery-approach goals and both utility and intrinsic value

(Linnenbrink, 2005; Shim & Ryan, 2005).

1.4.8 Choking under Pressure

Pressure of high-level performance from either stereotype threat or performance-

approach goals can create mental distractions that compete for working memory resources

that would normally be used for executing the task in hand (Beilock & Carr, 2005). To

understand this process, Beilock et al., (2004) talk about the term choking under pressure

which is defined as performing more poorly (across diverse task domains) than expected in a

high-stake situation, given one’s skill level (Beilock et al., 2004). This happens particularly

when the desire for high-level performance is maximal. Choking under pressure has been

mostly explained by explicit monitoring theories rather than distraction theories. Beilock and

Carr (2001) investigated golf playing performance under pressure with the help of a golf

putting task to further understand whether practice at explicit attention or distraction would

reduce pressure-induced failure of the task. It was concluded that choking occurred for those

individuals who were trained on the putting task in the single-task condition (used as a

baseline) and also for the individuals trained in the dual-task environment that caused

distraction for the participants. Nonetheless, choking did not occur for those trained in the

self-conscious condition. In other words, the self-consciousness training allowed the

participants to inoculate against the negative consequences of over-attending to a well-

learned performance process. According to explicit monitoring theories these are the

mechanisms that are responsible for performance decrements in high-pressure situations.

40

Attending to skills that are proceduralized (e.g., putting) can hurt the overall performance

(Beilock & Carr, 2001).

Most of the explicit attention studies have used sensorimotor skills as a test bed which

might not be the right environment for investigating the distraction theory and its effect on

complex cognitive processes (e.g., mental arithmetic). Beilock (2001) investigated choking

under pressure by examining mental arithmetic performance under pressure in the

mathematical problem-solving domain (with the help of modular arithmetic tasks).

Experiment 1 concluded that there were performance decrements in the difficult and

unpractised modular arithmetic tasks when in the high-pressure condition. Additionally, it

was demonstrated that these pressure-induced failures only occurred when the most difficult

(unpractised) and capacity demanding equations were used (Experiment 2). These findings

lend their support to the distraction theories of choking in the domain of mathematical

problem solving.

In another study, Beilock et al., (2004) tested the idea that increased pressure caused

by a high-stakes situation can constrain individuals to allocate their limited working memory

resources both to the task at hand, and to the management of the outcome concerns. In their

study, the participants were asked to solve a series of arithmetic tasks under either low or

high evaluative pressure situation. There were three different ways of creating the high-stakes

environment (high evaluative pressure): monetary rewards (e.g., scholarships and research

opportunities), peer pressure, and social evaluation (e.g., mentors, teachers, and peers). All

the three sources of pressure were at play in an academic setting. The high-pressure situation

compared to the non-pressure condition taxed the available working memory resources which

resulted in a decrement of mental arithmetic performance, and particularly for the high-load

working memory tasks (Beilock et al., 2004).

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1.4.9 Evaluative Pressure

There are various empirical studies that have looked at the cognitive consequences of

evaluative pressure on academic performance. However, little is known about the feelings of

evaluative pressure that might be caused by achievement goals and normative goal pursuit in

particular. Current literature suggests that there are two main ways of explaining why

performance might fall in stressful situations. Explicit monitoring (self-focus) theories

suggest that performance pressure about performing well on the task increases the

individual’s self-consciousness and anxiety. This focus in turn, increases the attention to skill

processes and their step-by-step control. However, attention to performance at such

component specific level is thought to disrupt the automated processes of high-level skills

that are normally run outside the scope of working memory system. This is in contrast to

distraction theory that suggests that the additional pressure fills working memory with

thoughts about the stressful situation and its importance that compete with the attention that is

normally allocated to the execution of the task. This additional pressure serves to create a

dual-task environment where the additional pressure and the task in hand compete for the

same limited working memory resources (Beilock et al., 2004). Whilst working memory is a

short-term memory system that maintains a limited amount of information required to

complete the demanding cognitive task at hand (e.g., mental arithmetic task), it

simultaneously aims to prevent distractions from the environment (including irrelevant

thoughts), (Kane & Engle, 2000). It has been argued that the impact of distracting thoughts

and anxiety about mental arithmetic performance derives from the disruption of the central

executive component of working memory which has the function of controlling and applying

of the sequence of arithmetic operations during problem solving (e.g., carrying during

addition and borrowing during subtraction), (Ashcraft & Kirk, 2001). Finally, Beilock and

Carr (2005) reported that performance pressure harmed individuals most qualified to succeed

42

by consuming the working memory capacity that they relied on for their superior maths

performance (Beilock & Carr, 2005).

Additionally, Beilock and DeCaro (2007) demonstrated that individual differences in

working memory capacity can impact the strategies used to solve complex math problems

and the type of testing situations (low or high pressure) can alter the strategy that has been

used to come to the solution. Experiment 1 found that under low-pressure conditions, the

higher the individual’s working memory capacity the more likely they were to use

computationally demanding algorithms (vs. the simpler shortcuts) to solve the required maths

problems and the more accurate their math performance. Higher WM individuals used

simpler problem-solving strategies (under high-pressure conditions) and their accuracy

suffered. Experiment 2 used a math task where a simpler strategy was optimal; accurate

maths performance was achieved with a few problem steps. When in the low-pressure

conditions, the lower individuals' WM, the better their maths performance as they relied on a

simple, but accurate problem strategy. When in the high- pressure condition, higher WM

individuals performed optimally by using the simpler strategies (the same ones the lower

WM individuals had employed). In sum, the level of working memory capacity influences

how individuals approach maths problems. Additionally, the nature of the task (simple

strategy or difficult strategy) and the performance environment (high or low pressure) make a

clear difference on the maths performance (Beilock & DeCaro, 2007).

Activation of performance-approach goals creates an evaluative context as the

individual is focused on outperforming others. The determination and focus of winning and

being the best can create distractive thoughts and worries. This can be problematic when the

performance-approach goals have been activated under immediate and demanding testing

situations. Performance-approach goal pursuits can have different cognitive outcomes

depending on the timing of the testing. There are differences whether one focuses on an

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immediate testing situation or on a period of an academic semester. There can be a divided-

attention situation that can generate goal attainment concerns in short-term setting. However,

for the long-term setting, there are benefits with the long-term setting as it allows for tactical

planning for course-specific demands (Crouzevialle & Butera, 2013).

1.4.10 The Effects of Performance-Approach Goals on Working Memory Capacity

There is a wealth of research on achievement goals and their effects on academic

performance, but much less is known about the cognitive processes of these goals, and

particularly the effects on the working memory. Crouzevialle and Butera (2013) concluded

that the pressure to outperform others (performance-approach goal) can generate anxiety that

depletes available working memory resources. In their first experiment, the induction of the

performance-approach goal during a demanding task reduced task performance. Their second

experiment confirmed this as there were distractive concerns that drew on the verbal

resources of the working memory (phonological loop). The final study concluded that the

performance drop was due to performance-approach goal related thoughts (Crouzevialle &

Butera, 2013). The same authors also looked at the high working memory students (the high

achievers) and tested whether this group of individuals would experience the high working

memory capacity as a burden because of high level of disruptive outcome concerns that

would have a causal effect on the maths performance. It was proposed that anxiety might be

higher for students who are used to succeeding in an academic setting. Study 1 concluded that

the higher the individual’s working memory capacity the lower the maths performance during

performance-approach goal. Study 2 confirmed that this pattern was caused by uncertainty to

outperform others (Crouzevialle, Smeding, & Butera, 2015).

In another study, the influence of achievement goal pursuits on working memory

capacity was investigated when varying levels of executive load were used. When high

executive load (3-back) was used, there were achievement goal effects on working memory

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but this same pattern could not be found under the less demanding loads (1-back, 2-back).

Under the high executive load, there was poorer working memory processing during the

performance-approach goal than when mastery-approach goal or no-goal control were used

(Avery & Smillie, 2013).

Interestingly, Avery et al., (2013) reported that the largest performance decrement

occurs in a mastery-approach goal condition suggesting that mastery-approach goal is more

strongly influenced by working memory load than performance-approach goal. This was in

line with previous research that indicated that mastery-approach goals are linked with higher

working memory engagement (Harackiewicz & Linnenbrink, 2005). Participants in the Avery

et al., (2013) study were presented with a 4 x 4 letter matrix and required to make as many

words as possible. This task was used because working memory has been suggested to play a

role in word formation games, allowing the retrieval of verbal information from long-term

memory (Halpern & Wai, 2007). This primary word game was then interleaved with a

secondary task (digit order: high load or low load). Study 2 examined the role of working

memory further (in relation to achievement goal) using a primary task known to vary in

working memory intensity (modular arithmetic tasks: high/low working memory load). As in

Study 1, the primary task (modular arithmetic tasks) was interleaved with a secondary task

(letter order). But this time, self-reported strategy use was also used as a means of

understanding the link between achievement goals and working memory capacity. Those

pursuing a mastery-approach goal experienced the largest performance decline under high

secondary load on those parts of task that placed high demands on working memory

resources (Avery, Smillie, & De Fockert, 2013).

1.4.11 Achievement Goals and Cognition

Graham and Golan (1991) investigated the underlying processes linking motivation

(achievement goals, in particular) and cognition. The authors concluded that when deep

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processing on a memory task was required, participants in the mastery-approach goal

condition showed better recall than participants in the performance-approach goal condition.

Children (5th and 6th grade) were assigned to either task-focused motivational condition

(mastery goal), an ego-focused condition (performance goal), or a control group. They were

then given a list of 60 words manipulated to be encoded at either shallow (Phonemic: Does

the word rhyme with make?) or deep levels of processing (Category: Is the word a kind of

animal? and Sentence: Does the word fit in the sentence?), followed by an unexpected recall

test (Graham & Golan, 1991). Additionally, DiCintio and Parkes (1997) investigated how

achievement goals are linked to working memory. The authors reported that the mastery-

focused individuals had larger working memory spans compared with performance-focused

participants (Dicantio & Parkes, 1997). In another study, it was found that mastery-approach

goals were positively related to working memory and that working memory mediated the

overall maths performance. However, it was reported that children (year 4 and 6) who were

pursuing performance-approach goals had a negative relationship with working memory and

maths performance. These findings suggest that reduced working memory resources could

explain the reduced maths performance for the children with more normative goal

endorsement (Lee, Ning, & Goh, 2014).

1.5 Working Memory

According to Baddeley and Hitch (1974, updated in 2000), working memory is a

multicomponent system for temporarily storing and managing information that is required to

carry out cognitive tasks (e.g., learning, reasoning and comprehension), (Baddeley & Hitch,

1974). This limited capacity system is mainly involved in processing and short-term storing

of information either in verbal or visual format. The phonological loop of the working

memory is involved in the short-term storage of verbal information (phonological

information). The visuo-spatial sketchpad on the other hand, is for short-term storage of

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visual or spatial information. The central executive is involved in the planning and allocation

of resources (e.g., in a multi-step maths task, deciding where to go next to complete the

computation). According Kane and Engle (2002), working memory represents executive

attention. Working memory has limited ability to keep task relevant information and goal

representations accessible in case of interference form task-irrelevant information (e.g., worry

caused by stereotype threat or distractive thoughts caused by performance-approach goals). In

other words, working memory is an executive process that also coordinates cognition and

controls behaviour to achieve performance goals of the individual (Kane & Engle, 2002).

Furthermore, high working memory capacity allows the ability to control attention and

simultaneously minimize the influence of intrusive thoughts while completing a resource-

demanding cognitive task. Thus, working memory is critical for efficient thought regulation

in situations that place heavy demands on attention (e.g., stereotype threat, performance-

approach goal endorsement), (Kane & Engle, 2002).

Dual-process theory differentiates two distinctive processes (associative process and

rule-based process) that support performance in decision-making and reasoning. To begin

with, associative processes comprise of similarity-based associations that have been built up

over repeated exposure to existing events. These processes operate relatively spontaneously

and therefore make few demands on working memory resources (Rydell, McConnell,

Mackie, & Strain, 2006). Rule-based processes on the other hand, rely on explicit knowledge

as conventions to guide processing (e.g., multistep mental arithmetic tasks with carrying or

borrowing). Hence, the use of the explicit rules, puts heavy demand on working memory

resources (Stevenson & Carlson, 2003).

In the Beilock and DeCaro (2007) study, modular arithmetic tasks were used to

investigate mathematical problem solving in evaluative pressure situations (Beilock &

DeCaro, 2007). These tasks are useful as not only are they in a format that is normally

47

unrecognisable by the participant [32 ≡ 8 (mod 4)] but also, they can be solved in two

different ways, depending on whether rule-based or associative process is utilised. In order to

go through the required computation multitude of steps have to be taken and interim totals

stored in the working memory. First, 8 is subtracted from 32 (32 – 8 = 24). The answer is

then divided by 4 (24/4 = 6). Additionally, the participant needs to state whether the answer is

a whole number or not (true or false). This type of computation is based on rule-based

processes, and evidently in order to compute the task, working memory is heavily relied on

(for short-term storage and processing or computational information). On the other hand, the

computation can be completed without any calculations (use of associative processes). If the

numbers are even then the response is true. This type of reasoning is based on prior exposure

to the numbers used as part of the computation. Beilock and Carr (2005) concluded that in the

low-pressure condition, the high WM individuals outperformed the low WM individuals.

However, situation induced pressure impaired the maths performance of the high working

memory individuals. However, the performance of the low working memory individuals was

not affected under the pressure condition. These results were explained by higher WM

individuals relying more on rule-based computations that tax the existing working memory

resources heavily (Beilock & Carr, 2005). Together with the added pressure, the working

memory resources of the high WM were compromised, and as a consequence maths

performance suffered.

1.5.1 Working Memory and Intrusive Thoughts

According to Engle (2002), working memory capacity (executive attention) is of

particular importance when there are conditions (situations) that can lead to retrieval of

response tendencies that conflict with the task in hand. Additionally, working memory system

enables one to deal with the relevant task at hand while inhibiting irrelevant information

(Miyake & Shah, 1999). Individuals who have low working memory spans are less able than

48

people with high working memory spans of completing the mental work required to block

distracting information (Engle, 2002). Rosen and Engle (1998) conducted two experiments to

explore whether there was a relationship between an individual’s working memory capacity

and the ability to suppress intrusive thoughts and behaviours. Participants learned three lists

in a modified paired-associates task that contained pairs of cue-response items. During the

first experiment when speed was stressed, individuals with high working memory produced

fewer first-list intrusions during the second list learning. During the second experiment,

accuracy was stressed and the high working memory individuals were slower than the control

group to retrieve first-list responses on the list 3. The participants had already suppressed the

first-list responses during the second-list learning. The low working memory individuals were

faster than the individuals in the control condition. There was a relationship between an

individual’s working memory capacity and their ability to suppress intrusive thoughts. In

other words, people who have high working memory capacity are good at suppressing task-

irrelevant information. Finally, there is a domain free limitation in ability to control attention

in working memory (Rosen & Engle, 1998).

1.5.2 Working Memory and Mental Arithmetic

Working memory plays a vital role in mental arithmetic. When a double-digit sum

(e.g., 24 + 66) is performed, all three areas of the multicomponent working memory model

(central executive, phonological loop, and visuospatial sketchpad) are used to complete the

sum. Central executive keeps a track of the overall process and that which part of the

calculation has already been completed. Additionally, it also directs the actions of

phonological loop (speech-based information) and visuospatial sketchpad (visual

information). The role of the phonological loop is to maintain the intermediate results of the

calculation. The visuospatial sketchpad functions as a space where the actual problem and the

solution to it could be visually represented (DeStefano & LeFevre, 2004).

49

1.6 Maths Anxiety

Evaluative pressure (e.g., stereotype threat or achievement goals) can make individuals

feel more anxious about the task in hand. Hence, maths anxiety was measured as part of this

investigation. Maths anxiety is defined as ‘a feeling of tension, apprehension, or fear that

interferes with maths performance’ (Richardson & Suinn, 1972, p. 551). The first systematic

instrument to measure maths anxiety was the Mathematics Anxiety Rating Scale (MARS)

published by Richardson and Suinn in 1972. This test was created to test the participants’

maths anxiety levels in everyday situations with a mathematics component (e.g., calculating a

restaurant bill or taking a mathematics test), (Richardson & Suinn, 1972). Ashcraft claimed

that individuals who are high in maths anxiety have less practice than individuals with low

levels of maths anxiety due to negative thoughts and the avoidance of the subject and any

maths related situations. Due to this avoidance tendency, high maths anxious individuals get

less practice, and exposure in mathematics. General achievement tests show no competence

differences between the high maths anxious individuals and the low maths anxious

individuals. However, when the tests are timed the maths anxiety effects on whole-number

arithmetic problems can be seen (e.g., 46 + 27), (Ashcraft, 2002). The individuals with high

maths anxiety have negative attitudes towards mathematics and they have negative self-

perceptions about their skills in mathematics. However, there is only a weak link between

maths anxiety and overall intelligence (a small correlation of -.17). Individuals who are high

in maths anxiety score high on other anxiety tests too. The strongest link is between test

anxiety and maths anxiety (.52 correlation). When it comes to gender differences, women

report more feelings of maths anxiety but this might be due to the fact that women are more

honest about their feelings (Ashcraft, 2002).

Arithmetic problems with larger numbers (e.g., multiplication problems and two-column

additions) have shown two important maths anxiety effects. The individuals who are high in

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maths anxiety respond quickly to the maths tasks which is typical of avoidance behaviour.

However, by being as quick as possible can lead to a sharp increase in errors. Addition

problems that have a carrying element are difficult for the high maths anxious individuals due

to the extra burden on the working memory (Ashcraft, 2002). Additionally, individuals who

are high in maths anxiety, demonstrate smaller working memory spans. This is particularly

evident with a computation-based span task. There is an increase of reaction times and errors

when the mental additions are performed concurrently with a memory load task. Maths

anxiety causes a transitory disruption of working memory. The lower working memory

capacity of high maths anxious individuals is partially responsible for the maths performance

decrements. This reduced working memory capacity is on on-line effect that disrupts

information processing in maths tasks (Ashcraft & Kirk, 2001).

In support of this idea, a meta-analysis reported an average correlation of -.31 between

mathematics anxiety and maths achievement for college students and an average correlation

of -.34 for school students (Hembree, 1990). Ma (1999) included 26 studies in her meta-

analysis to investigate the relationship between maths anxiety and achievement in

mathematics (elementary and secondary school children). It was confirmed that the common

population correlation for this relationship is significant (-.27), (Ma, 1999). Additionally,

there is a strong link between maths anxiety and mathematics self-efficacy. People who think

that they are not particularly good at mathematics are also more likely to be maths anxious

(Hembree, 1990).

1.6.1 Onset of Maths Anxiety

Whenever a maths anxious individual is asked to perform mathematics in a high-stakes

and timed setting, the individual’s maths anxiety is aroused and causes an affective drop, a

decline in performance. It is also likely that a student’s maths anxiety is aroused in the maths

classroom itself and particularly when a student is asked to answer or solve a mathematical

51

problem. Finally, maths anxiety is certainly aroused when a student takes a maths test

(Ashcraft & Moore, 2009). Finally, there are no gender differences in standardized maths

tests through elementary and middle school. These differences start from the high school and

go through college and adulthood (Hyde, Fennema, & Lamon, 1990).

1.6.2 Maths Anxiety and Mathematical Problem Solving

Ashcraft and Faust (1994) have shown that people who are high in maths anxiety can find

two column additions (e.g., 34 + 28) difficult due to the element of carrying. Carrying puts

extra pressure on the working memory resources. The individuals with high maths anxiety

took 3 times more time (when the problems were answered correctly) than the low maths

anxious participants on the maths problems that required carrying. When the participants

were faced with relatively difficult arithmetic tasks, there were higher error rates on these

problems for the high maths anxious individual. And often showing classic speed-accuracy

trade-offs; participants wanting to be as quick as possible and ignoring the level of accuracy.

The participants wanted to avoid these types of calculations and be as quick as possible.

Faust, Ashcraft, and Fleck (1996) reported that maths anxiety and maths competence are not

fully confounded. In their study, there was equal maths performance across the different

maths anxiety groups when simple one- and two-column additions and multiplication

problems were completed in a pencil and paper format and when the tasks were not timed

(Faust, Ashcraft, & Fleck, 1996). However, Lyons and Beilock (2012) concluded that it is not

the actual maths that causes the anxiety, but the anticipation of doing the maths task that

causes the anxiety. The higher an individual’s maths anxiety levels were the more increased

brain activity was detected in the areas associated with visceral threat detection and there can

also be the actual feel of pain itself (bilateral dorso-posterior insula). This relationship was

not seen during the actual maths activity (Lyons & Beilock, 2012a).

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1.6.3 Mathematics Anxiety and Working Memory

Working memory is involved in mathematical problem solving and particularly when the

operands get bigger (problem-size effect). When the size of the operands increases, the errors

and response latencies also increase. This increase can be explained by the larger arithmetic

problems occurring less frequently and therefore these types of problems are stored in

memory at lower levels of strength. Another explanation is that the larger mathematical

problems are solved via a non-retrieval processes (strategy-based trials). These kinds of

processes are slower and there is more room for errors. Strategy based solutions are more

demanding on working memory. Retrieval is fast and relatively fast process, with little

demand on working memory. High maths anxiety works like a dual-task setting. The anxious

thoughts about maths performance function as a resource demanding secondary task

(Ashcraft & Krause, 2007).

Mathematics anxiety affects performance by overloading working memory (Hopko,

Ashcraft, Gute, Ruggiero, & Lewis, 1998). According to the processing efficiency theory,

when a person is anxious about something, these worrying thoughts may distract attention

from the task and therefore overload working memory. General anxiety is associated with

working memory deficits. The intrusive thoughts compete with the ongoing cognitive task for

the limited working memory resources. This can cause slowing of performance or reduced

accuracy (lower cognitive efficiency), (Eysenck & Calvo, 1992). Similarly, maths anxious

individual might be preoccupied with the dislike of mathematics and the previous bad

experiences of this area and as a consequence the working memory gets taxed. These

intrusive thoughts act like a secondary task, reducing the attention from the actual task in

hand (Ashcraft, 2002).

Maths anxiety may tax working memory. Indeed, Ashcraft and Kirk (2001) Study 1

concluded that participants who were high in maths anxiety had significantly lower working

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memory capacity scores than the participants who were low in maths anxiety. In the second

study, a dual-task was used to measure working memory capacity. A demanding secondary

task (memory task) was combined with a primary task of completing a mental addition task.

These two tasks were competing for the working memory resources for a successful

performance. When the mental addition tasks increased in difficulty, the working memory

was overloaded and this in in turn caused an increase in reaction times or errors. The

manipulation of the difficulty of the mental additions was whether it included a carrying or

not. It was concluded that the more difficult addition problems with carrying relied strongly

on working memory capacity and maths performance was compromised when the working

memory system was also taxed with the memory load task (secondary task). The third study

confirmed that maths anxiety affected performance in maths-related tasks and that this effect

was a transitory disruption of working memory. It was suggested that this effect took place in

the central executive of working memory. This is also the location where intrusive thoughts

and worry are initially registered (Ashcraft & Kirk, 2001). Finally, individuals who are higher

in maths anxiety, also score lower on a measure of working memory capacity (Ashcraft,

2002).

1.6.4 Emotional Processing and Maths Anxiety

In another study, it was confirmed that the preoccupation of the emotional content of

the maths stimuli can consume the existing working memory resources which can cause

decreased deactivation of areas that are associated with the default mode network (DMN)

which are activated during emotional processing. Eighteen individuals with high maths

anxiety were matched with 18 low maths anxious individuals and their BOLD-response

(Blood Oxygenation Level Dependent Signal) was matched for mathematical performance to

number comparison and number bisection tasks. There was stronger deactivation within the

DMN in low maths anxious individuals but only restricted to the mathematical tasks. This

54

effect was more pronounced when the stimuli required inhibitory functions. DMN

deactivation is an indication of processing efficiency and these results indicate that the HMAs

have reduced processing efficiency during mathematical cognition. However, there were no

differences in BOLD-response in task-related activation areas between HMAs and LMAs

(Pletzer, Kronbichler, Nuerk, & Kerschbaum, 2015).

1.6.5 Maths Anxiety and Individuals with High Working Memory

There are studies to suggest that the negative link between maths anxiety and maths

performance is the strongest with individuals who have high working memory capacity.

Maths anxiety affects the individual’s with high working memory capacity use of working

memory intensive strategies (Ramirez, Gunderson, Levine, & Beilock, 2013). In another

study, 154 first year and second year children were tested on maths achievement and working

memory capacity. There was a negative relation between maths anxiety and maths

achievement for children high in working memory. Children with high working memory

capacity rely more on working memory as they use working memory intensive strategies to

complete mathematical problems and these strategies can be disrupted by maths anxiety

(Ramirez et al., 2013). However, further studies have shown that this only relates to

individuals with high working memory who have low attentional control (measured with a

flanker task). Finally, higher attentional control prevent pressure-induced worries from co-

opting working memory resources (Sattizahn, Moser, & Beilock, 2016).

Impaired attentional mechanisms could also affect mathematical problem solving due to

attentional bias towards maths-related stimuli. High maths anxious individuals are slower at

identifying the colours of maths related words in an emotional Stroop task, compared with

neutral words. It was concluded that maths anxious individuals find maths related stimuli

threatening and therefore it impairs their ability to allocate their attention to relevant aspects

of the current task (Suárez-Pellicioni, Núñez-Peña, & Colomé, 2015).

55

1.6.6 Physiological Factors Linked to Maths Anxiety

There are some physiological factors that might explain some of the math

performance gap between low maths anxious individuals and high maths anxious individuals.

Individuals with high working memory have increased salivary cortisol concentration which

predicts poor maths performance (Mattarella-Micke, Mateo, Kozak, Foster, & Beilock,

2011). There is increased activation in brain regions that are normally associated with pain

perception in dorso-posterior insula (Lyons & Beilock, 2012a) and negative emotional

processing that can be indexed as hyperactivity in right amygdala. There is also reduced

activity in the brain regions that are associated with working memory and numerical

processing, dorsolateral prefrontal cortex and posterior parietal lobe (Young, Wu, & Menon,

2012).

To investigate how a person’s physiological arousal relates to their maths

performance as a function of individual differences in working memory (WM) capacity,

participants completed difficult maths problems and salivary cortisol levels were measured

before and after the maths tasks. Salivary cortisol levels were measured because these

hormone levels are associated with stressors in humans and these hormones can also have

effects on working memory. The performance of the lower working memory individuals was

not dependant on cortisol concentration or maths anxiety level. However, the higher the

concentration of salivary cortisol for the high working memory individuals with high maths

anxiety levels, (after the demanding maths task) the worse their performance. For the higher

working memory individuals (lower in maths anxiety), the higher their salivary cortisol

concentration, the better their performance. In other words, the relation between

physiological response (cortisol concentration) and maths performance, depended on a

participant’s maths anxiety and working memory capacity. For the participants who were low

in maths anxiety, stress boosted their performance (Mattarella-Micke et al., 2011). Ashcraft

56

and Kirk (2001) investigated maths competence and maths anxiety further. It was concluded

that simple whole number arithmetic problems (e.g., 5 + 6, 8 x 5) showed no maths anxiety

effects. However, for the high math anxiety individual there was a decline in performance

with more difficult arithmetic tasks (e.g., mixed fractions), (Ashcraft & Kirk, 2001).

1.6.7 Maths Anxiety and Stereotype Threat

Girls may experience more maths anxiety because of stereotype threat about girls and

mathematics. This can happen when girls are told that they are not as good at mathematics as

are boys. Girls would therefore feel that they are at risk of confirming a negative stereotype

about a group that they belong to (Steele, 1997). However, it is also possible that stereotype

threat does not increase maths anxiety levels and that the reason the girls’ maths performance

suffers is because girls decide to conform to social expectations (Dowker, Sarkar, & Looi,

2016). There are, of course, also environmental and social factors that are equally important

in trying to explain that how maths anxiety relates to maths performance (e.g., parents’ maths

anxiety, parents’ support, teacher’s maths anxiety, and the classroom environment), (Chang

& Beilock, 2016).

1.7 Conclusion

The section above has given summary of the current literature on distributed cognition

and how it can be used for off-loading working memory and improving mathematical

problem-solving performance. Additionally, we presented existing findings of negative

stereotyping about female maths performance and about the role of achievement goals on

working memory. The next section (chapter two) will now move on to presenting the

empirical findings of the thesis.

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Chapter 2: The Effects of Stereotype threat on Girls’ Mathematics Performance: The

Role of Distributed Cognition

Numeracy skills are an important part of the primary and secondary school

curriculum. Therefore, there is a strong emphasis on achievement in mathematics.

Unfortunately, however, some groups may not perform well in mathematics because of

stereotypes, or more specifically, stereotype threat. Stereotype threat is the risk of confirming

a negative stereotype expectation about one’s group. Females and African-Americans are

more likely to underperform in various test-taking situations (e.g., mathematics tests) if a

negative stereotype has been evoked than when it has not (Steele, 1997). The purpose of the

research reported here was to investigate the role of interactivity (distributed cognition) in

defusing the impact of gender stereotype threat on difficult mental arithmetic tasks.

Additionally, the effects of negative stereotyping on working memory and maths anxiety

were also investigated as part of the study.

2.1.1 Stereotype Threat and Working Memory

Women risk being judged based on the negative stereotype of not performing well in

mathematics tests. Stereotype threat can induce task-related thoughts and worries related to it.

Additionally, under stereotype threat there is an expectation for poor maths performance

(Spencer, Steele, & Quinn, 1999). Women underperform on difficult maths tests when told

that there have been gender differences in the past (Spencer et al., 1999). Stereotype threat

may influence maths performance by reducing working memory capacity. Schmader and

Johns (2003) found a lower working memory performance for women and Latinx participants

after receiving a stereotype threat manipulation when compared to the candidates in a control

group who did not receive a stereotype threat manipulation. The authors also conducted a

follow-up test that confirmed that stereotype threat led to poorer maths performance in the

stereotype condition which was mediated by working memory capacity.

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Stereotype threat may also harm maths performance, particularly maths problems that

rely heavily on phonological areas of working memory (modular arithmetic problems, in

horizontal format). In a study conducted by Beilock, Rydell, and McConnell (2007),

participants completed a mixture of horizontal and vertical modular arithmetic tasks at the

same time as a phonological secondary task. The modular arithmetic tasks and the

phonological task used the same pool of working memory resources. When stereotype threat

was made salient, there were performance decrements when the modular arithmetic tasks

were high in working memory demands (e.g., requiring borrowing) and when they were

presented in a horizontal fashion (Beilock et al., 2007).

2.1.2 Maths Anxiety

Maths anxiety is closely related to stereotype threat in that it also has a negative effect

on the overall performance of relatively simple mental arithmetic tasks (DeStefano &

LeFevre, 2004). Maths anxiety and stereotype threat are distinct constructs but they share the

same underlying mechanisms; stereotype threat and maths anxiety compromise the working

memory capacity that people have available for mathematics performance (Maloney,

Schaeffer, & Beilock, 2013).

There has been a great deal of research around the area of maths anxiety since the

publication of the Mathematics Anxiety Rating Scale (MARS) by Richardson and Suinn

(1972). Individuals who are maths anxious are preoccupied with maths fears and bad

experiences in the past and the overall capacity of working memory gets affected. This

preoccupation functions as a secondary task and is particularly resource demanding (Ashcraft

& Krause, 2007). There is poorer performance in mathematics for maths anxious individuals

when the maths problems are more complex, for example when a carry or borrow operation is

used as part of the calculation (Faust et al., 1996). Furthermore, processing efficiency theory

states that cognitive performance is affected by anxiety and worry because working memory

59

resources are concentrated on rehearsing negative thoughts about past failures (Eysenck &

Calvo, 1992).

Maths anxiety is a multidimensional construct and a full list of the causes is still

undetermined (Ashcraft, 2002). This type of anxiety can be defined as a feeling of

apprehension and tension in a mathematical setting (e.g., ordinary arithmetic problems in a

timed task). It is a fear that can also affect overall maths performance. Females normally

score higher than males in maths anxiety tests (Hembree, 1990). One possible reason for the

gender differences in maths anxiety is stereotype threat. It is possible that negative

stereotyping about girls’ mathematics performance can increase maths anxiety and therefore

reduce maths performance. Unfortunately, however, empirical studies do not normally

include a state maths anxiety measure to test this. Another explanation is that maths

performance is reduced when the participants decide to conform to social expectations rather

than because of increased levels of maths anxiety (Dowker et al., 2016).

Individuals who are high in maths anxiety avoid maths as a topic; they choose fewer

elective maths courses in secondary school and university. This avoidance causes individual

with maths anxiety to perform lower than people with less maths anxiety because the former

have had less practice with mathematics. Maths anxious individuals hold negative attitudes

toward maths and have negative self-perceptions about their maths skills and abilities

(Ashcraft, 2002). Another explanation is that it is the thought of solving maths that causes

maths anxiety and not the maths itself. Brain scans have revealed that the area of the brain

that is triggered when someone is highly maths anxious overlaps with the same area of the

brain where bodily harm is registered (bilateral dorso-posterior insula), (Lyons & Beilock,

2012b).

2.1.3 Mental Arithmetic and Working Memory

Working memory has an important role in mental arithmetic and in mathematical

60

cognition. When the size of the mathematical operands become larger, the latencies and

errors increase (the problem-size effect), (Zbrodoff & Logan, 2005). It is easier to calculate 2

+ 3 and 4 x 5 than 6 + 7 and 9 x 6. One explanation for this is that people see the larger

mathematical problems less frequently than smaller mathematical problems and therefore

they are not stored in long-term memory as strongly. Furthermore, larger problems are not

simply solved through memory retrieval but based on computational processes that are slower

and rely on working memory resources. Memory retrieval, in contrast, is a quick and almost

an automatic process, making very little demand on working memory resources (Tronsky,

2005).

Problems requiring carrying have much higher error rates and take longer than

problems that do not require carrying (Ashcraft & Kirk, 2001). Addition problems that

require carrying cause additional working memory processing because there is additional

cognitive processing involved. When there are multiple number additions, working memory

must be used to obtain the correct answer and such calculations require interim totals and

executive functioning skills to plan and sequence activities (Ashcraft, 1995). These

calculations require interim totals but also executive function skills to direct the individual’s

attention to decide what to do next. The opportunity to manipulate the external environment

to facilitate more effective thinking encourages different arithmetic strategies. However, any

possible working memory limitations can be compensated by off-loading the process to the

external environment (e.g., by using pen and paper), (Neth & Payne, 2011).

2.1.4 External Representations

External representations are created to assist people to make sense of different

situations and problems. These representations can save internal memory and therefore

enhance a person’s cognitive resources. It might be easier to understand a particular sentence

by drawing a picture of it rather than just thinking internally. And therefore, with the help of

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the drawing the overall cognitive cost of sense making is also reduced. This is closely linked

to computing mental arithmetic tasks. These tasks are completed without the help of pen and

paper, but the cognitive process required can benefit from using these external artefacts

(Kirsh, 2010). These are extra actions that facilitate comprehension. They are complementary

strategies that function as an organizing activity that use the external environment to reduce

the overall cognitive load (e.g., pointing, arranging of the nearby objects, writing things

down, and manipulation of artefacts). In one study, the complementary strategies were

particularly used when people were trying to make sense of origami instructions. The

candidates pointed on the instruction sheet on the different elements. But additionally, the

participants also moved the paper, gestured, and muttered (Kirsh, 2010). The same pattern

was found with people who were not experienced cooks who tried to follow cooking

instructions. The participants kept place with their finger to arrange the ingredients in the

right order, they read the recipe aloud, they asked themselves questions, and they muttered.

Rather than just reading instructions, people used these various types of superfluous actions

to facilitate comprehension. These actions are vital in understanding the instructions and it is

not incidental that they take place (Kirsh, 1995a).

In another study, a simple coin-counting experiment was conducted where it was

observed whether complementary strategies could enhance simple maths performance. The

participants were asked to sum a set of coins as quickly and as accurately as possible. There

were two testing conditions: 1) a no-hands condition where the candidates were not allowed

to do any pointing or moving of their hands or fingers, and 2) a hands condition where they

could point and move their hands. Performance was enhanced with the increased

interactivity. The error rate in the no-hands condition was 68% which decreased to 42% in

the hands condition. Additionally, there was a reduction of the time to complete the task as

well (i.e., an average of 22.50 seconds in the no-hands condition compared to 18.70 seconds

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in the hands condition), (Kirsh, 1995a). People use the space around them (intelligent use of

space) to enhance performance (e.g., enhanced reliability of execution and the number of

different jobs that a human agent can manage to do at the same time). People might not be

aware of this informational and structural structuring at their workplace, but it is something

that happens all the time. This structuring is an important part of the way that humans think,

plan, and behave and is not just something that happens without a purpose (Kirsh, 1995b)

Another study was conducted to test if physical manipulation of letters would help

produce more words in a Scrabble task (Maglio et al., 1999). The key to beneficial interactive

skill was that the benefits of taking physical actions outweigh the costs of doing it. The main

aim of the word game was to create as many words as possible from seven Scrabble letters.

There were two testing conditions: in the first one the participants could manipulate the

letters but in the second one, they could not. More words were produced in the hands

condition that allowed physical manipulation of the letters than in the no-hands condition.

Additionally, there was a significant interaction between the physical manipulation condition

(use of hands) and specific letters chosen. By physically re-arranging the letters, there was

enhanced performance only with one of the two sets of letters; this was the letter string with

which less frequent words could be produced and therefore harder for the participants to

generate. Thus, the word generation process with these letters was augmented by

interactivity, more so than when the Scrabble task involved a set of letters that could produce

more familiar higher frequency words. The participants did not have enough skill in

generating these words because they were less frequent and therefore it was more beneficial

for the subjects to manipulate physically the words in this condition to improve performance

(Maglio et al., 1999).

The manipulation of the external environment increased performance and reduced the

pressure of the internal resources (e.g., working memory) in a word production task. The

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study examined the effects of manipulating the order of different letter tiles in a word

production task in children with developmental dyslexia (Webb & Vallée-Tourangeau, 2009).

As in Maglio et al., (1999), the participants were expected to create words from sequences of

letter tiles in a hands condition and no hands condition. The manipulation of the word tiles

significantly increased the word production of children with dyslexia with an easy set of

letters but not with the hard set. Hence, it was concluded that the manipulation of the external

environment is relative to the task difficulty together with the cognitive abilities of the

candidate (Webb & Vallée-Tourangeau, 2009).

2.1.5 Mental Arithmetic and Interactivity

Studies have examined the different forms of interactivity and how they help the

participants think and create smart solutions in a mathematical context. In one study, Neth

and Payne (2011) asked participants to add coins on a computer screen in two different

conditions (move versus look). The coins could not be physically touched in the move

condition as they were on a computer screen but a drag and drop condition was used instead.

The evidence suggested that the participants moved the coins because they wanted to sort

them by value to put them into clusters rather than just marking them by location and this

clustering then helped them to create smart solutions. Accuracy increased with interactivity

but not speed which contrasts with Kirsh (1995a) who found that elevated interactivity

increased both accuracy and speed. Neth and Payne (2011) reported a non-significant result

regarding latencies which failed to confirm that there might have been a trade-off between

accuracy and speed. In other words, when a participant tries to increase the accuracy of the

calculations, there might be a cost in time (Neth & Payne, 2011).

Both accuracy and speed were increased with the help of using hands (in the pointing

condition) when counting arrays of items ( acting as a simple arithmetic task) (Carlson,

Avraamides, Cary, & Strasberg, 2007). When pointing was not allowed, the candidates used

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nodding instead. Nodding was equally associated with increased accuracy (Carlson et al.,

2007). Thus, gestures do not just have communicative functions, but they might help with

cognitive functions as well. Efficiencies in accuracy and speed can be achieved with the help

of gestures (Goldin-Meadow & Wagner, 2005). There is evidence to suggest that interactivity

can enhance performance and in particular, accuracy and efficiency when it comes to longer

sums involving 11 single-digit numbers (Vallée-Tourangeau, 2013). Thinking efficiency was

studied in a mental arithmetic task using two different testing conditions (static and

interactive) with short and long sums (7 or 11 numbers). Thinking efficiency was measured

as a ratio of accuracy over the time invested to complete the sums. There was a significant

interaction between condition and the set size and therefore it was confirmed that by allowing

the participants to manipulate the tokens the accuracy and efficiency was enhanced.

However, for the shorter sums the subjects performed better without manipulating the tokens

which indicated that performance is relative to the degree of task difficulty and cognitive

ability of the individual (Vallée-Tourangeau, 2013).

Finally, Vallée-Tourangeau, Sirota, and Villejoubert (2013) concluded that there was

a strong negative correlation between maths anxiety and mental arithmetic performance only

in a static condition. There were two conditions used in the study to complete a set of simple

sums: a static condition where the participants were not allowed to use their hands and an

interactive condition where a set of tokens were used to assist with the calculations. The

participants’ working memory capacity was also measured with a computation span task.

There was a statistically significant relationship between maths anxiety and working memory

capacity. Additionally, there was a statistically significant interaction between maths anxiety

level and the level of interactivity. With increased maths anxiety levels, there were fewer

errors in the interactive condition than in the static condition (Vallée-Tourangeau, Sirota, &

Villejoubert, 2013).

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2.2 The Present Experiment

In sum, many studies have looked at the benefits of external representations and how

to use interactivity to increase maths performance (accuracy and latency to solution). This is

particularly important when participants are highly maths-anxious or face negative

stereotyping in a mathematical context. Both constructs can place additional pressures on

working memory. However, if candidates can be given the chance to combine the resources

of their working memory with external resources (e.g., by using pen and paper), it can lead to

a stronger cognitive system that can increase the capacity of working memory resources and

reduce the overall demands of working memory. Although previous investigations have

shown that negative stereotypes about girls’ maths performance can lead to lower maths

performance, there are no studies that have tried to alleviate these effects with the help of

increased interactivity. Additionally, state maths anxiety is not typically measured in a

stereotype threat context. The present study focused on these two aspects. The experiment

reported here explored whether increased interactivity might alleviate the impact of negative

stereotyping about women’s maths performance on difficult mental arithmetic tasks, working

memory, and maths anxiety. Difficult multi-digit mental arithmetic tasks were completed in a

stereotype threat or control condition crossed with interactivity or no interactivity.

In line with previous research, our first hypothesis (Hypothesis 1) was that

interactivity would increase maths performance (accuracies and latencies to solution). Our

second hypothesis (Hypothesis 2) was that negative stereotyping about women’s maths

ability would impair the performance of the difficult mental arithmetic tasks. However, these

mental arithmetic performance decrements could be alleviated with the help of increased

interactivity (e.g., using pen and paper). Third, we hypothesized that there would be a

reduction of working memory capacity when the negative stereotype about women’s maths

performance was made salient. It was also expected that reduced working memory capacity

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would have a causal role in the reduced mental arithmetic performance. In other words, a

reduction in working memory would mediate the effect of stereotype threat on girls’ mental

arithmetic performance (Hypothesis 4). We also hypothesized that that participants would

feel more maths anxious in the stereotype condition than in the control condition (Hypothesis

5). Our final hypothesis (Hypothesis 6) was that the participants who were allowed to utilise

distributed cognition while computing the maths tasks than those who were not allowed

would feel less maths anxious after the experiment.

2.3 Method

2.3.1 Participants

Eighty-four 16-year-old girls participated in this study. The participants were

recruited from secondary schools in the south of England and were year 12 pupils. The

testing took place in an educational setting. After consenting to participate in the study, the

subjects were randomly assigned to one of the experimental conditions (stereotype threat or

control crossed with interactivity or no interactivity). The participants were briefed after the

experiment. A statistical power analysis (GPower, a priori) was performed for sample size

estimation. With an alpha = .05 and power = 0.80, the projected sample needed with the

medium effect size of 0.09 (partial eta squared) was N = 80.

2.3.2 Materials

Arithmetic skill. Basic arithmetic skill (BAS) was measured with the help of 45

simple expressions in a 60-second period (e.g., 10-5). The participants were asked to

complete as many mathematical expressions as they could in 60 seconds.

Mathematics self-efficacy. Mathematics self-efficacy was tested with the help of

Mathematics Self-efficacy and Anxiety Questionnaire (MSEAQ, shortened) by May (2009).

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This test is administered with seven questions (e.g., I believe I am the kind of person who is

good at mathematics) which are measured on scale of 1 to 5 (May, 2009).

Arithmetic task. The participants completed 10 difficult multi-digit mental arithmetic

tasks in primed conditions (stereotype threat or control, crossed with interactivity or no

interactivity). The mental arithmetic tasks included all 4 operands of mathematics (adding,

subtraction, division, and multiplication) and the tasks were up to 3-digit numbers (e.g., 433

+ 288, 93-37, 168/4 and 7x29). Multi-digit arithmetic requires the candidates to maintain

intermediate results as well as managing the carry or borrow demands of the calculation

(DeStefano & LeFevre, 2004). The mental arithmetic tasks were completed in Qualtrics to

measure time (latencies) and accuracy (percentage correct).

Computation span (C-span). Working memory capacity was measured with the help

of a computation-based span test by Salthouse and Babcock (1990). The participants were

asked to read a simple arithmetic expression and announce their answer aloud to the

researcher. Additionally, the subjects were asked to remember the second number of each

equation (e.g., 5+2=?) to be recalled later. The sequences of the simple arithmetic tasks

varied from 1 to 7 tasks (Salthouse & Babcock, 1990). According to Ashcraft and Kirk

(2001), people with maths anxiety have smaller working memory spans. This smaller span

can lead to increased reaction times and errors when mental mathematics is completed at the

same time as a memory load task.

Maths anxiety (state). Maths anxiety was measured with the 23-item Mathematics

Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This test has been

designed to measure maths anxiety levels of UK undergraduates. The test comprises

statements that relate to everyday situations that have a mathematics component (e.g., adding

up a pile of change). The participants are expected to respond by confirming the level of

anxiety that they feel on a 5-point Likert-type scale. This scale ranges from not at all to very

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much. MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday maths

anxiety, and maths observation anxiety (Hunt et al., 2011).

2.3.3 Procedure

The subjects were asked two weeks before the experimental session to complete a

pre-testing session that comprised of a timed basic arithmetic test and a mathematics self-

efficacy measurement. The data from the two tasks were used as covariates in the main

statistical analysis of the dependent variables due to their known effects on the variables.

Additionally, latencies were used as a covariate in order to avoid any speed-accuracy trade-

off. The participants were tested individually and the pre-testing session lasted approximately

5 minutes. The current study was a 2 (experimental condition: stereotype threat or control) x

2 (level of interactivity: interactivity or no interactivity) between-groups study. In the

stereotype condition, participants were told that the test was diagnostic of mathematical

ability and it had shown gender differences previously. The participants were also told that

girls performed worse than boys in these type of tests (explicit stereotype threat activating

cue). The participants were asked to provide their gender before starting the experimental

session. In the control condition, the participants were advised that the test measured the

capacity of their working memory. All participants were informed that that they could receive

feedback at the end of the experimental session.

Participants assigned to the interactive condition were given the option of using pen

and paper to write down interim totals to complete the mental arithmetic tasks (interactive

condition), whereas those assigned to the control condition did not utilise any external

artefacts. The experimental session started with the difficult mental arithmetic tasks. The

participants were randomly assigned to one of the experimental conditions (stereotype threat

or control crossed with interactivity or no interactivity). The mental arithmetic task was

administered in Qualtrics so that the performance of these tasks (accuracy and time) could be

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measured. Finally, the experimental session concluded with the computation span test

(working memory) and the maths anxiety measurement. The participants were tested

individually in an educational setting and the testing session took approximately 20 minutes.

The dependent variables of the research reported here were accuracies of the mental

arithmetic tasks, solution latencies, working memory capacity, and maths anxiety. Participant

accuracy was assessed with the help of Qualtrics where the mental arithmetic tasks were

computed by both participant groups (interactive or non-interactive). This allowed us to

record accuracy and time to complete the mental arithmetic tasks. Latency to solution was

calculated based on the page submit function of Qualtrics (the time from first click to the time

of the final click). Working memory was assessed by the performance of the simple mental

arithmetic expressions (e.g., 10-5) that were computed at the same time with a memory load

task (second digit of the expression). Finally, measures of participants’ level of maths anxiety

were obtained from the questionnaire which is described in the materials section.

2.4 Results

2.4.1 Data Analysis Plan

To investigate the hypotheses, four separate 2 (experimental condition: stereotype

threat or control) x 2 (level of interactivity: interactivity or no interactivity) between-groups

analysis of covariance (ANCOVA) were conducted with percentage correct, latencies,

working memory (computation span), and maths anxiety as dependent variables. The

covariates were basic arithmetic skills and mathematics self-efficacy (measured during the

pre-testing phase) and were chosen specifically because of their known effects on the

dependent variables. The mean values and standard deviations of these variables can be seen

in Table 1. It is of importance to mention here that whilst it was only the mental arithmetic

tasks that were computed in the interactive condition, the study expected to see carry-on

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effects of both stereotype threat and interactivity on working memory capacity and maths

anxiety that were measured after the mental arithmetic tasks.

A detailed correlational analysis was conducted for all of the four dependent variables

across the different experimental conditions. Additionally, if there was an effect of stereotype

threat on maths performance, then a mediation analysis would be conducted (to confirm that

a reduction in working memory capacity would mediate the effect of stereotype threat on

girls’ maths performance). Before the actual statistical analysis was conducted, it was

reported that there were no group differences between the stereotype-threatened participants

and the participants in the control group condition on the basic arithmetic skills (F < 1) that

was measured during the pre-testing phase. It was therefore confirmed that the groups did not

differ in their ability to complete mental arithmetic tasks under timed conditions.

Additionally, there were no group differences on the mathematics self-efficacy measure

either (F < 1) confirming that the participants did not differ in their levels of mathematic self-

efficacy.

2.4.2 Percentage Correct (Solution Accuracy)

To test the first and second hypotheses, the percentage correct of the mental

arithmetic tasks was examined. The mental arithmetic performance was elevated with

distributed cognition. Table 2 shows the performance of the mental arithmetic tasks in the

interactive condition (M = 74.80%, SE = 4.20%) and in the non-interactive condition (M =

43.20%, SE = 4.20%). A 2 (stereotype threat or control) x 2 (interactivity or control)

between-groups analysis of covariance (ANCOVA) was conducted. The scores from the

basic arithmetic skills test (pre-test) were used as a covariate. The covariate, basic arithmetic

skills, was significantly related to the percentage correct, F(1, 78) = 23.23, p < .001, ŋp2 = .23.

Additionally, the covariate (latencies) was significantly related to the percentage correct, F(1,

78) = 7.90, p = .006, ŋp2 = .09. Confirming the first hypothesis, the main effect of interactivity

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was significant, F(1, 78) = 64.34, p < .001, ŋp2 = .45. The main effect of experimental

condition was not significant (F < 1) failing to support the second hypothesis. Finally, the

interaction between the experimental condition and level of interactivity was not significant

as F < 1.

Table 1

Descriptive Statistics: Means and Standard Deviations (Pre-Testing Data)

M SD

Basic arithmetic skills 23.12 8.87

Maths self-efficacy 20.43 5.31

Note. Participants were not primed to complete the pre-testing tests. The pre-testing was completed two weeks

before the actual experiment. The pre-testing comprised of a basic arithmetic skills test and a mathematics self-

efficacy questionnaire. The scale for basic arithmetic skills is from 0 to 45 and the scale for mathematics self-

efficacy is from 0 to 35.

Table 2

Descriptive Statistics: Means and Standard Errors (Post-Testing Data)

STI STNI NSTI NSTNI

n = 21 n = 22 n = 19 n = 22

Performance scores M SE M SE M SE M SE

Percentage correct 78.40 4.20 40.30 4.30 74.80 4.20 43.20 4.20

Latencies (seconds) 32.83 2.89 38.72 2.91 32.33 2.89 39.30 2.89

Working memory 21.22 1.28 19.62 1.29 24.62 1.28 21.63 1.28

Mathematics anxiety 57.24 3.01 60.73 3.00 64.00 3.00 57.84 3.00

Note. STI = stereotype threat, interactive; STNI = stereotype threat, non-interactive;

NSTI = non-stereotype threat, interactive; NSTNI = non-stereotype threat, non-interactive.

The scale for the working memory measure is 0 to 56 and the scale for mathematics anxiety is from 0 to 115.

Only the mental arithmetic tasks were completed in the interactive or non-interactive conditions.

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2.4.3 Latency to Solution

We next looked at the latency to solution of the difficult mental arithmetic tasks to

test the first and the second hypotheses. Clearly, interacting with physical resources allowed

participants to complete the mental arithmetic tasks more quickly. Table 2 shows the

performance of the girls in the interactive condition (M = 32.33 s, SE = 2.89 s) and in the

non-interactive condition (M = 39.30 s, SE = 2.89 s). A 2 (stereotype threat or control) x 2

(interactivity or control) between-groups analysis of covariance (ANCOVA) was conducted.

The scores from the basic arithmetic skills test (pre-test) were used as a covariate. The

covariate, basic arithmetic skills, was significantly related to latency to solution, F(1, 79) =

18.34, p < .001, ŋp2 = .19. There was a main effect of interactivity, F(2, 79) = 4.97, p = .03, ŋp

2

= .06 supporting the first hypothesis. There was no effect of experimental condition (F < 1)

which failed to support the second hypothesis. Finally, the interaction between the

experimental condition and level of interactivity was not significant as F < 1.

2.4.4 Working Memory

We next examined the effects of negative stereotyping on working memory

(third hypothesis). Table 2 shows the performance of participants in the non-stereotype

condition (M = 21.63, SE = 1.28) and in the stereotype condition (M = 19.62, SE = 1.29). A 2

(stereotype threat or control) x 2 (interactivity or control) between-groups analysis of

covariance (ANCOVA) was conducted. The scores from the basic arithmetic skills test (pre-

test) were used as a covariate. The covariate, basic arithmetic skills, was significantly related

to working memory, F(1, 79) = 27.53, p < .001, ŋp2 = .26. There was a main effect of

experimental condition, F(2, 79) = 4.49, p = .04, ŋp2 = .05 confirming the third hypothesis.

There was no main effect of interactivity as F < 1. Finally, the interaction between the

experimental condition and level of interactivity was not significant as F < 1.

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Mediation analysis for the fourth hypothesis could not be conducted as there was no

statistically significant effect of stereotype threat on the mental arithmetic performance.

2.4.5 Mathematics Anxiety (State)

To test the fifth hypothesis, a 2 (stereotype threat or control) x 2 (interactivity or

control) between-groups analysis of covariance (ANCOVA) was conducted for maths

anxiety. The scores from the maths self-efficacy measure were used as a covariate to control

for individual differences. The covariate, maths self-efficacy, was significantly related to

maths anxiety, F(1, 79) = 7.20, p = .009, ŋp2 = .08. However, there was no significant effect of

experimental condition on maths anxiety (F < 1) failing to confirm the fifth hypothesis. There

was no effect of interactivity on maths anxiety (F < 1) failing to support the final hypothesis.

Finally, the interaction between the experimental condition and level of interactivity was not

significant as F < 1.

2.4.6 Correlational Analysis

A correlational analysis was conducted on the four primary dependent variables

(percentage correct, solution latencies, working memory, and mathematics anxiety) across the

experimental conditions (stereotype threat or control, crossed with interactivity or no

interactivity). As expected, working memory capacity was a strong predictor of mental

arithmetic performance in the stereotype threat condition without interactivity (Table 4),

r(84) = .64, p = .01 confirming existing empirical findings (Allen & Vallée-Tourangeau,

2016; Vallée-Tourangeau, 2013). However, when the stereotype-threatened participants were

given the opportunity to reconfigure the environment (with the help of pen and paper) this

same pattern could not be found anymore (Table 3). The potential working memory

limitations were compensated by externalizing the internal cognitive process to the outside

world. Additionally, there was a strong negative correlation between working memory

capacity, and maths anxiety (Table 4), r(84) = - .46, p = .03 in the stereotype threat condition

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without interactivity confirming existing literature (Ashcraft, 2002). This same pattern did

not exist in the interactive condition as interactivity allowed the individual to rely on the

extended working memory resources. Additionally, there was a strong positive correlation

between working memory capacity and accuracy in the non-interactive condition (without

stereotype threat), r(84) = .56, p = .01 (Table 6). However, this same pattern could not be

found in the interactive condition (Table 5). When the coupling of internal and external

resources was not allowed both the stereotype-threatened individuals and the control group

participants relied solely on their working memory resources. Working memory predicted the

mental arithmetic performance of the participants in both participant groups but more so for

the stereotype-threatened individuals. This same pattern could not be found in the interactive

condition. Interactivity provided the role of working memory by reducing the demands on the

working memory resources and allowing it to be augmented.

Table 3

Correlation Matrix for the Performance Measures (Percentage Correct, Latencies, Working

Memory, and Mathematics Anxiety) in the Stereotype Threat, Interactive Condition

1 2 3 4

% Correct Latencies WM MAS

1 1 .01 .22 -.03

2 1 -.12 .27

3 1 -.10

4 1

Note. % Correct = accuracy in the mental arithmetic tasks in percentage; Latencies = the time it took for the

participants to complete the task in seconds; WM = Working memory measurement (computation span); MAS =

maths anxiety measure.

** Correlation is significant at the 0.01 level, * Correlation is significant at the 0.05 level.

***The Bonferroni cut-off is 0.0125.

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Table 4


Memory, and Mathematics Anxiety) in the Stereotype Threat, Non-Interactive Condition

1 2 3 4


1 1 -.09 .64** -.39

2 1 -.40 -.13

3 1 -.46*

4 1






Table 5


Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Interactive Condition

1 2 3 4


1 1 -.14 .33 -.40

2 1 -.13 .26

3 1 .03

4 1





The Bonferroni cut-off is 0.0125.

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Table 6


Memory, and Mathematics Anxiety) in the Non-Stereotype Threat, Non-Interactive

Condition

1 2 3 4


1 1 .26 .56** -.40

2 1 -.13 .07

3 1 -.26

4 1






2.5 Discussion

The current study explored the cognitive mechanisms governing stereotype threat in a

mathematical context. In this study, girls completed difficult multi-digit mental arithmetic

tasks in stereotype threat or control condition, crossed with interactivity or no interactivity.

The primary dependent variables were performance on the mental arithmetic test (accuracy

and latencies), working memory capacity, and maths anxiety. Accuracy was substantially

improved with elevated interactivity confirming our first hypothesis. The participants who

were given the opportunity to externalize their internal cognitive process, performed better

and were quicker than the participants in the non-interactive condition. Clearly, recruiting

artefacts (e.g., using pen and paper) can transform mental arithmetic performance. Past

research findings by Kirsh (1995a) and Carlson et al., (2007) have confirmed that elevated

interactivity increased both accuracy and speed to come to the solution. Clearly, there was no

cost in time to improve accuracies. The increased speed of the current study contrasts with

Neth and Payne (2011) study which failed to confirm a significant result regarding speed. It

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failed to confirm that there might be a trade-off between accuracy and speed. When a

participant tries to improve the accuracy of the calculations, there might be a cost in time.

There were no significant effects of stereotype threat on maths performance (accuracies and

latencies) failing to confirm our second hypothesis set in the introduction. This finding is in

contrast with existing studies that have confirmed that negative stereotyping impairs maths

performance (Schmader & Johns, 2003; Beilock et al., 2007).

However, there was a performance decrement in the working memory performance

for the participants in the stereotype condition confirming the third hypothesis. According to

Schmader and Johns (2003), stereotype threat reduces the capacity of working memory

available to complete mathematical computations (e.g., mental arithmetic tasks). In their

study, stereotype threat led to poorer maths performance for women and Latinx participants

in the stereotype condition; this impaired performance was mediated by working memory

capacity. Stereotype threat can also co-opt working memory resources, particularly verbal

resources (Beilock et al., 2007). Additionally, the detailed correlation analysis of the current

study revealed that working memory capacity was a strong predictor of mental arithmetic

performance in both conditions (stereotype threat or control) and in particular when

stereotype threat was made salient. The lack of this correlational pattern in the interactive

condition, allowed us to draw the conclusion that distributed cognition allowed the

participant to extend their working memory capacity and that is why this correlation could

not be seen in the interactive condition.

However, the current study failed to support the causal role of working memory in

reducing maths performance under stereotype threat (Hypothesis 4). One possible reason for

this is that the candidates of the current investigation were 16-year-old girls who had recently

completed the GCSE assessments (General Certificate of Secondary Education, British)

where mathematics is one of the compulsory subjects. Mental arithmetic skills play an

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important role in the mathematics part of the examination. The students had the required skill

and experience to manage the type of mental arithmetic tasks that were utilised in the current

experiment and were not affected by the negative stereotyping while completing these tasks,

unlike the working memory assessment that was used. The working memory test did not

follow the expected format of testing and the candidates felt the extra burden of not being

expected to succeed. Therefore, there was a performance decrement in the working memory

performance but not a significant effect on the maths performance as measured by accuracies

and latencies.

Finally, maths anxiety was not affected by the manipulation of the experimental

condition (stereotype threat or control). In other words, stereotype threat did not increase the

participants’ feeling of being more maths anxious, failing to confirm Hypothesis 5. It is

evident that the participants conformed to social expectations about their maths abilities and

thus their working memory capacity was reduced. However, this reduction in working

memory capacity was not because of increased levels of maths anxiety. It is possible that

there were no significant statistical effects of stereotype threat on maths anxiety because the

maths anxiety measure that was used comprised of statements that related to everyday

situations that have a mathematics component rather than the actual task in hand.

Additionally, the research reported here did not find any carry-over effects of interactivity on

maths anxiety. The participants who interacted with physical resources while completing the

mental arithmetic tasks, were not less maths anxious at the end of the experiment compared

to their non-interactive counterparts. It is possible that these types of carry-on effects of

interactivity can only be felt immediately after the interactive task. It is also possible that self-

reported maths anxiety measures like the one used as part of this experiment do not

successfully detect correct anxiety levels and in particular when interactivity has been

utilised. Past interactivity research has not measured state maths anxiety.

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2.6 Limitations

Whilst the findings of the research reported here were encouraging, there were

limitations to the study. This study employed only 10 difficult mental arithmetic tasks and it

is possible that it was not enough to demonstrate any statistically significant findings. The

current research only employed one type of maths task and it is clear that the study would

have benefited in having additional maths tasks in different formats in order to compare the

effects of stereotype threat on mental arithmetic performance. This study also utilised a task

that was in a known format to the participants. By being in a known format, it could be

argued that it was not measuring what it was supposed to measure as the students were more

automated with these types of mental arithmetic tasks. Whilst the level of working memory

processing was not measured as part of this investigation, it was evident that the automation

of completing the tasks, allowed the participants to rely less on the working memory

resources than if they had been in a format that required deeper processing. Additionally, the

current study only utilised one level of interactivity (the use of pen and paper). Past empirical

studies have employed various forms of interactivity (e.g., use of pointing and adding up

wooden tokens) to further explore the positive effects of distributed cognition on maths

performance. Finally, it is possible that the priming that was given to the control participants

(when told that the test was a measure of working memory capacity) triggered performance-

approach goals. It is possible that the participants felt pressure to perform well in comparison

to others doing the same test.

2.7 Future Studies

In summary, this study has provided evidence that interactivity enhances maths

performance and particularly accuracies and latency to solution. Additionally, it has been

shown that working memory resources are compromised from stereotype threat for 16-year-

old girls in an educational setting. In other words, an increase in negative comments about

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girls’ maths performance caused the participants in the stereotype threat condition to have a

lower working memory performance compared to the control participants. However, there

was no causal role of working memory in reduced maths performance under stereotype

threat. Therefore, it is suggested that for future studies, modular arithmetic tasks should be

used as the mental arithmetic problems (e.g., 5 mod 3 ≡ 2 which means 2 is the remainder

when you divide 5 by 3). Modular arithmetic tasks rely heavily on working memory

resources but are in a format not easily recognised by participants and therefore would

require different processing skills than the ones that were used in the current experiment. And

it is therefore anticipated that there will be a reduction of maths performance in the stereotype

condition and this performance decrement will be mediated by reduced working memory

performance. The mental arithmetic tasks of the current study were in a format that was

easily recognized by the candidates. Future studies would also benefit from measuring trait

maths anxiety as part of the pre-testing phase to be able to use it as a covariate when the state

maths anxiety analysis is conducted. This would be a more accurate analysis of the maths

anxiety levels of the participant at the end of the experiment.

Chapter 3: The Effects of Stereotype threat on Female University Students’ Maths

Performance: The Role of Distributed Cognition

Previous research (Study 1) indicated that there were no mental arithmetic

performance decrements when stereotype threat about girls’ and maths was made salient to

16-year-old girls. In other words, stereotype threat about girls’ maths performance did not

cause the participants to perform worse in the difficult mental arithmetic tasks compared to a

non-stereotype threat condition. It was assumed that the students had the required skill and

experience to deal with the type of mental arithmetic tasks that were utilised and were not

affected by the negative stereotyping while completing the tasks. However, negative

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stereotyping caused working memory performance to be lower than when negative

stereotyping was not made salient without reduced mental maths performance. It is possible

that the working memory test did not follow the expected format of testing and therefore it

was suggested that the participants felt the extra burden of not being expected to succeed

(situation-induced stress). It was therefore plausible to suggest that the combination of not

recognising the format of the working memory measure and the additional stress caused by

the stereotype threat caused a working memory performance drop. Finally, interactivity

elevated the mental arithmetic performance (percentage correct and solution latency) when

stereotype threat about girls’ maths performance was not present (control condition).

Based on the findings of the first study, it was concluded that the format of the mental

arithmetic tasks should be in a format not easily recognisable by the participants. Modular

arithmetic tasks were suggested because they are based on common mathematical procedures,

but are in an uncommon format. Thus, previous task experience is controlled because most

students have not seen the format before (Beilock & Carr, 2005). The participants need to

learn the required steps to complete the tasks first and to store this information in working

memory.

Finally, the aim of the study reported here (Study 2) was to look at the effects of

negative gender related stereotypes (female maths performance) on mental arithmetic

performance (known format) and modular arithmetic performance that was in a novel format

(low WM load and high WM load), and working memory. There were two levels of difficulty

of modular arithmetic tasks to further explore the impact of stereotype threat on maths

performance. We further explored whether the negative effects on the mental arithmetic

performance and modular arithmetic performance could be mitigated with the help of

distributed cognition. Additionally, the current study investigated whether there were any

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carry-over effects of stereotype threat and interactivity on maths anxiety that was measured at

the end of the experiment.

3.1.1 Maths Anxiety and Interactivity

Maths anxious individuals’ thoughts are dominated by fears of mathematical tasks

and how to compute them successfully; this can have a causal effect on the individual’s

overall working memory capacity. This preoccupation functions as a secondary task (dual

task set-up) that is heavily working memory resource demanding. Maths anxiety is

significantly correlated with working memory capacity. When there is an increase of maths

anxiety levels, there is a drop on the working memory capacity (Ashcraft, 2002). Due to the

additional worries, the highly maths-anxious individual is faced with two simultaneous tasks:

the worry about the successful completion of the task and the actual task requirement

(including possible borrowing or carrying over), (Ashcraft & Krause, 2007). Higher levels of

maths anxiety causes a transitory disruption of working memory, causing diminished working

memory resources to deal with maths tasks. This reduced working memory capacity is an on-

line effect that disrupts information processing in maths tasks. This reduced level of working

memory capacity of high maths anxious individuals is partially responsible for the maths

performance decrements. (Ashcraft & Kirk, 2001). However, the benefits of interactivity for

the highly maths anxious individual are well established (Allen & Vallée-Tourangeau, 2016;

Vallée-Tourangeau et al., 2016). When a participant is interacting with the external

environment it allows the individual to access greater cognitive resources which in turn can

mitigate the effect of maths anxiety on maths performance. However, what is less clear is

whether maths anxiety itself is mitigated in the interactive condition. The study reported here

aims to answer this question by measuring maths anxiety at the end of the experiment.

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3.2 Pilot Study

Before the actual experiment, a pilot study with ten participants was conducted to

further understand the right difficulty level of modular arithmetic tasks for the second study.

Clearly, attempts to determine the effectiveness of externalising the internal cognitive process

to the outside world in helping individuals to solve mathematical problems must be

relativized to the cognitive abilities of the individual and to the difficulty of the task (Vallée-

Tourangeau & Wrightman, 2010). The original Beilock and Carr (2005) study employed up

to two-digit modular arithmetic tasks because all of the participants were required to

complete the experiment without any external artefacts: the low load tasks used single-digit

numbers and high load tasks employed two-digit numbers (Beilock & Carr, 2005). The

experiment reported here allowed half of the participants to utilise interactivity (i.e., to use

pen and paper) to reach a solution and therefore the tasks needed to be at the right difficulty

level for the participants to make use of this option. Kirsh (2010) reported that interactivity

changes the cost structure of the required cognitive process and therefore people will do

whatever is easier to perform the task. If the task is too easy, the participant will not feel the

need to externalize the process to complete the tasks. Instead, the participant will work out

the answer by relying on their internal cognitive resources only (Kirsh, 2010).

3.3 Method

3.3.1 Participants

Ten female undergraduate psychology students from the University of Surrey (M =

19.30, SD = 0.95) participated in this study for exchange of SONA credits. After consenting

to participate in the study, the subjects were randomly assigned to one of the experimental

conditions (stereotype threat or control crossed with interactivity or no interactivity). The

experimental sessions (both pre-testing and post-testing) were conducted in a psychology lab

at the University of the Surrey.

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3.3.2 Material and Measures


simple expressions in a 60-second period (e.g., 10-5). The participants were asked to

complete as many expressions as they could in 60 seconds.



This test is administered with seven questions (e.g., “I believe I am the kind of person who is

good at mathematics”) which are measured on scale of 1-5 (May, 2009).

Mathematics anxiety (trait). Maths anxiety was measured with the 23-item

Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The test

comprises statements that relate to everyday situations that have a mathematics component

(e.g., adding up a pile of change). The participants are expected to respond by confirming the

level of anxiety that they feel on a 5-point Likert-type scale. This scale ranges from not at all

to very much. MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday

maths anxiety and maths observation anxiety (Hunt et al., 2011). This measurement and the

two previous ones constituted the pre-test.

Computation span. Working memory capacity was measured with the help of a

computation-based span test by Salthouse and Babcock (1990). The participants were asked

to read a simple arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer

aloud to the researcher (7, 3). Additionally, the participants were asked to remember the

second number of each equation to be recalled later (2, 6). The sequences of the simple

arithmetic tasks varied from 1 to 7 tasks. The computation span task requires both on-line

processing for the problem solution which is simultaneous with storage and maintenance of

information in working memory for serial recall (Salthouse & Babcock, 1990). According to

Ashcraft and Kirk (2001), people with maths anxiety have smaller working memory spans.

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This smaller span can lead to increased reaction times and errors when mental mathematics is

completed at the same time as a memory load task (Ashcraft & Kirk, 2001).

Arithmetic task. The arithmetic task of the pilot study consisted of 30 modular

arithmetic tasks that relied heavily on working memory resources. The tasks were adapted

from Beilock and Carr, (2005) original study. The purpose of these type of modular

arithmetic tasks is to judge the validity of maths problems like 61 ≡ 18 (mod 4). The middle

number is subtracted from the first number (i.e., 61-18) and then the difference is divided by

4. If the answer is a whole number the maths problem is true (Beilock & Carr, 2005).

Modular arithmetic tasks as laboratory tasks are advantageous because although the tasks are

based on common mathematical procedures, most students have not seen them before and

therefore previous task experience is controlled.

The participants in the pilot study solved modular arithmetic problems that varied as a

function of the demands on the working memory (low WM demand or high WM demand).

Fifteen problems were low-demand problems where single-digit numbers were used [e.g., 8 ≡

2 (mod 2)], while the remaining 15 problems were high-demand problems where two-digit

numbers were utilised [e.g., 32 ≡ 8 (mod 6)]. It was assumed that if situation-induced

pressure (e.g., stereotype threat) impacted working memory capacity, then mental arithmetic

performance should be more likely to decline on high-demanding problems in comparison to

low-demanding problems. The dependent variable of the modular arithmetic tasks was the

number of true responses.

The modular arithmetic tasks of the pilot study were presented in a horizontal format. The

horizontal presentation of the maths problems is more reliant on phonological resources (the

verbal resources) because individuals maintain the required problem steps in their memory

verbally. The anxiety of stereotype threat put extra burden on the working memory

(phonological loop, in particular), and together with the horizontally presented maths

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problems there can be maths performance decrements under stereotype threat (Beilock et al.,

2007). The mental arithmetic tasks were completed in Qualtrics to measure time (latencies)

and accuracy (percentage correct). The mental arithmetic tasks that were used as part of the

first study, were not utilised as part of the pilot study.


Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The state maths

anxiety was measured with the same questions as the trait anxiety measure, but this time the

questionnaire referred to the current time (now), (Hunt et al., 2011). This measure and the

previous two measures constituted the post-test.

3.3.3 Procedure

There was a pretesting sessions two weeks before the actual experiment comprising of

basic arithmetic skills test, maths-self efficacy questionnaire, and maths anxiety (trait)

measurement. During the actual experiment, the participants started with the computation

span which was followed by the modular arithmetic tasks. This was followed by the state

maths anxiety measurement.

3.4 Pilot Study Findings

We did not conduct any statistical analysis of the pilot study data, only qualitative

observations were made during the experiment. The main purpose of the pilot study was to

investigate the right difficulty level of the modular arithmetic tasks for the interactive option

to work. If the task is too easy, there are no benefits of combining internal and external

resources (Kirsh, 2010). The qualitative observations were done by monitoring the

participants while they were completing the maths tasks. We had predicted that there would

be limited benefits in employing interactivity with the low WM load tasks due to these tasks

utilising single-digit numbers and therefore there would be limited use of borrowing and

carrying that tax working memory. It was therefore assumed that these types of tasks would

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be quicker and easier to be computed in the head only. The behaviour of the pilot participants

was observed during the experiment and particularly whether the participants utilised the pen

and paper option to compute the tasks. Some of the pilot study participants did not make use

of the interactive option when working on the tasks. Perhaps the external artefacts that were

offered to the participants were in their way and distracting the performance. This was

particularly evident during the single-digit tasks. Hence, the pilot study concluded that the

second study would require a higher level of difficulty of the modular arithmetic tasks that

was employed in the original Beilock and Carr (2005) study.

Whilst it was not directly measured, it seemed that the participants did not feel the

need to employ the interactive option to complete the tasks. It was assumed that they had the

required skill and the internal cognitive resources e to compute the tasks without the

externalising of the internal cognitive process. Similar findings have been made by Vallée-

Tourangeau and Wrightman (2010) who examined these factors in a simple word production

task utilizing letter tiles. Two sets of letter tiles were used with differing word production

difficulty. The participants were told to produce as many words as they could from the letter

tiles. There was an interactive condition where the participants were encouraged to touch and

rearrange the tiles when producing words. In the non-interactive condition, the participants

could not point to the tiles or interact with them in any way. There was also a distinction

between a low and high verbal fluency group as a function of the participants’ score on the

Thurstone word fluency test. For the high-fluency participants the word production

performance was not enhanced with the interaction of the letter tiles. However, in the low

verbal fluency group, letter rearrangement elevated the word production performance (both in

the hard and easy set of tiles). The benefits of the external restructuring of the letter tiles was

more beneficial for the participant with lower cognitive abilities and with a more taxing task

(Vallée-Tourangeau & Wrightman, 2010). Based on the findings of the pilot study, it was

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suggested that up to three-digit numbers would be employed in the high WM load to better

allow for the benefits of increased interactivity in the actual experiment. The low WM load

would consist of numbers that were up to two-digits and the high load tasks would use

numbers that were up to three-digits.

3.5 The Current Study

Based on the findings of the first study, the first hypothesis for the second experiment

(Hypothesis 1) was that the externalising of the internal cognitive process to the outside

world by using pen and paper would increase maths performance in terms of accuracy

(percentage correct) of the mental arithmetic tasks and modular arithmetic tasks (high WM

load and low WM load). Furthermore, it was predicted that increased accuracy would be

stronger for the high WM load modular arithmetic tasks than the low WM tasks. The second

hypothesis (Hypothesis 2) stated that interactivity would reduce the solution latencies

(allowing the participant to complete the tasks faster) for the mental arithmetic tasks and the

modular arithmetic tasks (low WM load and high WM load) as per findings of the Study 1.

The third hypothesis (Hypothesis 3) was that negative stereotyping about women’s maths

ability would impair the performance of the modular arithmetic tasks and not the mental

arithmetic task performance as per findings of the Experiment 1. However, these modular

arithmetic performance decrements were expected to be alleviated with the help of increased

interactivity (e.g., using pen and paper), (Hypothesis 4) as per existing empirical findings

(Vallée-Tourangeau, 2013). Additionally, it was expected that interactivity would be most

beneficial for the high WM load modular arithmetic tasks. We hypothesized that there would

be a reduction of working memory capacity when the negative stereotype about women’s

maths performance was made salient (Hypothesis 5) as per existing findings by Schmader

and Johns (2003). It was also expected that the reduced working memory capacity would

have a causal role in the reduced modular arithmetic performance (Hypothesis 6).

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Additionally, we predicted that interactivity would reduce the participants’ state maths

anxiety levels (Hypothesis 7) as per existing findings on interactivity allowing the maths

anxious individuals to improve their maths performance (Allen & Vallée-Tourangeau, 2016;

Vallée-Tourangeau et al., 2016). We expected the participants to feel more maths anxious

(state) in the stereotype condition than in the control condition when tested at the end of the

experimental session (Hypothesis 8). Finally, our final hypothesis was that there would be a

two-way interaction in that interactivity would reduce the levels of maths anxiety (state) in

the stereotype threat condition (Hypothesis 9).

3.6 Method

3.6.1 Participants

Ninety-six female undergraduate psychology students from the University of Surrey

(M = 23.70 SD = 7.60) participated in this study for exchange of (SONA) credits. After

consenting to participate in the study, the subjects were randomly assigned to one of the

experimental conditions (stereotype threat or control crossed with interactivity or no

interactivity). Both the pre-testing and post-testing took place in a psychology lab, at the

University of Surrey. A statistical power analysis (GPower, a priori) was performed for

sample size estimation. With an alpha = .05 and power = 0.80, the projected sample needed

with the medium effect size of 0.09 (partial eta squared) was N = 80.



simple expressions in a 60-second period (e.g., 10-5).




Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This

90

measurement and the two previous ones constituted the pre-test which were identical with the

pre-testing measures of the pilot study.

Computation span. Working memory capacity was measured with the help of a

computation-based span test by Salthouse and Babcock (1990). The participants were asked

to read a simple arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer

aloud to the researcher (7, 3). Additionally, the participants were asked to remember the

second number of each equation to be recalled later (2, 6). The sequences of the simple

arithmetic tasks varied from 1 to 7 tasks. This task was identical with the pilot study.

Arithmetic tasks. The participants completed two sets of mental arithmetic tasks.

The first one consisted of 10 difficult multi-digit mental arithmetic tasks in primed conditions

(stereotype threat or control, crossed with interactivity or no interactivity). The first task was

identical to the task used in the Study 1. The mental arithmetic tasks included all 4 operands

of mathematics (adding, subtraction, division and multiplication) and the tasks were up to 3-

digit numbers (e.g., 433 + 288, 93-37, 168/4 and 7x29). Multi-digit arithmetic requires the

candidates to maintain intermediate results as well as managing the carry or borrow demands

of the calculation (DeStefano & LeFevre, 2004).

The second mental arithmetic task consisted of modular arithmetic tasks (30 tasks, in

primed conditions) that relied heavily on working memory resources, adapted from Beilock

and Carr (2005). The participants of the current study had to solve modular arithmetic

problems that varied as a function of the demands on working memory (low WM demand or

high WM demand). Fifteen problems were low-demand problems where two-digit numbers

that required a carry were used [e.g., 83 ≡ 27 (mod 8)] while the remaining 15 problems were

high-demand problems where up to three-digit numbers requiring a carry were utilised [e.g.,

135 ≡ 69 (mod 6)]. If situation-induced pressure impacts working memory capacity, then

modular arithmetic performance should be more likely to decline on high-demanding

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problems [e.g., 135 = 69 (mod 6)] in comparison to low-demanding problems [e.g., 83 ≡ 27

(mod 8)] of the present study.

Like the pilot study, the modular arithmetic tasks of the current experiment were

presented in a horizontal format (rather than vertical format). The horizontal presentation of

these types of problems is more reliant on phonological resources (the verbal resources)

because the required problem steps are stored in the memory verbally. The distractive

thoughts of stereotype threat can put extra burden on the working memory (phonological

loop, in particular), and together with the horizontally presented maths problems there can be

depleted maths performance under stereotype threat (Beilock et al., 2007).


Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This questionnaire

(which was identical with the pilot study) and the two previous tasks constituted the post-test.

3.6.3 Procedure

Two weeks before the experimental session participants completed a pre-testing

session that comprised of the basic arithmetic test, Mathematics Self-Efficacy Questionnaire,

and Mathematics Anxiety Scale (trait). The participants were tested individually in a

psychology testing lab for 5 minutes. The participants were randomly assigned to one of the

experimental conditions (stereotype threat or control crossed with interactivity or no

interactivity). When the actual experimental session started, the participants in the stereotype

threat condition were advised that the test was diagnostic of their mathematical ability and

that the tests had shown gender differences previously. The participants were also told that

girls performed worse than boys in these type of tests (explicit stereotype threat activating

cue). The participants were asked to provide their gender before starting the experimental

session. The participants in the non-stereotype threat condition were advised that the study

was testing the participants’ working memory capacity. After the priming of negative gender

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stereotypes, the participants completed the computation span test (measure of working

memory) and this was followed by the 10 mental arithmetic tasks and 30 modular arithmetic

tasks (low and high WM load). Participants assigned to the interactive condition were

allowed to use pen and paper to write down interim totals to complete the mental arithmetic

tasks and modular arithmetic tasks (interactive condition), whereas those assigned to the

control condition could not do so. The mental arithmetic tasks and the modular arithmetic

tasks were administered in Qualtrics so that the performance of these tasks (accuracy and

time) could be measured. Finally, the experimental session was concluded with the Maths

Anxiety Scale (state). The participants were tested individually in the psychology testing lab

for approximately 30 minutes.

The primary dependent variables of the current study were working memory capacity,

accuracies of the mental arithmetic tasks (known format) and modular arithmetic tasks (novel

tasks), solution latencies (for both types of maths tasks), and maths anxiety (state) with trait

maths anxiety as a covariate. As before, working memory was assessed by the performance

of the simple mental arithmetic expressions (e.g., 10-5) that were computed at the same time

with a memory load task (second digit of the expression). The accuracy of the maths tasks

was assessed with the help of Qualtrics where the mental arithmetic tasks and modular

arithmetic tasks were computed by both the interactive and non-interactive participants. This

allowed us to record accuracy and time to complete both types of math tasks. Latency to

solution was calculated based on the page submit function of Qualtrics (the time from first

click to the time of the final click). Finally, measures of participants’ level of maths anxiety

(state) were obtained from the questionnaire which is described in the materials section. The

maths anxiety measure (trait) that was measured during the pre-testing phase was used as a

covariate.

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3.7 Results


To investigate the hypotheses, three separate 2 (experimental condition: stereotype

threat or control) x 2 (level of interactivity: interactivity or control) between-groups analysis

of covariance (ANCOVA) were conducted with percentage correct (accuracies), latencies,

and state maths anxiety as dependent variables. There was an equal number of participants in

each condition (n = 24). The covariates were basic arithmetic skills and maths anxiety (trait)

that were measured during the pre-testing phase. Additionally, latencies were used as a

covariate to avoid speed-accuracy trade-off when the maths tasks were computed. They were

chosen specifically because of their known effects on the dependent variables. Past research

has found a positive correlation between basic arithmetic skills and working memory capacity

(Guthrie & Vallée-Tourangeau, 2018). Additionally, the pre-existing arithmetic skills

(measured with the help of basic arithmetic skills test) were expected to affect the maths

performance of the actual experiment. It was noted during the first study that one of the

limitations of the study was that trait maths anxiety was not measured during the pre-testing

phase and therefore our state maths anxiety measure did not reflect the pre-existing levels of

maths anxiety. The level of maths anxiety (trait) that the participant felt prior to the

experiment was expected to affect the state maths anxiety at the end of the experiment. We

also conducted a one-way (experimental condition: stereotype threat or control) between

groups analysis of variance (ANOVA) with working memory capacity as the dependent

variable.

The order of the second study was different to the first study in that working memory

was measured directly after the priming. In the first study, the mental arithmetic tasks were

completed before the working memory measure. Only the mental arithmetic tasks and the

modular arithmetic tasks were computed in the interactive condition and hence a one-way

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ANOVA was conducted for working memory capacity. Additionally, the current study

profiled participants in relation to their basic arithmetic skills, maths self-efficacy, maths

anxiety (trait), and working memory. A detailed correlational analysis was conducted to

explore the degree to which the individual differences correlated with mean modular

arithmetic performance (both low WM load and high WM load) in the interactive condition

and in the non-interactive condition. Finally, a mediation analysis (to confirm that a reduction

in working memory capacity would mediate the effect of stereotype threat on maths

performance) could not be conducted (to test hypothesis seven) because negative stereotyping

about the female students’ maths performance did not significantly affect participants’ mental

arithmetic performance and modular arithmetic performance.

3.7.2 Group Differences

Before the statistical analyses related to the hypotheses were completed, baseline

analyses were conducted. There were no group differences between the stereotype-threatened

participants and the participants in the control condition on the basic arithmetic skills that was

measured during the pre-testing phase, F < 1. The groups did not differ in their ability to

complete mental arithmetic tasks under timed conditions. Furthermore, there were no group

differences on the mathematics self-efficacy measure either, F(1, 92) = 3.27, p = .07, ŋp2

= .03. Finally, there were no group differences between the two experimental conditions

(stereotype threat or control) on the trait maths anxiety measure (F < 1) confirming that the

individuals did not differ on their pre-existing maths anxiety levels.

3.7.3 Percentage Correct (Mental Arithmetic Tasks)

To test the first, third, and fourth hypotheses, percentage correct (accuracy) of the

mental arithmetic tasks was examined. As predicted, participants were more accurate in the

interactive condition (M = 78.12%, SE = 3.50%) than in the non-interactive condition (M =

59.43%, SE = 3.50%). A summary of the descriptive statistics can be seen in Table 7 (pre-

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study) and Table 8 (post-study). A 2 (experimental condition: stereotype threat or control) x 2

(level of interactivity: interactive or non-interactive) between-groups analysis of covariance

(ANCOVA) was conducted and the scores from the basic arithmetic skills test (pre-test) were

used as a covariate. The covariate, basic arithmetic skills, was significantly related to the

percentage correct, F(1, 90) = 28.11, p < .001, ŋp2 = .24. The covariate (latencies) was not

significantly related to the percentage correct as F < 1. Confirming the first hypothesis, the

main effect of interactivity was significant, F(1, 90) = 16.81, p < .001, ŋp2 = .16. However, the

main effect of experimental condition (stereotype threat or control) was not significant, F < 1,

failing to confirm the third hypothesis. The interaction between the experimental condition

and the level of interactivity was not significant either, F < 1 which did not support the fourth

hypothesis.

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Table 7


M SD

Basic arithmetic skills 27.63 10.73

Maths self-efficacy 20.62 5.80

Maths anxiety (trait) 52.64 11.62

Note. Participants were not primed to complete the pre-testing tests. The pre-testing comprised of basic

arithmetic skills, mathematics self-efficacy, and mathematics anxiety (trait). The scale for basic arithmetic skills

is from 0 to 45. The scale for mathematics self-efficacy is from 0 to 35 and the scale for mathematics anxiety is

from 0 to 115.

Table 8

Descriptive Statistics: Means and Standard Errors (Post-Testing Data)

STI STNI NSTI NSTNI

Performance scores M SE M SE M SE M SE

Percentage correct (MAT) 74.12 3.60 64.21 3.40 78.12 3.50 59.43 3.50

Latencies (s) 30.93 2.13 30.62 1.92 31.14 2.02 31.32 2.02

Percentage correct (MA LL) 90.00 2.70 87.30 2.70 90.00 2.70 84.90 2.60

Latencies (s) 17.92 1.12 14.45 1.00 18.34 1.00 16.43 1.02

Percentage correct (MA HL) 78.00 2.90 72.70 2.90 81.70 2.80 69.00 2.80

Latencies (s) 26.63 1.82 18.94 1.74 26.03 1.84 23.24 1.83

Working memory N/A N/A 26.03 1.13 N/A N/A 25.22 1.12

Mathematics anxiety (state) 54.12 2.42 60.72 2.34 52.25 2.43 63.13 2.41

Note. STI = stereotype threat, interactive; STNI = stereotype threat, non-interactive; NSTI = non-stereotype

threat, interactive; NSTNI = non-stereotype threat, non-interactive. MAT = mental arithmetic tasks, MA LL =

modular arithmetic tasks, low load; MA HL = modular arithmetic tasks, high load.

The scale for working memory is from 0 to 56 and the scale for mathematics anxiety is from 0 to 115.

Working memory test was not completed in an interactive condition.

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3.7.4 Percentage Correct (Modular Arithmetic Tasks, Low WM Load)

To test the first, third and fourth hypotheses, percentage correct (accuracy) of the

modular arithmetic tasks (low WM load) was examined. Table 7 (pre-study) and Table 8

(post-study) display the descriptive statistics of the current study. As expected, the maths

performance was elevated with increased interactivity (M = 90.00%, SE = 2.70%) compared

with no interactivity (M = 84.90%, SE = 2.60%). A 2 (experimental condition: stereotype

threat or control) x 2 (level of interactivity: interactive or non-interactive) between-groups

analysis of covariance (ANCOVA) was conducted. The scores from the basic arithmetic

skills test (pre-test) were used as a covariate. The covariate, basic arithmetic skills, was

significantly related to the percentage correct, F(1, 90) = 17.00, p < .001, ŋp2 = .16.

Additionally, the covariate (latencies) was significantly related to the percentage correct, F(1,

90) = 5.53, p = .02, ŋp2 = .06. Confirming the first hypothesis, the main effect of interactivity

was statistically significant, F(1, 90) = 2.00, p = .02, ŋp2 = .02. There was no significant main

effect of experimental condition (stereotype threat or control), F < 1, failing to confirm the

third hypothesis. Additionally, the interaction between the experimental condition and the

degree of interactivity was not statistically significant, F < 1 which did not support the fourth

hypothesis.

3.7.5 Percentage Correct (Modular Arithmetic Tasks, High WM Load)

To test the first, third, and fourth hypotheses, percentage correct (accuracy) of the

modular arithmetic tasks (high WM load) was examined. The descriptive statistics can be

seen in Table 7 (pre-study) and Table 8 (post-study). Interactivity increased the accuracy of

the modular arithmetic tasks (M = 81.70%, SE = 2.80%) compared with the maths

performance in non-interactive condition (M = 69.00%, SE = 2.80%). A 2 (experimental

condition: stereotype threat or control) x 2 (level of interactivity: interactive or non-

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interactive) between-groups analysis of covariance (ANCOVA) was conducted. The scores

from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate was

significantly related to the percentage correct, F(1, 90) = 24.21, p < .001, ŋp2 = .15.

Additionally, the covariate (latencies) was significantly related to percentage correct, F(1, 90)

= 8.93, p = .004, ŋp2 = .09.Confirming the first hypothesis, the main effect of interactivity was

statistically significant F(1, 90) = 9.35, p = .003, ŋp2 = .09. The main effect of experimental

condition (stereotype threat or control) was not statistically significant, F < 1, failing to

confirm the third hypothesis. The interaction between the experimental condition and the

level of interactivity was not statistically significant, F(1, 90) = 1.78, p = .19, ŋp2 = .02 which

did not support the fourth hypothesis.

3.7.6 Latencies (Mental Arithmetic Tasks)

To test the second, third and fourth hypotheses, solution latency was examined. A 2

(experimental condition: stereotype threat or control) x 2 (level of interactivity: interactive or

non-interactive) between-groups analysis of covariance (ANCOVA) was conducted. The

descriptive statistics can be seen in the Table 7 (pre-study) and Table 8 (post-study). The

scores from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate

was significantly related to the latency to solution, F(1, 91) = 24.62, p < .001, ŋp2 = .21. The

main effect of interactivity was not statistically significant, F < 1 and it failed to confirm the

second hypothesis. The main effect of experimental condition (stereotype threat or control)

was not statistically significant either, F < 1, failing to support the third hypothesis.

Additionally, the interaction between the experimental condition and the level of interactivity

was not statistically significant, F < 1 which did not support the fourth hypothesis.

3.7.7 Latencies (Modular Arithmetic Tasks, Low WM Load)

To test the second, third, and fourth hypotheses, solution latency was examined. Table

7 (pre-study) and Table 8 (post-study) summarize the descriptive statistics. Interactivity

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slowed the participants down when completing the low WM load modular arithmetic tasks

(M = 18.34 s, SE = 1.00 s) compared with the latency to solution in the non-interactive

condition (M = 16.43 s, SE = 1.02 s). A 2 (experimental condition: stereotype threat or

control) x 2 (level of interactivity: interactive or non-interactive) between-groups analysis of

covariance (ANCOVA) was conducted and the scores from the basic arithmetic skills test

(pre-test) were used as a covariate. The basic arithmetic skills (covariate), was significantly

related to the latency to solution, F(1, 91) = 53.72, p < .001, ŋp2 = .37. Confirming the second

hypothesis, the main effect of interactivity was statistically significant F(1, 91) = 6.99, p

= .01, ŋp2 = .07. The main effect of experimental condition (stereotype threat or control) was

not significant, F < 1, failing to support the third hypothesis. The interaction between the

experimental condition and the level of interactivity was not significant either, F < 1 which

did not support the fourth hypothesis.

3.7.8 Latencies (Modular Arithmetic Tasks, High WM Load)

To test the second, third, and fourth hypotheses, latency to solution was examined for

the high WM load modular arithmetic tasks. The summary of the descriptive statistics can be

seen in the Table 7 (pre-study) and Table 8 (post-study). Interactivity slowed the participants

down when completing the high WM load modular arithmetic tasks (M = 26.03 s, SE = 1.84

s) compared with the latency in the non-interactive condition (M = 23.24 s, SE = 1.83 s). A 2

(experimental condition: stereotype threat or control) x 2 (level of interactivity: interactive or

non-interactive) between-groups analysis of covariance (ANCOVA) was conducted. The

scores from the basic arithmetic skills test (pre-test) were used as a covariate. The covariate,

basic arithmetic skills, was significantly related to the latency to solution, F(1, 91) = 14.12, p

< .001, ŋp2 = .13. Confirming the second hypothesis, the main effect of interactivity was

statistically significant F(1, 91) = 9.00, p = .003, ŋp2 = .09. The main effect of experimental

condition (stereotype threat or control) was not statistically significant, F < 1, failing to

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confirm the third hypothesis. Finally, the interaction between experimental condition and the

level of interactivity was not significant either, F < 1 which did not support the fourth

hypothesis.

3.7.9 Working Memory

To test hypothesis five, working memory capacity (computation span) was examined. Table 7

(pre-study) and Table 8 (post-study) summarize the descriptive statistics. A one-way

(experimental condition: stereotype threat or control) between-groups analysis of variance

(ANOVA) was conducted. The main effect of experimental condition was not significant, F <

1 which did not support the hypothesis five. Additionally, the main effect of interactivity was

not significant as F < 1. Finally, the interaction between experimental condition and level of

interactivity was not significant either as F < 1.

3.7.10 Maths Anxiety (State)

To test the seventh, eighth, and ninth hypotheses, maths anxiety levels after the

experimental session were examined. Table 7 (pre-study) and Table 8 (post-study) outline the

descriptive statistics of the current study. A 2 (experimental condition: stereotype threat or

control) x 2 (level of interactivity: interactive or non-interactive) between-groups analysis of

covariance (ANCOVA) was conducted and the scores from the maths anxiety (trait anxiety

that was measured during the pre-test) were used as a covariate. Maths anxiety (trait), the

covariate, was significantly related to maths anxiety (state), F(1, 91) = 65.23, p < .001, ŋp2

= .42. The participants who were in the interactive condition were less maths anxious (M =

52.25, SE = 2.43) than the participants in the control condition (M = 63.13, SE = 2.41).

Confirming the seventh hypothesis, the main effect of interactivity was statistically

significant F(1, 89) = 13.63, p < .001, ŋp2 = .13. The main effect of experimental condition

(stereotype threat or control) was not statistically significant, F < 1, failing to confirm the

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eigth hypothesis and the interaction between the experimental condition and the level of

interactivity was not not significant either, F < 1 which did not support the final hypothesis.

3.7.11 Individual Differences

We profiled participants in terms of their basic arithmetic skills (BAS), maths self-

efficacy, maths anxiety (trait), and working memory (measured with a computation-span).

Because half of the participants were conditioned to the stereotype threat condition during the

experimental session, their working memory data could not be used for the detailed

correlation analysis explained here. Therefore, only the data (basic arithmetic skills, maths

self-efficacy, state maths anxiety, and working memory) from the control group (n = 48) was

employed for this part of the analysis. Additionally, only the modular arithmetic tasks (both

low and high load) were part of the analysis. In line with previous research (Guthrie &

Vallée-Tourangeau, 2018), the measure of basic arithmetic skills (BAS) was correlated with

working memory capacity, r(96) = .54, p < .001. Additionally, there was a positive

correlation between maths self-efficacy and basic arithmetic skills (BAS), r(96)= .30, p = .04

confirming previous literature (e.g., Pajares & Graham, 1999). And as expected, maths self-

efficacy and maths anxiety (trait) were moderately correlated, r(96) = -.46, p < .001

confirming previous findings (e.g., Lee, 2009).

Of greater interest was the degree to which the individual differences correlated with

mean modular arithmetic performance (both low WM load and high WM load) in the

interactive condition and in the non-interactive condition. Correlational analyses indicated

that in the non-interactive condition, participants’ maths performance (accuracy) reflected

their arithmetic skill. Basic arithmetic skills (BAS) was a moderate predictor of modular

arithmetic performance for both the low WM load, r(96)= .48, p = .02 and high WM load,

r(96) = .39, p = .06 modular arithmetic performance. As expected, basic arithmetic skills

(BAS) was not correlated with the modular arithmetic performace in the interactive

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condition. Interactivity allowed the participant to externalize the internal cognitive process to

the outside world. The participant became more effective, was able to deal with more difficult

problems, and to compute more deeply and precisely.

In the non-interactive condition, participants’ latencies to solution reflected their basic

arithmetic skills and working memory capacity. Basic arithmetic skills (BAS) was a strong

predictor of low WM load latencies, r(96) = -. 63, p < .001 and a moderate predictor of high

WM load latencies, r(96) = -.40, p = .05. Additionally, working memory was moderately

correlated with low WM load latencies, r(96) = -.41, p = .05. However, only the basic

arithmetic skills (BAS) predicted the latencies in the low WM load, r(96) = -.56, p = .004 and

high WM load, r(96) = -.43, p = .04, in the interactive condition. These results suggest that

interactivity allowed working memory capacity to become augmented in the interactive

condition and therefore WM was not a predictor of latencies to solution any more.

When looking at maths anxiety (state) in the non-interactive condition, there was a

moderate correlation between maths self-efficacy and maths anxiety (trait), r(96) = -.56, p

= .005. Additionally, there was a strong positive correlation between the participant’s trait

maths anxiety levels (measured during the pre-testing phase) and the state maths anxiety

levels that were measured at the end of the experiment, r(96) = .71, p < .001. Level of maths

anxiety (state) was predicted by the level of maths self-efficacy and pre-existing maths

anxiety levels. However, this same pattern could not be found in the interactive condition

which suggested that interactivity offered the participant the opportunity to feel less maths

anxious (this same pattern has also been shown by Vallée-Tourangeau, 2013).

3.8 Discussion

The purpose of the current experiment was to investigate the effects of stereotype

threat on mental arithmetic performance and modular arithmetic performance (accuracies and

latency to solution), working memory, and maths anxiety. Additionally, the experiment

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investigated the role of distributed cognition in reducing the negative effects of stereotype

threat on maths performance, and on maths anxiety. It was hypothesised that the female

students would feel more state maths anxious after the situational manipulation of stereotype

threat. The intrusive thoughts and worry about being able to succeed with the required task

would consume valuable cognitive resources, and particularly working memory resources. It

was predicted that there would be a dual-task set up whereby the additional worry and the

cognitive task would compete for the same existing working memory resources. As

mentioned in the introduction, working memory is seen as a short-term memory system with

a limited capacity (Miyake & Shah, 1999) and therefore the combination of the additional

worries and task requirement would put pressure on the limited working memory resources.

Additionally, working memory capacity can be seen as the ability to focus one’s attention on

a given task while keeping task-irrelevant thoughts at bay (Engle, 2002). Hence, stereotype

threat might put an extra burden on the female participants’ cognitive resources, and on

working memory. Clearly, individuals with high working memory are better at suppressing

task-irrelevant information (e.g., stereotype threat priming) than individuals with low

working memory (Engle, 2002). Finally, the depleted working memory capacity, caused by

stereotype threat was predicted to have a causal role in reduced mental arithmetic

performance and modular arithmetic performance. Moreover, it was hypothesised that the

participants in the stereotype threat condition would feel more maths anxious (state) after the

experiment. However, it was predicted that allowing the participant to externalise the internal

cognitive process to come to the solution would reduce the negative effects of the stereotype

threat on maths anxiety.

Maths anxiety (state) measured after the experiment, confirmed that the participants

did not feel more worried or anxious about their maths abilities in the stereotype threat

condition. Maths anxiety (state) levels were not elevated and therefore there was no

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additional burden on working memory. The fact that working memory capacity was predicted

by the participant’s basic arithmetic skills rather than stereotype threat priming, is an

indicator that it was the level of the maths skill that contributed to working memory capacity

rather than the stereotype threat priming. The participants did not feel a threat because their

ability in maths was strong enough. There was no need for the participants to doubt their

abilities when in the stereotype threat condition.

Unlike the first study, this experiment failed to show reduced working memory

capacity in the stereotype threat condition. This is in contrast with Schmader and Johns

(2003) who showed that priming self-relevant negative stereotypes reduced women’s

(Experiment 1) and Latinx participants’ (Experiment 2) working memory capacity. In their

final study, it was confirmed that a reduction in working memory capacity mediated the

effect of stereotype threat on women’s maths performance (Schmader & Johns, 2003). In the

current study, the working memory capacity score was predicted by strong basic arithmetic

skills rather than by negative stereotyping about female maths performance, confirming a

previous finding by Guthrie and Vallée-Tourangeau (2018) where arithmetic skills were also

a predictor of working memory capacity (Guthrie & Vallée-Tourangeau, 2018). What is

more, the current study failed to show reduced maths performance (mental arithmetic and

modular arithmetic tasks) when stereotype threat was made salient. Clearly, there was no

causal link between reduced working memory capacity and reduced maths performance.

However, it was confirmed that interactivity elevated maths performance (accuracy)

when stereotype threat was not present (control condition) confirming previous research (e.g.,

Guthrie & Vallée-Tourangeau, 2018; Vallée-Tourangeau, 2013). Additionally, as predicted

maths anxiety (state) was reduced for participants who were allowed to externalize their

internal cognitive process, by using pen and paper (interactive condition). The dual task set

up (maths anxiety and task requirement) did not exist anymore. The agent did not need to

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fight for the same working memory resources; the increased interactivity had provided the

additional cognitive resource. Previous studies have shown that working memory is

negatively associated with maths anxiety (Ashcraft & Kirk, 2001). Vallée-Tourangeau and

his colleagues have concluded that interactivity improves mental arithmetic performance in

maths anxious participants (Allen & Vallée-Tourangeau, 2016; Vallée-Tourangeau et al.,

2016). However, the Vallée-Tourangeau studies have only looked at trait maths anxiety. The

current study explained here has measured state maths anxiety after the experimental session

and has shown reduced maths anxiety in the interactive condition (without stereotype threat).

To our knowledge, this is the first study that has measured maths anxiety (state), after

allowing the participants to complete the maths tasks in an interactive setting.

3.9 Limitations

Whilst the findings of this study are encouraging, the research reported here has some

limitations to it. The findings in this report are subject to at least two limitations. First,

examination of the wording of the control condition (when the control participants were told

that the experiment measured their working memory capacity) suggests that it may not have

functioned as a neutral control condition as planned. Instead, the control condition might

have been primed for performance-approach goals and to the idea that working memory is

fixed (Dweck, 1986) rather than being a true control. Endorsing an entity theory of

intelligence can lead to performance-approach goals. Indeed, this might serve as an

alternative explanation for the lack of a significant difference in maths performance between

the two conditions (stereotype threat or control). Second, the study lacks external validity as

it was conducted in a lab-based setting rather than in a more applied context (e.g., in an

educational setting) in which mental arithmetic tasks are regularly computed.

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3.10 Future Studies

To sum up, Study 1 and 2 reported that girls’ maths performance was not depleted

with negative stereotyping compared to a control condition. However, because the control

condition might have primed performance-approach goals, achievement goals were examined

in more detail in the final two studies (Studies 3 and 4). Additionally, it would be of interest

to investigate whether distributed cognition could be used as an innovative way of reducing

the negative effects of evaluative pressure caused by the achievement goals.

Chapter 4: Achievement Goals and Mental Arithmetic: The Role of Interactivity

Findings from Study 1 and 2 of this programme of research indicated that stereotype

threat about women’s maths performance did not negatively affect their academic

performance. Participants’ mental arithmetic performance did not suffer while the

participants were primed with negative stereotypes pertaining to women’s maths ability.

Studies 1 and 2 failed to find any statistically significant differences in the mental arithmetic

performance between the stereotype threat condition and the control group. However, in the

first study, working memory capacity was reduced with stereotype threat about girls’ maths

performance, but this had no effect on mental arithmetic performance. Consistent with this

view, Pennington et al., (2018) also reported that stereotype threat did not impair women’s

inhibitory control or mathematical performance. Given no negative effects of stereotype

threat on mental arithmetic performance in Studies 1 and 2 of this thesis, there were no

benefits of using distributed cognition when stereotype threat had been made salient either.

One reason that women in the stereotype threat may not have seen decrements in

performance compared to those in the control condition is that the control condition may have

inadvertently primed performance goals. Similar to stereotype threat, achievement goals, and

performance-approach goals in particular, can have detrimental effects on the existing

working memory resources (due to worries about outperforming others), (Crouzevialle &

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Butera, 2013). If performance-approach goals and the distractive thoughts of performing

better than others handicaps working memory resources, then interactivity could be used as

an innovative way of mitigating these negative effects. The aim of the present study was to

further understand how mastery-approach goal and performance-approach goal engage

working memory resources, and whether distributed cognition (e.g., use of pen and paper)

could be used to defuse any of the negative effects of performance-approach goals on maths

performance. Additionally, we wanted to further our understanding whether the mastery-

approach goal individuals would benefit in externalising internal cognitive processes. The

current study (Study 3) acted as a Pilot Study to Study 4 to further investigate whether there

were any detrimental effects of performance-approach goals on maths performance. The

study only focused on maths performance and did not have any additional measurements. The

sample size for this study was small (41 participants) as the main purpose of the study was to

see that whether there was an effect of achievement goals on maths performance and whether

interactivity could be used to alleviate the possible negative effects before investigating with

a bigger sample.

4.1.1 Achievement Goals

Achievement goals reflect the aim of an individual’s achievement pursuits. They are

frameworks that can help to understand how individuals react to various achievement

situations (Poortvliet & Darnon, 2010). There is a wealth of research on achievement goals

and their effects on academic performance. However, much less is known about the effects

on working memory. The present study examined how motivational approach goals

differentially impact upon working memory capacity. Additionally, we studied the role of

distributed cognition in relation to achievement goals (mastery-approach goal and

performance-approach goal) and maths performance.

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4.1.2 Mastery-Approach Goals and Performance-Approach Goals

There is a widely supported conceptualisation of achievement goals that distinguishes

between mastery-approach goals where the individual is aiming for knowledge acquisition

and task mastery and performance-approach goals where demonstrating competence in the

subject field and aiming for outperforming others is the main goal (Crouzevialle & Butera,

2017). When individuals focus on performance, they strive to look good in front of peers.

Due to the focus of outperforming others rather than concentrating on the actual learning

process and knowledge acquisition, there are behavioural patterns individuals follow when

they are focused on performance goals in order to reach their academic targets. When

pursuing performance-approach goals, individuals listen to the cues about the future

academic assignments and adjust their learning based on these cues. Students’ academic

achievements are higher when focusing on areas that are deemed important by the teacher

and tested as part of the curriculum (Broekkamp et al., 2007). Additionally, students focusing

on performance concentrate on memorisation rather than elaboration and knowledge

construction of the topic (Entwistle, 1988). Unfortunately, this type of exam preparation can

lead to surface learning and rote learning (Harackiewicz & Linnenbrink, 2005).

Normative comparisons allow the individual to compete with people around them and

to outperform others doing similar tasks. Additionally, the individual focusing on

performance has outcome goals that are focused on attaining a positive outcomes in the form

of good exam grades (Grant & Dweck, 2003). However, striving for academic success and

the worry to rise above others might cause elevated feelings of pressure (Crouzevialle &

Butera, 2013). Pressure can create mental distractions that compete for existing working

memory resources. Additionally, the pressure can reduce working memory capacity that

would normally be allocated to skill execution (Beilock & Carr, 2005). Hence, the

programme of research reported here is focusing on performance-approach goals only (with

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mastery approach-goals functioning as a comparison group). If there is additional taxation on

the working memory, then it is the individuals who are pursuing performance-approach goals

who would benefit from combining the internal and external cognitive resources.

4.1.3 Achievement Goals and Modular Arithmetic Tasks

We utilised modular arithmetic tasks as our testbed. Modular arithmetic tasks [e.g., 52

≡ 16 (mod 8)] involve judging mathematical equations’ true value. When the answer to the

equation is a whole number, the answer to the problem is true. Clearly, these equations can be

computed in different ways with varying levels of working memory taxation. Whilst these

tasks can be computed by executing working memory demanding procedures [e.g., (52 –

16)/8 = true or false] there are also less working memory resource demanding shortcuts that

can be employed. It could be assumed that modular arithmetic problems employing even

numbers are true because dividing two even numbers is not normally associated with

remainders and the purpose of the MA tasks is to judge whether the answer is a whole

number or not (i.e., no remainders). On the contrary, when dividing two numbers of different

parity, it is more likely that there are reminders, and therefore the answer would be false. It is

possible that even numbers can produce the correct answer [e.g., 34 ≡ 18 (mod 8)] in some

cases but not always [e.g., 52 ≡ 16 (mod 8)], (Beilock, 2008). The pursuit of performance-

approach goals allows for a more implicit way of dealing with the modular arithmetic tasks.

One the contrary, the mastery-focused individual focuses on the explicit processing of the

tasks that are more resource demanding rather than using quick shortcuts to come to the

solution (Avery et al., 2013).

4.1.4 Achievement Goals and Working Memory

Performance-approach goals may produce distraction and therefore have negative

consequences on task focus and performance. The concerns about competition and peer

comparisons of the more performance-focused goal can distract individuals from the task

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focus (Brophy, 2005). Beilock, Holt, Kulp and Carr, (2004) tested this in a laboratory setting,

under either low or high evaluative pressure. The study concluded that the high-pressure

scenario taxed a large part of the working memory resources and as a consequence there was

a performance decrement for the most demanding maths problems (high WM load tasks)

compared with the low WM load tasks (Beilock et al., 2004). Similar findings have been

made by Crouzevialle and Butera (2013) whose results revealed that there was impaired

maths performance in the performance-approach goal environment. As before, this reduced

maths performance could only be observed with the highly demanding problems.

Performance-approach goals distract participants from full engagement of the task

(Crouzevialle & Butera, 2013). Additionally, the pressure to perform better than others

consumes the verbal resources of the working memory. It is like an inner language that is

focused on concerns about the evaluative situation and which in turn impairs the overall

cognitive performance (Decaro, Rotar, Kendra, & Beilock, 2010.) This is like a dual-task set-

up where the distractive thoughts and task execution compete for the same working memory

resources. Additionally, Avery and Smillie (2013) examined the influence of achievement

goal pursuits on working memory with varying levels of executive load. Under the high

executive load, there was poorer working memory processing during the performance-

approach goal than when mastery-approach goal or a no-goal control were used (Avery &

Smillie, 2013).

4.1.5 The Benefits of Interactivity

Interacting with external representations elevates and transforms thinking and

mathematical problem solving. Internal cognitive processes go to wherever they are more

cost effective. In other words, if an agent has a pen and paper available and if the sentence is

complex enough, it might be more beneficial to draw a picture of the information held

internally in the head which might in turn reduce the overall cognitive cost of the sense

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making (Kirsh, 2010). Additionally, by creating these external structures, individuals can

compute more efficiently, and create forms that allow the individual to share their internal

thoughts (Kirsh, 2010).

However, there are factors that can determine whether the reshaping of the physical

environment in problem solving is beneficial. The experience of the reasoner and cognitive

abilities of the individual determine the possible benefits of the external manipulation. Webb

and Vallée-Tourangeau (2009) explored this further with an interactive word production task

with dyslexic children (with less efficient working memory abilities) and typically

developing children (aged between 9 and 11 years). The children were asked to create words

from two different word tiles (with a varying difficulty: difficult and easy) in an interactive

condition (where the children were allowed to touch the tiles and physically manipulate

them) and in a non-interactive condition (where the manipulation of tiles was not allowed).

By allowing physical interaction with the tiles the dyslexic children were able to enhance

word production with the easy set of word tiles but not with the more difficult set. However,

typically developing children did not benefit from the external manipulation of the tiles to

produce words. Instead, there was a performance drop with the easy letter set when

interactivity was employed. Thus, the effectiveness of the physical problem space is relative

to the level of task difficulty as well as the cognitive abilities of the reasoner (Webb &

Vallée-Tourangeau, 2009).

In another word production study, participants were required to generate words with

any length (with seven different letter sets) for a period of 5 minutes. The experiment allowed

the hands group to manipulate the tiles (interactive condition) and in the non-hands group

(non-interactive condition) this externalisation of internal cognitive process was not

employed. When a word was generated the participant said the word and then spelled it. The

experimenter then wrote down the answer. The word production performance was different

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for participants who were classified as either low or high fluency group (measured by their

performance on the Thurstone word fluency test). For the high-fluency group, there were few

benefits of restructuring the external environment to produce the words. The individuals had

the cognitive abilities to deal with the demands of the task. However, for the low-fluency

group interactivity significantly enhanced the word production. The task was more working

memory resource taxing and by the external manipulation of the word sets, enhancement of

the performance was achieved (Vallée -Tourangeau & Wrightman, 2010)

4.2 Present Study (Pilot Study to Study 4)

The aim of the experiment reported here was to further examine the influence of

achievement goal states on working memory and whether interactivity could be used to

mitigate any of the possible negative effects of achievement goals on maths performance. If

the working memory is loaded due to outcome related worry then there is additional taxation

on working memory (Crouzevialle & Butera, 2013). Together with the horizontally presented

maths problems (modular arithmetic tasks) there can be maths performance decrements when

in the performance-approach goal condition (Beilock, 2008). We reasoned that, if worries of

outperforming others lead to poor maths performance, then giving students the opportunity to

externalize the internal cognitive process would reduce internal working memory demands

and enhance task performance. Additionally, if the working memory capacity of individual

with a mastery-approach goal is unaffected by the lack of distractive thoughts, there might be

little benefits to manipulate the external world.

4.2.1 Hypotheses of the Study

Based on the findings of the first two studies of this programme of research, the first

hypothesis for the current study (Hypothesis 1) was that externalising the internal cognitive

process to the outside world would enhance accuracy of the modular arithmetic tasks. The

second hypothesis (Hypothesis 2) stated that interactivity would increase the solution

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latencies (allowing the participant to complete the tasks slower) for the modular arithmetic

tasks as per findings of the Study 2.

Additionally, we predicted that the participants of the mastery-approach goal

condition would have higher maths performance (higher accuracy) than the participants in the

performance-approach goal condition (Hypothesis 3). And at the same time, the maths

performance of the individuals in the performance-approach goal condition was expected to

suffer (Hypothesis 4). It has been suggested that there are less worries in the mastery-

approach goal environment and therefore the working memory of the individual is not as

heavily taxed as when performance-goal has been made salient (Crouzevialle & Butera,

2013). However, these performance decrements of the performance-focused individuals were

expected to be alleviated with the help of external artefacts (e.g., using pen and paper),

(Hypothesis 5) as per existing empirical findings (Vallée-Tourangeau, 2013).

Additionally, it was predicted that the individuals in the mastery-approach goal

condition would not benefit from interactivity due to less taxation of the working memory. In

fact, it was predicted that their performance would be poorer when they were allowed to use

pen and paper to come to the solution than when they were not (Hypothesis 6). If an

individual has the cognitive abilities or resources (e.g., working memory) to complete the

task, interactivity can cause a performance drop (Vallée-Tourangeau & Wrightman, 2010;

Webb & Vallée-Tourangeau, 2009). If there are less distractive thoughts in the mastery-

approach goal environment, then there is more capacity available for the task in hand

(Crouzevialle & Butera, 2013). Hence, interactivity might not bring the same benefits to the

mastery-focused participant as to the performance-focused participant.

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4.3 Method

4.3.1 Participants

Forty-one female undergraduate psychology students (M = 21.88, SD = 3.90)

participated in this study for exchange of SONA credits. After consenting to participate in the

study, subjects were randomly assigned to one of the experimental conditions. The

participants were tested individually in a psychology lab, at the University of Surrey (UK).


Arithmetic task. There were two blocks of 24 modular arithmetic tasks that relied

heavily on working memory resources, adapted from Beilock and Carr (2005). The task

comprised of high WM load tasks only. As mentioned before, the purpose of the tasks is to

judge the validity of maths problems like [61 ≡ 18 (mod 4)]. The middle number is subtracted

from the first number (i.e., 61-18) and then the difference is divided by 4. If the answer is a

whole number the maths problem is true (Beilock & Carr, 2005). Modular arithmetic tasks as

laboratory tasks are advantageous because most students have not seen them before and

therefore previous task experience is controlled. Additionally, the performance is not

proceduralized and therefore working memory resources are required to assist in solving the

tasks.

High-demand problems [e.g., 42 ≡ 27 (mod 3)] requiring a double-digit subtraction

operation were used because they required borrowing, resulting in using more working

memory resources. Half of the maths problems required a true response by the participant.

The order of the questions was randomized and each question was asked only once. The

original tasks used by Beilock and Carr (2005) were a mixture of high demand problems

(two-digit numbers requiring borrowing) and low-load questions (single-digit numbers,

without borrowing), (Figure 1). The study reported here utilised the high-demand problems

only because of limited benefits of employing interactivity with low-demand tasks.

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Figure 1. Examples of low-load and high-load modular arithmetic tasks. This figure is

adapted from (Beilock, 2008).

The modular arithmetic tasks were presented in a horizontal format as opposed to a

vertical format (also called column subtraction), (Figure 2). The horizontal presentation of the

maths problems is more reliant on phonological resources (the verbal resources) because

individuals maintain the required problem steps (e.g., interim totals) in their memory verbally

(DeStefano & LeFevre, 2004). In the case of modular arithmetic tasks, the possible worries of

performing better than others places much heavier demands on working memory

(phonological loop, in particular).

Figure 2. Examples of vertical and horizontal modular arithmetic problems. This figure is


Experimental manipulations. Participants were informed after completing the

baseline block of modular arithmetic tasks (24) that they were required to complete a second

block (24) of modular arithmetic tasks; this time their performance would be recorded. The

participants in the performance-approach goal condition read the following instructions

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Vertical MA tasks: 52

≡ 24 (mod 3)

Horizontal MA tasks:52 ≡ 24 (mod 3)

Low-load tasks:9 ≡ 3 (mod 2)

High-load tasks:52 ≡ 24 (mod 3)

before starting the task that were aimed at activating performance-approach goals based on

previous research:

During the recorded part of the task, the experimenters will assess your performance.

It is important for you to be proficient, to perform well and obtain a high score, in

order to demonstrate your competence. You should know that a lot of students will do

this task. You are asked to keep in mind that you should try to distinguish yourself

positively, that is, to perform better than majority of students. In other words, what we

ask you here is to show your competencies, your abilities. (Darnon, Harackiewicz,

Butera, Mugny, & Quiamzade, 2007, p. 816 )

The participants in the mastery-approach goal condition read instructions that were

designed to activate mastery-approach goals. There was no social comparison and the

instructions were aimed to create task interest. Additionally, there was no mention of scores

or task performance:

In previous research, we have observed that practice of the arithmetic task you are

solving right now has benefits to cognitive functioning and leads to a progressive

improvement of mental processes. Hence, this task solving can be proven to be

beneficial in the long-term. It is however necessary that you focus your attention on

calculation mastery, so as to quickly and accurately solve each problem, in order to

experience these benefits. Try to master this task as much as you can; keep in mind its

practice can be beneficial to you. (Crouzevialle et al., 2015, p. 7 )

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Interactivity. The participants in the interactive condition were allowed to use pen

and paper while computing the mental arithmetic tasks. When using the pen and paper the

participants first worked out the answers on the paper and then transferred the answers to

Qualtrics. The participants in the non-interactive condition were not allowed to use any

external artefacts to come to the solution. They answered all the questions directly in

Qualtrics.

4.3.3 Procedure

Participants were tested individually in a testing laboratory (School of Psychology) at

the University of Surrey. The experimenter remained in the testing room across all of the

experimental conditions. After consenting to participate in the study, participants were

randomly assigned to one of the experimental conditions (performance-approach goal or

mastery-approach goal crossed with interactivity or no interactivity). There was a short

training session consisting of two modular arithmetic tasks before starting the first block. The

first block of questions (24) functioned as a baseline and the performance (accuracy and

latencies) was recorded in Qualtrics. However, the participants were told that it was a training

block, and that their performance was not recorded to avoid any achievement goal activation.

Before starting the second block, the participants were told that their performance was

recorded this time. The priming of the participants was done between the training block and

actual block of maths tasks. The order of the maths tasks was counterbalanced in both blocks.

Finally, the participants were briefed and thanked for their participation at the end.

The current study had two primary dependent variables: accuracy of the tasks and

solution latency (in seconds). Accuracy of the participants was measured during the first

block and second block (percentage correct) and a difference score (B2 – B1) was calculated.

The accuracy of the maths tasks was assessed with the help of Qualtrics where the modular

arithmetic tasks were computed by both the interactive and non-interactive participants. This

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allowed us to record accuracy and time to complete the required tasks. Latency to solution

was calculated based on the page submit function of Qualtrics (the time from first click to the

time of the final click). Additionally, solution latency (with the help of a difference score, B2

– B1 solution latency) also functioned as a covariate when the primary statistical analysis was

being conducted. Studies 3 and 4 are based on the same study design as the original paper by

Crouzevialle and Butera (2013) and therefore the solution latencies were only used as

covariates in these studies, rather than dependent variables.

4.4 Results


To investigate the hypotheses, two separate 2 (instruction: performance-approach goal

or mastery-approach goal) x 2 (level of interactivity: interactivity or control) between-groups

analysis of covariance (ANCOVA) were conducted with percentage correct (accuracies) and

latencies, as primary dependent variables. Accuracy difference score was calculated by

subtracting the modular arithmetic performance of block 1 from block 2. Furthermore, a

difference score in latencies was used as a covariate to avoid any speed-accuracy trade-offs

for the participants.


Before concentrating on the actual performance measures of the study, it was

concluded that there were no group differences between the participants in the mastery-

approach goal condition and performance-approach goal condition on the baseline modular

arithmetic performance (block 1), F(1, 36) = .08, p = .78, ŋp2 = .002 confirming that the

groups did not differ in their ability to complete the modular arithmetic tasks. Additionally,

there were no group differences on the baseline (block 1) latencies to solution either, F(1, 36)

= .17, p = .69, ŋp2 = .004 confirming that the participants did not vary in their speed to

complete the modular arithmetic tasks, during the baseline assessment.

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Table 9 summarises the descriptive statistics and standard errors of modular

arithmetic performance in block 1. Table 10 is a summary of the mean accuracies for block 2

(only in the interactive condition, for comparison). Table 11 is a summary of descriptive

statistics for block 2 across the different experimental conditions.

Table 9

Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracy

and Latencies to Solution) in Block 1

Interactive Non-Interactive

M SE M SE

Accuracy (%) 91.62 2.20 82.83 2.20

Latency (seconds) 14.33 1.11 15.13 1.10

Note. There was no priming of achievement goals (mastery-approach goal or performance-approach goal) in

block 1. Participants completed the modular arithmetic tasks in interactive or non-interactive condition only.

Table 10


and Latencies to Solution) in Block 2 (Interactive Condition)


M SE M SE

Accuracy (%) 87.43 2.20 82.34 2.20

Latency (seconds) 12.82 0.86 13.16 0.84

Note. This is the interactive condition only in order to get a comparison with block 1.

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Table 11

Descriptive Statistics and Standard Errors of Modular Arithmetic Performance (Accuracies


PAG-INT PAG-NI MAG-INT MAG-NI

n = 10 n = 12 n = 9 n = 10

M SE M SE M SE M SE

Accuracy (%) 85.93 3.20 74.74 3.20 88.92 3.20 90.02 3.10

Latency (seconds) 13.22 1.21 12.33 1.21 12.56 1.21 14.03 1.16

Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance- approach goal without

interactivity; MAG-INT = mastery-approach goal with interactivity; MAG-NI = mastery-approach goal with no

interactivity. Priming of achievement goals was utilised during block 2. Participants were also in either

interactive or non-interactive condition.

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4.4.3 Accuracy

Our main performance measure was accuracy of the modular arithmetic tasks (high

WM load). Accuracy difference score was calculated by subtracting the modular arithmetic

performance of block 1 from block 2 (B2 - B1). Furthermore, a difference score in latencies

was used as a covariate in order to avoid any speed-accuracy trade-off of the participants.

A 2 (instruction: performance-approach goal or mastery-approach goal) x 2 (level of

interactivity: interactivity or control) between-groups analysis of covariance (ANCOVA) was

conducted. The covariate (difference score in latencies) was significantly related to the

modular arithmetic accuracy, F(1, 36) = 5.76, p =.02, ŋp2 = .14. There was no statistically

significant main effect of interactivity as interactivity did not improve the overall modular

arithmetic performance, F(1, 36) = 1.13, p = .30, ŋp2 = .03 which failed to support the first

hypothesis.

There was a main effect of instruction (mastery-approach goal or performance-

approach goal), F(1, 36) = 9.70, p = .004, ŋp2 = .21 . As we had anticipated, the modular

arithmetic performance (accuracy difference score, S2 – S1) of the mastery-approach goal

participants was higher (M = 1.53, SE = 1.72) than the performance-approach goal

participants’ performance (M = -6.16, SE = 1.76), (Figure 4), confirming the third and fourth

hypotheses.

Additionally, there was a statistically significant interaction of interactivity and

instruction on problems solved correctly, F(1, 36) = 4.39, p = .043, ŋp2 = .11. As expected, the

participants in the mastery-approach goal condition performed better (M = 5.44, SE = 2.38)

than performance-focused participants (M = -7.43, SE = 2.50) when interactivity was not

used (Figure 3) confirming the third hypothesis, F(1, 18) = 11.08, p = .004, ŋp2 = .38.

Additionally, the individuals in the mastery-approach goal condition had a performance drop

in the interactive condition (M = -2.37, SE = 2.50) compared with their performance in the

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non-interactive condition (M = 5.44, SE = 2.38) (Figure 3), confirming the sixth hypothesis,

F(1, 18) = 4.90, p = .04, ŋp2 = .21 (Table 12).

Table 12

Descriptive Statistics and Standard Errors of Modular Arithmetic Performance Difference

(B2 - B1) across the Experimental Conditions

PAG-INT PAG-NI MAG-INT MAG-NI

M SE M SE M SE M SE

Accuracy (%) -4.89 -2.50 -7.43 -2.50 -2.37 -2.50 5.44 2.38

Latency (seconds) -1.26 -0.90 -2.02 -0.90 -1.61 -0.90 -1.99 -0.85

Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance- approach goal without

interactivity; MAG-INT = mastery-approach goal with interactivity; MAG-NI = mastery-approach goal with no

interactivity.


-10

-8

-6

-4

-2

0

2

4

6

8

-4.89

-7.43

-2.37

5.44

Interactivity x Instruction (Accuracy Difference Score, B2 - B1)

Performance-Approach Goal Mastery-Approach Goal

Mod

ular

Arit

hmet

ic P

erfo

rman

ce (%

)

Figure 3. Mean difference in modular arithmetic performance (%) as a function of


interactivity or control).

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-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

-6.16

1.53

Instruction (Accuracy Difference Score, B2 - B1)M

odul

ar A

rithm

etic

Per

form

ance

(%)


experimental condition (performance-approach goal or mastery-approach goal).

4.4.4 Latencies

Our second dependent variable was solution latency as part of the overall maths

performance of the modular arithmetic tasks. As before, a difference score was calculated by

subtracting the solution latency of block 1 from block 2 (B2 - B1). A 2 (instruction:

performance-approach goal or mastery-approach goal) x 2 (level of interactivity: interactivity

or control) between-groups analysis of variance (ANOVA) was conducted. There was no

main effect of instruction (mastery-approach goal or performance-approach goal) as F < 1,

failing to support the third and fourth hypotheses set in the beginning. Additionally, there was

no main effect of interactivity on the time it took for the participants to complete the task (F

< 1) which did not support the second hypothesis. Additionally, there was no two-way

interaction of instruction and interactivity (F < 1) which did not support the fifth and sixth

hypotheses that were set in the beginning. It is important to mention here that solution latency

(difference score, B2 - B1) was used as a covariate when the accuracy of maths tasks was

computed as part of the main statistical analysis.

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4.5 Discussion

The current study examined how motivational approach goals differentially impact

upon working memory resources. Additionally, the study aimed to further investigate how

interactivity influenced the effects of achievement goals on modular arithmetic performance.

We wanted to find out whether the detrimental effects of performance-approach goals on

academic performance could be alleviated with the help of distributed cognition and whether

there would be benefits in utilising distributed cognition for the mastery-focused individual.

The provision of a performance-approach goal reduced the modular arithmetic performance

compared to the mastery-approach group. Additionally, mastery-focused individuals suffered

a larger decrement than the performance-focused individuals in their modular arithmetic

performance when the participants were allowed to interact with external resources (with the

use of pen and paper).

There were no significant main effects of interactivity when looking at the modular

arithmetic performance of the current study, failing to support Hypothesis 1 and 2. Similar

findings have been reported in the Vallée-Tourangeau (2013) study where distributed

cognition allowed elevated performance only for the longer sums (11 single-digit numbers)

but not for the shorter sums (7 single-digit numbers). Participants performed marginally

better when they only relied on their internal cognitive resources. The degree to which the

design of an extended cognitive system can elevate cognitive performance is clearly relative

to the actual degree of task difficulty. With shorter sums, participants did not feel the need to

externalise the internal cognitive process as they were more efficient when relying on their

own internal cognitive resources and working memory. There was less effort required to

complete the task in the head alone (Vallée-Tourangeau, 2013). Similarly, the modular

arithmetic tasks of the current study were easy enough to be completed in the head alone and

there were no benefits to externalising this process.

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Earlier on, Study 1 of this PhD thesis reported a statistically significant main effect of

interactivity on modular arithmetic performance. The modular arithmetic tasks used in Study

1 had a higher level of difficulty; the numbers used were either double-digit or triple-digit

numbers and like the present study the tasks were presented in a horizontal format.

Distributed cognition allowed the participants to reach higher accuracy and efficiency.

However, there were no effects of stereotype threat on the maths performance but

interactivity allowed the participants to increase modular arithmetic performance.

We found that when women were primed into a performance-approach goal, there

was a drop in the mental arithmetic performance compared to a mastery-approach goal,

confirming the fourth hypothesis. One explanation for these findings was that when the

mastery-focused individuals showed higher mental arithmetic performance (confirming the

third hypothesis), it was assumed that these differences were related to the lack of the

outcome related anxiety confirming existing findings by Crouzevialle and Butera (2013).

Mastery-focused learning allows the individual to focus on their own learning and not

compare their academic performance to others. Hence, the lack of performance-based anxiety

may allow the participant to have higher mental arithmetic performance. Previous research

has suggested that the anxiety of outperforming others can tax working memory. Together

with the high-load working memory tasks, working memory resources may be further

compromised by performance-focused goals (Crouzevialle & Butera, 2013). Additionally,

under high working memory load, when a performance-approach goal has been made salient,

there is poorer working memory processing than in the mastery-approach goal environment

or when there is no go-goal control, leading to a performance drop (Avery & Smillie, 2013).

Another explanation for the reduced maths performance of the performance-focused

individual might be due to the implicit processing that is less working memory resource

demanding of the modular arithmetic tasks (Avery & Smillie, 2013). Perhaps there is more

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working memory capacity available to deal with the distractive thoughts which reduce task

focus and overall cognitive performance. Additionally, the mastery-focused individuals may

rely more on the WM resources due to explicit processing (deeper level of processing),

(Avery et al., 2013) and therefore their cognitive performance might deteriorate. However,

the current findings run contrary to the existing findings by Avery et al., (2013). The mastery-

approach goal participants’ maths performance in the present study was higher than the

performance-approach goal individuals and therefore does not support the findings of Avery

et al., 2013.

Interactivity did not allow any augmented maths performance for the participants in

the mastery-approach goal condition, confirming the final hypothesis (Hypothesis 6). On the

contrary, the maths performance of the mastery-approach goal participants was lower with

the use of pen and paper compared to when they did not use interactivity (control). This

finding suggests that there was a limited need to extend the current working memory

resources of the mastery-focused individual. It was assumed that their working memory

resources were not compromised due to the outcome related distractive thoughts or anxiety.

As mastery-focused individuals do not tend to worry about other people’s academic

performance and only focus on the benefits of their own learning, working memory is not as

heavily taxed as performance-focused individuals’ working memory. In other words, there is

no dual-task set-up for the mastery-focused individual. Interactivity may allow the agent to

extend their working memory resources when there is a need for this. Similarly, in another

study, dyslexic children (aged between 9 – 11 years) benefited the most from rearranging the

letter tiles (interactive condition) in a word production task. By reshaping the physical

presentation of the letters, their less efficient working memory capabilities could be

compensated. The control group (typically developing children) did not benefit from

externalising the internal cognitive process. In fact, their performance was poorer (with the

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easy set of letters) when they manipulated the tiles to produce words than when they did not

(Webb & Vallée-Tourangeau, 2009).

Finally, the study reported here used high WM load tasks only to see the possible

benefits of employing distributed cognition. The high-load tasks require the participant to

rely heavily on working memory resources to compute the task. There are computational

steps that need to be recalled (subtraction and division) and interim totals that require storing

in the working memory in order to compute the task efficiently. In the original Beilock and

Carr (2005) study, a mixture of low-load and high-load tasks were used to see the effects on

the cognitive performance, and in particular on working memory. Their study concluded that

the performance of the high-load tasks deteriorated if there were feelings of evaluative

pressure caused by situation-laden environments (e.g., stereotype threat) while working on

the required tasks. Similarly, the current study found that the performance-focused

individuals’ performance was lower in the non-interactive condition than in the interactive

condition.

4.6 Limitations of the Study

Whilst the findings of this study are encouraging, there are various limitations. The

current study only looked at the effects of distributed cognition on mental arithmetic

performance in relation to two different achievement goals. It could be argued that it is

actually the performance-avoidance goal that is more taxing on working memory due anxious

thoughts about not being able to complete the task in hand (Avery & Smillie, 2013). Whilst

the study reported here talked about increasing levels of anxiety of the performance-focused

students, there were no anxiety measures taken to show that performance goal individuals felt

more anxious, and that their working memory resources were taxed by this additional worry.

The current study has utilised existing empirical findings in this field. There was also no

measurement of working memory resources in the beginning of the study to show that the

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groups did not differ in their levels of working memory capacity measured before the priming

of the candidates.

Additionally, this study did not utilise any manipulation checks to make sure that the

priming of the achievement goals worked the way that they had been designed to work,

lacking internal validity. The present experiment, only utilised the statistical evidence to

demonstrate the findings of the study. Finally, the priming of the performance-approach goal

could be misunderstood as a performance-avoidance goal but as there were no manipulation

checks in place, this could not be investigated further.

4.7 Future Studies

Future studies would benefit in measuring maths anxiety of the participants both

before the experiment (trait maths anxiety) and after (state maths anxiety). If maths anxiety is

elevated when performance-approach goals are made salient then there should be more

benefits of externalizing the internal cognitive process to the outside world (interactivity) for

the performance-focused individual. Interactivity allows the agent to extend their working

memory capacity by allowing the use of external artefacts (e.g., pen and paper). It would also

be of interest to further understand the positive and negative effects that the participants

might experience after being allowed to use interactivity to compute the modular arithmetic

tasks. Interestingly, not all of the participants make use of the external artefacts; some of the

students compute the tasks without the help of a pen and paper. Hence, it could be argued that

even the thought of knowing that the option of writing things down (if needed to) could make

the participants feel more positive, and that on its own might help to improve the maths

performance. Future studies would also benefit in measuring basic arithmetic skills, and

working memory as an individual difference measurement to see that what generally drives

modular arithmetic performance, and to show that there are no group differences in the levels

of arithmetic skills and working memory.

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Chapter 5: Achievement Goals, Maths Performance, and Interactivity

The previous study of this PhD thesis (Study 3) found that the maths performance of

the participants in a mastery-approach goal condition was higher than that of individuals in a

performance-approach goal condition when interactivity was not employed. Additionally, the

mental arithmetic performance of the mastery-focused participants was compromised when

the use of pen and paper was allowed. We therefore concluded that there were no benefits of

externalizing the internal cognitive process to the outside world for this group of individuals.

The purpose of the present experiment is to further our understanding about

achievement goals and how they differently affect working memory resources. As before, we

are looking at the role of distributed cognition and whether both of the achievement goal

groups would benefit in interacting with the external world. Finally, one omission in Study 3

is that we did not measure maths anxiety. The current study will measure state maths anxiety

at the end of the experiment to see that if there are any maths anxiety differences between the

two achievement goal endorsements. We will also measure positive and negative affect in

order to see that if there are any positive effects of interactivity on maths performance.

Additionally, we will conduct a mediation analysis to investigate whether an increase in the

state maths anxiety levels will mediate the effect of achievement goals on maths

performance, in interactive or non-interactive condition.

5.1.1 Maths Anxiety

Maths anxiety is defined as a feeling of tension, apprehension, or fear that interferes with

maths performance. Maths anxious individuals often have less practice than low maths

anxious individuals because of negative thoughts, the avoidance of the subject, and any

maths-related situations. Individuals who are maths anxious get less practice and exposure in

mathematics because they avoid maths (Ashcraft, 2002). However, general achievement tests

show no competence differences between the highly maths anxious individuals and the low

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maths anxious individuals. However, when tests are timed the maths anxiety affects whole-

number arithmetic problems (e.g., 46 + 27), (Ashcraft, 2002). Additionally, individuals who

are maths anxious have negative attitudes towards mathematics and they have negative self-

perceptions about their skills in maths. However, there is only a weak link between maths

anxiety and overall intelligence (a small correlation of -.17). Highly maths anxious

individuals score high on other anxiety tests. The strongest link is between test anxiety and

maths anxiety (.52 correlation). Women report more feelings of maths anxiety. However, this

might be due to the fact that women are more honest about their feelings (Ashcraft, 2002;

Hembree, 1990).

Arithmetic problems with larger numbers (e.g., multiplication problems and two-column

additions) have shown two important maths anxiety effects. First, individuals with higher

levels of maths anxiety respond quicker to maths tasks than do individuals with lower levels

of maths anxiety. The quicker responses are typical of avoidance behaviour whereby

responding quickly, the highly maths anxious individuals reduce the amount of time that they

deal with the maths tasks. However, by doing the tasks quickly, there is a sharp increase in

errors. Secondly, the addition problems that have a carrying element are difficult for the

highly maths anxious individuals because of the extra burden on the working memory

(Ashcraft, 2002).

5.1.2 Maths Anxiety and Working memory

Individuals who have higher levels of maths anxiety demonstrate smaller working

memory spans (Ashcraft & Kirk, 2001). This is particularly evident with a computation-based

span task, similar to the task that this study has used. There is an increase of reaction times

and errors when mental additions are performed concurrently with a memory load task.

Maths anxiety causes a transitory disruption of working memory. The lower working

memory capacity of high maths anxious individuals is partially responsible for the maths

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performance decrements. This reduced working memory capacity is on on-line effect that

disrupts information processing in maths tasks (Ashcraft & Kirk, 2001).

Mathematics anxiety affects performance by overloading working memory (Hopko et

al., 1998). According to the processing efficiency theory, when a person is anxious about

something, worrying thoughts may distract attention from the task and therefore overload

working memory. General anxiety is also associated with working memory deficits. The

intrusive thoughts compete with the ongoing cognitive task for the limited working memory

resources. Intrusive thoughts can cause slowing of performance or reduced accuracy (lower

cognitive efficiency), (Eysenck & Calvo, 1992). Similarly, maths anxious individual might be

preoccupied with the dislike of mathematics and the previous bad experiences of this area,

and as a consequence working memory gets taxed. These intrusive thoughts act like a

secondary task, reducing the attention from the task (Ashcraft, 2002).

5.1.3 Achievement Goals and Maths Anxiety

There is a wealth of research about achievement goals and their effects on academic

performance but much less is known about the associations with anxiety, and maths anxiety

in particular. Butler (2013) reported that when people pursue performance goals (not mastery

goals) there are concerns about demonstrating superior abilities (performance-approach

goals) and masking any possible inferior abilities (performance-avoidance goals) that the

individual might have (Butler, 2013). According to Bong (2009), having a performance-

approach goal (not a mastery-approach goal) was correlated with maths anxiety (Bong, 2009;

Skaalvik, 1997). In another study, Linnenbrink (2005) reported that performance-approach

goals were detrimental for academic achievement and test anxiety, in particular (Linnenbrink,

2005). Additionally, Skalvik (1997) found that mastery goals predicted lower levels of maths

anxiety supporting the earlier findings. However, performance goals were not related to

anxiety. When an individual places the emphasis on avoiding a negative performance

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outcome, it can lead to increased anxiety. These are somewhat inconsistent findings in this

area and further research is required to fully understand the effects of achievement goals on

academic performance, and maths anxiety in particular. Anxiety is generally measured with

self-reported questionnaires and as such there can be inconsistent findings due to variety of

responses.

5.1.4 Positive Affect and Working Memory

There are various studies that have demonstrated a beneficial role of positive affect on

working memory. The current study examines if the use of interactivity during a mental

arithmetic task allows the individual to feel positive affect which in turn might allow

enhanced working memory resources and maths performance. In the Carpenter et al., (2013)

study, participants completed a computer administered card task (complex decision-making

task) in which they could gain monetary rewards if they chose from gain decks and lose

money if they chose from lose decks. The participants in the positive-feeling condition chose

generally better and made more money than the neutral-feeling participants. The participants

in the positive-feeling condition improved working memory capacity (Carpenter, Peters,

Västfjäll, & Isen, 2013). In another study, positive affect compared with neutral affect

enhanced working memory and controlled processing, in particular (measured with an

operations span task), (Yang, Yang, & Isen, 2013).

5.1.5 The Current Study

Study 3 reported that interactivity did not benefit the mastery-approach goal

participants. One explanation for the findings of Study 3 could be that mastery-focused

individuals did not feel the need to extend their existing working memory resources because

of lack of outcome related concerns. These worrying thoughts can tax working memory and

leave less capacity available to compute the mental arithmetic tasks (Crouzevialle & Butera,

2013). Solving mental arithmetic tasks at the same time with the worrying thoughts can place

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heavy demands on the limited working memory storage. Clearly, the taxing of working

memory seems to be more pronounced for performance-focused students than mastery-

focused students. Therefore, our first hypothesis (Hypothesis 1) is that mastery-approach goal

participants will have higher maths performance than performance-approach goal participants

because of lack of anxious thoughts about other people’s maths performance. It is predicted

that the maths performance of the performance-focused individuals will suffer in the non-

interactive condition (Hypothesis 2) because there are additional demands caused by anxiety

on working memory resources. We also predict (Hypothesis 3) that it will be the

performance-approach goal participants who will benefit more from distributed cognition

than the mastery-approach goal participants. Additionally, it is expected (as shown in Study

3) that the mastery-focused individuals will have a drop in their performance in the

interactive condition compared to those in the non-interactive condition (Hypothesis 4). One

reason that endorsing performance-approach goals (during the Study 3) may have led to a

greater decrement in performance compared to pursuing mastery-approach goals was because

of concerns about academic and maths performance because participants desired to achieve

better than others. Unfortunately, however, Study 3 failed to measure maths anxiety levels

(both before and after the experiment). Performance-focused individuals might show higher

levels of maths anxiety because of outcome related concerns in a mathematical domain

(Hypothesis 5). Experiment 4 therefore measured maths anxiety of the participants both

before the experiment (trait maths anxiety) and after (state maths anxiety). The pre-existing

maths anxiety levels were used as a covariate in the state maths anxiety statistical analysis to

show the actual effect of achievement goals on the maths anxiety level. Additionally, it was

argued that if the state maths anxiety is elevated when performance-approach goal is made

salient then clearly there should be more benefits of externalizing the internal cognitive

process to the outside world (interactivity) for the performance-focused individual

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(Hypothesis 6). Our seventh hypothesis was that the effects of achievement goal

endorsements on maths performance in the non-interactive condition would be mediated by

the increased state maths anxiety levels (Hypothesis 7).

We also hypothesized that participants in the mastery-approach goal conditions would

show higher levels of positive affect than participants in the performance-approach goal

condition due to lack of task-irrelevant thoughts and these thoughts not occupying the

working memory (Hypothesis 8). Linnebrink et al., (1999), reported that negative affect

mediated the positive relation between mastery-approach goals and working memory. There

was reduced negative affect for the mastery goal individuals. This in turn was related to

enhanced working-memory functioning. Performance goals had a negative indirect relation to

working memory by increasing negative affect (Linnenbrink et al., 1999). Another

explanation for the increased maths performance for the more performance-focused

individual in the interactive condition might be that there are more feelings of positive affect

with the help of the externalization of the internal cognitive process (Hypothesis 9). This

might consequently allow elevated working memory capacity, and mental arithmetic

performance. Finally, the research reported here also measured basic arithmetic skills (BAS)

and working memory capacity (computation span) before the modular arithmetic tasks in the

primed conditions to show that there were no pre-existing group differences between the

participants in the two different achievement groups.

5.2 Method

5.2.1 Participants

Seventy-eight female undergraduate psychology students (M = 19.12, SD = 1.60)

participated in this study for course credits. As in the Study 3, the current study only included

women because they evidence higher levels of maths anxiety than men (Hembree, 1990).

After consenting to participate in the study, the participants were randomly assigned to one of

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the experimental conditions (performance-approach goal or mastery-approach goal crossed

with interactivity or control). The participants were tested individually in a psychology lab at

the University of Surrey (UK), and the experimental session lasted 40 minutes. A statistical

power analysis (GPower, a priori) was performed for sample size estimation. With an alpha =

.05 and power = 0.80, the projected sample needed with the medium effect size of 0.09

(partial eta squared) was N = 80.



Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). The test

comprises statements that relate to everyday situations that have a mathematics component

(e.g., adding up a pile of change). The participants respond by confirming the level of anxiety

that they feel on a 5-point Likert-type scale. The scale ranges from not at all to very much.

MAS-UK measures three levels of anxiety: maths evaluation anxiety, everyday maths

anxiety, and observation anxiety.

Basic arithmetic skills. Basic arithmetic skill (BAS) was measured with the help of

45 simple expressions in a 60-second period (e.g., 10-5). The participants were asked to

complete as many expressions as they could in 60 seconds.

Computation span (Working memory). Working memory capacity was measured

with the help of a computation-based span test. The participants were asked to read a simple

arithmetic expression (e.g., 5 + 2 = ?, 9 – 6 = ?) and announce their answer aloud to the

researcher (7, 3). Additionally, the participants were asked to remember the second number

of each equation to be recalled later (2, 6). The sequences of the simple arithmetic tasks

varied from 1 to 7 tasks. The computation span task requires both on-line processing for the

problem solution which is simultaneous with storage and maintenance of information in

working memory for serial recall. People with maths anxiety have smaller working memory

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spans than people who are not maths anxious. This smaller span can lead to increased

reaction times and errors when mental mathematics is completed at the same time as a

memory load task (Ashcraft & Kirk, 2001).

Arithmetic task. The modular arithmetic tasks used here were identical to Study 3.

There were two blocks of 24 modular arithmetic tasks that relied heavily on working memory

resources, adapted from Beilock and Carr (2005). The purpose of the tasks is to judge the

validity of maths problems like 61 ≡ 18 (mod 4). The middle number is subtracted from the

first number (i.e., 61-18) and then the difference is divided by 4. If the answer is a whole

number the maths problem is true (Beilock & Carr, 2005). Modular arithmetic tasks as

laboratory tasks are advantageous as most students have not seen them before and therefore

previous task experience is controlled.

High-demand problems [e.g., 42 ≡ 27 (mod 3)] requiring a double-digit subtraction

operation were used as they required borrowing, resulting in using more working memory

resources. Half of the maths problems required a true response by the participant. The order

of the questions was randomized and each question was asked only once. The original tasks

used by Beilock and Carr (2005) were a mixture of high WM demand problems (two-digit

numbers requiring borrowing) and low-load questions (single-digit numbers, without

borrowing), (Figure 5). The study reported here utilised the high-demand problems only

because of limited benefits of utilising interactivity with low-demand tasks as shown with the

Pilot study before. Additionally, the tasks were in a horizontal format as opposed to a vertical

format (Figure 6).

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Low-load tasks:9 ≡ 3 (mod 2)

High-load tasks:52 ≡ 24 (mod 3)

Figure 5. Examples of low-load and high-load modular arithmetic tasks. This figure is


Figure 6. Examples of vertical and horizontal modular arithmetic problems. This figure is


Positive and Negative Affect Schedule (PANAS). The PANAS consists of two 10-

item mood scales and provides brief measures of positive affect. Respondents are asked to

rate the extent to which they have experienced each particular emotion within a specified

time period, with reference to a 5-point scale (from 1 to 5). A number of different time-

frames can be used with the PANAS, but in the current study the time-frame adopted was

right now (Watson, Clark, & Tellegen, 1988).

Mathematics anxiety (state). Maths anxiety was measured with the 23-item

Mathematics Anxiety Scale (MAS-UK) by Hunt, Clark-Carter, and Sheffield (2011). This

test was the same as the trait measurement used earlier during the experiment but this time

referring to present time (now). The participants responded by confirming the level of anxiety

that they felt after completing the experiment.

Experimental manipulations. The priming instructions were identical to Study 3.

Participants were informed after completing the baseline block of modular arithmetic tasks

(24) that they were required to complete a second block (24) of modular arithmetic tasks and

this time their performance would be recorded. The participants in the performance-approach

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Vertical MA tasks: 52

≡ 24 (mod 3)

Horizontal MA tasks:52 ≡ 24 (mod 3)

goal condition read the following instructions before starting the task that were aimed at

activating performance-approach goals:

During the recorded part of the task, the experimenters will assess your performance.

It is important for you to be proficient, to perform well and obtain a high score, in

order to demonstrate your competence. You should know that a lot of students will do

this task. You are asked to keep in mind that you should try to distinguish yourself

positively, that is, to perform better than majority of students. In other words, what we

ask you here is to show your competencies, your abilities. (Darnon et al., 2007, p. 7)

The participants in the mastery-approach goal condition read instructions that were

designed to activate mastery-approach goals. There is no social comparison being made and

the instructions are aimed to create task interest, use for everyday life, and there is no

mention about scores or task performance:

In previous research, we have observed that practice of the arithmetic task you are

solving right now benefits to cognitive functioning and leads to a progressive

improvement of mental processes. Hence, this task solving can be proven to be

beneficial on the long-term. It is however necessary that you focus your attention on

calculation mastery, so as to quickly and accurately solve each problem, in order to

experience these benefits. Try to master this task as much as you can; keep in mind its

practice can be beneficial to you. (Crouzevialle et al., 2015, p. 816)

Interactivity. As before the participants in the interactive condition were allowed to

use pen and paper to come to the solution. In other words, interactivity allowed the individual

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to off-load the working memory content to the external world. On the contrary, the

participants in the non-interactive condition were not allowed to use any external artefacts,

and were required to rely on their internal cognitive resources only.

5.2.3 Procedure

After consenting to participate in the current study, the participants commenced with

the trait maths anxiety questionnaire. This was then followed by the timed basic arithmetic

skills test where the participants were told to complete as many questions as they could in 6o

seconds. Before starting with the modular arithmetic tasks in primed conditions, computation

span (working memory capacity) was assessed. The working memory assessment was done

in an oral format with the researcher. The assessment required on-line processing and

maintenance of computation-based information. After that, there was a short training session

(2 questions) before starting the first block of the modular arithmetic problems (24) that acted

as a baseline. Only high-demand problems requiring a double-digit subtraction operation

[e.g., 42 ≡ 27 (mod 3)] were used as they required more of the working memory resources

compared to low-demand problems (single-digit operation, and no carrying required),

(Ashcraft & Kirk, 2001). The participants were primed to either performance-approach goal

condition or mastery-approach goal condition crossed with interactivity or control (during

block 1 and block 2 only). If in the interactive condition, the use of pen and paper was

allowed. After completing the second block of arithmetic tasks, the participants were required

to complete the PANAS questionnaire. Finally, the experimental session was concluded with

the state maths anxiety measurement that was the same measurement that was used earlier

(trait maths anxiety) but this time referring to the current time (now). The participants were

briefed and thanked after their participation in the experiment.

5.3 Results

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To investigate the hypotheses, three separate 2 (instruction: performance-approach

goal or mastery-approach goal) x 2 (level of interactivity: interactivity or control) between-

groups analysis of covariance (ANCOVA) were conducted with percentage correct

(accuracies), solution latencies, and state maths anxiety as dependent variables. Accuracy

difference score was calculated by subtracting the modular arithmetic performance of block 1

from block 2. Furthermore, a difference score in latencies was used as a covariate to avoid

any speed-accuracy trade-off of the participants. We also conducted, a 2 (instruction:

performance-approach goal or mastery-approach goal) x 2 (level of interactivity: interactive

or control) between-groups analysis of variance (ANOVA) with PANAS as the dependent

variable. Additionally, a detailed correlational analysis was included as part of the results

section. Finally, we conducted a mediation analysis to confirm whether an increase in the

state maths anxiety levels would mediate the effect of achievement goals on maths

performance in the non-interactive condition.


There were no group differences between the participants in the two achievement goal

groups on the baseline modular arithmetic performance (block 1), F(1, 74) = 1.77, p = .19, ŋp2

= .02, confirming that the groups did not differ in their ability to complete the modular

arithmetic tasks. Additionally, there were no group differences on the baseline (block 1)

latencies to solution either, F(1, 74) = 0.42, p = .52, ŋp2 = .006 indicating that the participants

did not vary in their speed to complete the modular arithmetic tasks during the baseline

assessment. Additionally, the two achievement goal groups did not have different levels of

working memory capacity, F(1 ,74) = 1.17, p = .28, ŋp2 = .02 when tested before priming to

the experimental conditions. Similar findings were made for basic arithmetic skills, F(1, 74)

= .28, p = 0.60, ŋp2 = .006 and trait maths anxiety, F(1, 74) = 0.39, p = .27, ŋp

2 = .02 (Table

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13). Table 14 summarises the block 1 means and standard errors and Table 15 is the means

and standard errors for block 2 (for comparison).

Table 13


M SD

Maths anxiety (trait) 52.54 10.34

Basic arithmetic skills (BAS) 22.82 8.35

Computation span (WM) 23.64 6.06

Note. Participants were not conditioned to complete the pre-testing tests. All the tests were

completed before priming. The pre-testing comprised of mathematics anxiety (trait), basic

arithmetic skills (BAS), and working memory. The scale for mathematics anxiety is from 0 to

115, basic arithmetic skills is from 0 to 45, and the scale for computation span is from 0 to

56.

Table 14



Interactive Non-interactive

M SE M SEAccuracy (%) 92.10 1.30 87.90 1.30

Latency (seconds) 16.62 0.80 13.15 0.80Note. There was no priming of achievement goals (mastery-approach goal or performance-

approach goal) in block 1. Participants completed the modular arithmetic tasks in interactive

or non-interactive condition only.

Table 15



Interactive Non-interactive

M SE M SE

Accuracy (%) 92.10 1.30 91.10 1.30

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Latency (seconds) 14.87 0.65 12.04 0.65

Note. This is the interactive or control condition only in order to get a comparison with block

1.

5.3.3 Accuracy

To test the hypotheses, accuracy difference score (block 2 - block 1) of the modular

arithmetic tasks was examined. A 2 (instruction: performance-approach goal or mastery-

approach goal) x 2 (level of interactivity: interactivity or control) between-groups analysis of

covariance (ANCOVA) was conducted with latency difference score as a covariate (Table 16

includes the means and standard errors based on the difference score of B2 – B1). To begin

with, the two main effects (interactivity or instruction) did not reach statistical significance

failing to support hypotheses 1 and 2. There was no significant difference in accuracy

between the participants in the interactive condition and the participants in the non-interactive

condition, F(1, 73) = 2.35, p = .13, ŋp2 = .03. Additionally, the main effect of instruction

(mastery-approach goal or performance-approach goal) did not reach statistical significance

(F < 1).

However, there was a significant two-way interaction of instruction (mastery-

approach goal or performance-approach goal) and interactivity (interactivity or control), after

controlling for a difference score in latencies, F(1, 73) = 10.04, p = .002, ŋp2 = .12. As

anticipated, the participants in the performance-approach goal condition benefited from

interactivity as their maths performance was higher (M = 3.70, SE = 1.80) than the

participants in the mastery-approach goal condition (M = -3.30, SE 1.90), confirming

Hypothesis 3 (Figure 5), F(1, 36) = 6.82, p = .01, ŋp2 = .16. As already shown in Study 3, the

maths performance of the participants in the mastery-approach goal condition was lower in

the interactive condition (M = -3.30, SE = 1.90) than in the non-interactive condition (M =

5.40, SE = 1.90) confirming the fourth hypothesis, (Figure 7), F(1, 36) = 10.67, p = .002, ŋp2

= .23.

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-4.00-3.00-2.00-1.000.001.002.003.004.005.006.00

3.70

0.60

-3.30

5.40

Interactivity x Instruction (Accuracy Difference Score, B2 - B1)


Mod

ular

Arit

hmet

ic P

erfo

rman

ce (%

)



interactivity or control).

Table 16

Descriptive Statistics and Standard Errors of the Primary Dependent Variables (Based on a

Performance Difference Score, B2 – B1)

PAG-INT PAG-NI MAG-INT MAG-NIn = 20 n = 21 n = 19 n = 18

M SE M SE M SE M SE

Accuracy (%) 3.70 1.80 0.60 1.80 -3.30 1.90 5.40 1.80

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Latency (seconds) -0.86 0.56 -1.50 0.57 -2.65 0.58 -0.71 0.56

PANAS (positive) 23.50 1.68 24.32 1.72 26.05 1.72 25.05 1.68

PANAS (negative) 17.25 1.32 16.32 1.35 15.68 1.35 16.45 1.32

Maths anxiety (state) 57.14 2.76 54.92 2.83 46.86 2.86 51.32 2.76Note. PAG-INT = performance-approach goal with interactivity; PAGNI = performance-

approach goal without interactivity; MAG-INT = mastery-approach goal with interactivity

and MAG-NI = mastery-approach goal with no interactivity. Only the modular arithmetic

tasks employed interactivity (accuracy and latency to solution).

5.3.4 PANAS

PANAS (positive affect) scores were analysed with the help of a 2 (level of

interactivity: interactivity or control) x 2 (instruction: performance-approach goal or mastery-

approach goal) between-groups analysis of variance (ANOVA). The two main effects of

interactivity or instruction did not reach statistical significance. There was no significant

difference in positive affect between the participants in the interactive condition and the

participants in the non-interactive condition, F < 1. Additionally, the main effect of

instruction (mastery-approach goal or performance-approach goal) did not reach statistical

significance (F < 1) failing to support Hypothesis 8. There was no significant two-way

interaction of interactivity (interactivity or control) and instruction (mastery-approach goal or

performance-approach goal) either, F < 1, failing to support Hypothesis 9 (Table 16).

PANAS (negative affect) scores were also analysed with a 2 (level of interactivity:

interactivity or control) x 2 (instruction: performance-approach goal or mastery-approach

goal) between-groups analysis of variance (ANOVA). The two main effects (interactivity or

instruction) did not reach statistical significance. There was no significant difference in

negative affect between the participants in the interactive condition and the participants in the

control condition, F < 1. Additionally, the main effect of instruction (mastery-approach goal

or performance-approach goal) did not reach statistical significance (F < 1). Finally, there

145

was no significant two-way interaction of interactivity (interactivity or control) and

instruction (mastery-approach goal or performance-approach goal) as F < 1.

5.3.5 Maths Anxiety (State)

A two-way between groups analysis of covariance (ANCOVA) was conducted to

compare the effects of interactivity on two levels of instructions that were given to the

participants (mastery-approach goals or performance-approach goals) when completing the

modular arithmetic tasks. After adjusting for pre-existing maths anxiety levels (trait maths

anxiety), there was a significant main effect of instruction (mastery-approach goal or

performance-approach goal) on state maths anxiety, F(1, 73) = 6.07, p = .02, ŋp2 = .08. The

participants in the performance-approach goal condition showed higher levels of maths

anxiety after completing the experiment in primed conditions (M = 56.03, SE = 1.98) than the

participants in the mastery-approach goal condition (M = 49.09, SE = 1.98) confirming the

Hypothesis 5 (Figure 6). The main effect of interactivity did not reach statistical significance

(F < 1) nor did the two-way interaction of instruction and interactivity, F (1, 73) = 1.42, p

= .24, ŋp2 = .02 failing to confirm Hypothesis 6.

Performance-Approach Goal Mastery-Approach Goal44

46

48

50

52

54

56

5856.03

49.09

Maths Anxiety (State)

Mat

hs A

nxie

ty

Figure 8. Mean difference in state maths anxiety levels as a function of experimental

condition (performance-approach goal or mastery-approach goal).

146

5.3.6 Mediation

We conducted a mediation analysis to further understand whether an increase in the

state maths anxiety levels in the non-interactive condition would mediate the effect of

achievement goals on maths performance. The mediation analysis was conducted as a

function of interactivity (interactive condition or control). There was no evidence of direct or

indirect mediation of state maths anxiety on maths performance in the non-interactive

condition as p = .17 [in path a (between achievement goal instruction and state maths

anxiety), b (between state maths anxiety and maths performance) and c (between

achievement goal instruction and maths performance)] failing to support the Hypothesis 7. In

the interactive condition, there was a direct effect of instruction (performance-approach goal

or mastery-approach goal) on the maths performance, t(78) = -2.89, p = .007. However, there

was no evidence of direct or indirect mediation as p = .15 (in path a and b) failing to support

Hypothesis 7.

5.3.7 Correlations

A correlational analysis of the performance-focused individuals was conducted to

further explore what was driving the mental arithmetic performance, and the state maths

anxiety levels for the more maths-anxious individuals (trait), (Table 17 and 18). Only the

participants in the performance-approach goal condition were included in the analysis here as

they were the more maths-anxious (state) participants. Additionally, it was these individuals

who benefited the most from coupling of the internal cognitive resources with the external

environment. We compared the correlations in the interactive condition with the control

condition to see any possible differences. As we anticipated, trait maths anxiety was strongly

correlated with the state maths anxiety in the interactive condition, r(78) = .59, p = .006.

Additionally, there was a strong correlation between trait maths anxiety and basic arithmetic

skills, r(78) = -.51, p = .02. In the non-interactive condition, there was a strong correlation

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between trait maths anxiety and state maths anxiety, r(78) = .60, p = .007. Additionally, trait

maths anxiety was strongly correlated with working memory, r(78) = -.50 p = .007. But more

importantly, the correlations revealed that in the non-interactive condition, there was a

marginally significant correlation of working memory capacity and state maths anxiety,

r(78) = -.41, p = .08. However, this same pattern could not be found in the interactive

condition suggesting that interactivity functioned as extended working memory capacity in

the interactive condition for the more maths-anxious performance-focused individual.

Interactivity allowed the more maths-anxious participant to extend their existing working

memory capacity.

Table 17

Summary of Correlations in the Performance-Approach Goal and Non-Interactive Condition onlyMeasure 1 2 3 4

1. Maths anxiety (trait) 1 -.34 -.50* .60**

2. Basic arithmetic skills -.34 1 .17 -.40

3. Working memory -.50* .17 1 -.41

4. Maths anxiety (state) .60** -.40 -.41 1

Note. * = correlation is significant at the .05 level, ** = correlation is significant at the .01 level.


Table 18

Summary of Correlations in the Performance-Approach Goal and Interactive Condition only

Measure 1 2 3 4

1. Maths anxiety (trait) 1 -.51* -.12 .59**

2. Basic arithmetic skills -.51* 1 .39 -.14

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3. Working memory -.12 .39 1 .14

4. Maths anxiety (state) .59** -.14 .14 1

Note. * = correlation is significant at the .05 level, ** = correlation is significant at the .01 level.


6 Discussion

The purpose of this study was to further our understanding on the effects of

interactivity on the maths performance of mastery-approach goals. We also wanted to

investigate whether the adverse effects of performance-approach goals on mental arithmetic

performance could be alleviated with the use of distributed cognition. We considered the role

of maths anxiety (state) and whether interactivity could be used as an innovative way of

defusing the possible impact of maths anxiety on mental arithmetic performance. We found

that participants in the two achievement goal conditions did not differ in their levels of

modular arithmetic task (block 1), latency (block 1), working memory, basic arithmetic skills,

and trait maths anxiety levels. Thus, the performance differences that were found as part of

the main analysis were not due to pre-existing achievement group differences.

As found in the Study 3, there was lower maths performance for the participants in the

mastery-approach goal condition with interactivity compared to the non-interactive condition,

supporting Hypothesis 4. Mastery-focused individuals did not feel the benefits of

externalising the internal cognitive process of computing the maths tasks. On the contrary,

there was a clear performance drop when interactivity was employed, replicating the finding

of Study 3 in this thesis. Similar findings have been made by Webb and Vallée-Tourangeau

(2009) who reported that dyslexic children (aged between 9 – 11 years) benefited the most

(compared to typically developing children) from rearranging letter tiles (interactive

condition) in a word production task. By allowing dyslexic children to reshape the physical

presentation of the letters, their less efficient working memory capabilities could be

compensated. There were no benefits of externalising the internal cognitive process for the

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typically developing children (control group), they had the required working memory

resources and capabilities to compute the tasks. In fact, their performance deteriorated (with

the easy set of letters) when they manipulated the tiles to produce words (Webb & Vallée-

Tourangeau, 2009).

There can be cognitive cost implications in relation to how beneficial and successful

the use of interactivity is. Sometimes it is quicker and easier to rely on the internal resources

only (Kirsh, 2010). The mastery-approach goal endorsement of the current study did not

affect the cognitive resources of the participants in a way that it would have been beneficial

to utilise the external resources to complete the task. However, as expected, the participants

in the performance-approach goal condition had higher maths performance compared to the

participants in the mastery-approach goal condition in the interactive condition supporting

Hypothesis 3. There were more benefits for the more performance-focused individual than

the mastery-focused individual to utilise the external resources that were provided to

complete the task. Clearly, the internal cognitive resources (including working memory) were

adversely affected by the performance-approach goal endorsement and there were clear

benefits of coupling the internal and external resources of the individual to come to the

solution. These findings are in line with Avery and Smillie (2013) who concluded that the

pursuit of performance-approach goals can have an adverse effect on the working memory

processing of the participants and can cause a performance drop (Avery & Smillie, 2013).

The current study added to this finding in that the opportunity to externalise the internal

cognitive process has allowed the extension of working memory resources (the processing

part in particular) and caused a positive effect on the maths performance.

We also found that the individuals in the performance-approach goal condition felt

higher levels of state maths anxiety after completing the maths tasks (supporting Hypothesis

5). This is in contrast with the Avery and Smillie (2013) study where it was reported that

150

there were no heightened state anxiety levels in the performance-approach goal condition.

The same authors concluded that under high load, the endorsement of performance-approach

goals resulted in poorer working memory processing (N-Back working memory task) than the

pursuit of mastery-approach goals or no-goal condition. The adverse effects on working

memory processing were only felt under high executive load (3-back) but not under the less

demanding tasks (1-back or 2-back), (Avery & Smillie, 2013). Additionally, there was no

direct measure of state maths anxiety in the Butera and Crouzevialle (2013) study either. A

performance drop of the performance-approach goal individuals was explained by distractive

thoughts (Study 1 and 2) that were due to the activation of performance-approach goal related

thoughts during the task solving (Study 3) rather than increased state anxiety levels. Study 3

used thought suppression manipulation to investigate this. When an individual tries to get rid

of a particular thought, an opposite reaction happens and there can be an increase in its

accessibility (Wegner, 1994). This effect is generally caused by a disruption of the

monitoring process. Additionally, there is a supervision process that searches for the

unwanted thought presence to point out a failure of suppression (not easily disrupted by

additional load). This disruption of monitoring thoughts can trigger accessibility to the

unwanted content (e.g., normative goal attainment concerns), (Wegner, 1994). Activation of

performance-approach goal-related content has been found to be responsible for distractive

effects (Crouzevialle & Butera, 2013) .

Additionally, the study reported here did not find a two-way interaction between

achievement goal endorsements and interactivity on state maths anxiety. Whilst it is evident

that performance-approach goal condition allowed the participants to feel higher levels of

maths anxiety, there was no evidence to suggest that the anxiety levels were reduced with the

help of interactivity and as a consequence, the working memory extended and maths

performance enhanced. Clearly, the endorsement of the achievement goals was still felt post-

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priming but not the interactivity that was utilized during the mental arithmetic tasks. The

participants in the performance-approach goal condition showed higher levels of maths

anxiety after the experiment but this anxiety was not reduced with coupling of the agent and

the environment. Finally, it is important to mention that the participants completed the

PANAS measurement straight after the mental arithmetic tasks in primed conditions. This

was then followed by the state maths anxiety measure.

There were no effects of interactivity that carried on to the subsequent tests (i.e.,

PANAS and state maths anxiety) in the experiment reported here. To our knowledge, there

are no empirical studies on interactivity that have measured maths anxiety post-experiment.

Most of the existing studies on interactivity have concentrated on the differences of low and

high maths anxious individuals and how their maths performance is affected by the increased

levels of interactivity. These studies have concluded that there are more benefits of

externalising the internal cognitive process to the outside world for the more maths anxious

individual (e.g., Allen & Vallée-Tourangeau, 2016).

Unlike the current study, Study 2 reported that there were strong carry-on effects of

distributed cognition on state maths anxiety after completing maths tasks in primed

conditions. Participants who were allowed to extend their existing working memory resources

felt less maths anxious after the experiment than before. The level of difficulty of the mental

arithmetic tasks that were utilised in Study 2 were higher (modular arithmetic tasks that were

up to three-digit numbers) than the current study (two-digit numbers) and would therefore

possibly explain the statistically significant result of interactivity reducing the levels of trait

maths anxiety. There were more benefits of using interactivity with the higher difficulty

level, and this had a causal effect on the trait maths anxiety levels too. Similar findings have

been found in Vallée-Tourangeau (2013) where increased interactivity allowed increased

performance only for the longer sums (11 single-digit numbers) but not for the shorter sums

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(7 single-digit numbers). Participants performed marginally better when they only relied on

their internal cognitive resources (Vallée-Tourangeau, 2013).

Additionally, we conducted a mediation analysis to investigate the role of state maths

anxiety on maths performance. The mediation analysis indicated that achievement goals did

not have a direct or indirect mediation effect of state maths anxiety on the maths performance

when in the non-interactive condition. In other words, the change in the state maths anxiety

levels did not mediate the maths performance when the maths tasks were not completed

without the assistance of interactivity. Instead, there was a direct effect of achievement goals

on maths performance in the interactive condition. This pattern could not be found in the non-

interactive condition.

This study failed to show any statistically significant results of positive affect. The

mastery-focused individuals did not feel more positive affect than the performance-focused

individuals failing to confirm hypothesis 8. It was predicted that the coupling of the internal

cognitive resources with the external environment would enhance the level of positive affect

for the participants in the interactive condition. This would consequently extend working

memory resources and increase the mental arithmetic performance, particularly for the

performance-goal participants. Interactivity did not increase the levels of positive affect

failing to confirm Hypothesis 9. We predicted that if the participants would show higher

levels of positive affect in the interactive condition, this affect would be more beneficial for

the performance-focused individual as part of their working memory resources were occupied

by worry about outperforming the others. If interactivity allowed the participants to feel more

positive affect, this affect would allow working memory to be augmented and maths

performance enhanced.

A correlational analysis (performance-approach goal only) revealed that in the non-

interactive condition, working memory was correlated with state maths anxiety. However,

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this correlation was not statistically significant in the interactive condition. This finding lends

its support to the important role of interactivity for the more maths anxious individual. With

elevated working memory resources, there was a reduction of state maths anxiety in the non-

interactive condition, for the performance-approach goal participant. In other words,

interactivity functioned as extended working memory capacity in the interactive condition for

the more maths-anxious performance-focused individual.

Finally, the mental arithmetic tasks that this study utilised relied heavily on working

memory resources in that only high working memory load tasks were employed (Beilock &

Carr, 2005). Thus, interactivity allowed working memory to be extended when performance-

approach goals were made salient but not for the less anxious mastery-focused individual. In

conclusion, distributed cognition hindered maths performance for the mastery-focused

individual who was less maths anxious after the experiment but allowed the more maths-

anxious individual (performance-approach goal) to improve mental arithmetic performance.

7 Limitations

Whilst the findings of this study are encouraging, the current experiment has only

looked at two of the four achievement goals. The experiment did not investigate the effects of

mastery-avoidance goals and performance-avoidance goals on mental arithmetic performance

and whether distributed cognition could be used as an innovative way of elevating maths

performance. According to Elliott and McGregor (2001) both of the avoidance goals are

linked to test anxiety (Elliot, & McGregor, 2001). If the avoidance goal participants

(performance-avoidance goal or mastery-avoidance goal) were the more anxious individuals,

then there might be more benefits of interactivity for this group of participants.

8 Future Studies

Future studies would benefit in further understanding the reasons behind the increased

maths anxiety levels. Written protocols could be included in any further experiments to

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further explore what is causing the anxiety in relation to the different achievement goals. It

would also be of interest to use different difficulty levels of the modular arithmetic tasks. As

was shown earlier, the more complicated tasks that were used in Study 2 allowed the benefits

of externalising the internal cognitive process to be more visible. Additionally, the current

study only had female participants. Future studies would benefit in having both males and

females to investigate gender differences in relation to the effects of achievement goals on

working memory.

Chapter 6: Discussion

Across four empirical studies, this thesis investigated the role of distributed cognition,

and whether interactivity could be employed as an innovative way to maintain working

memory capacity and mental arithmetic performance while experiencing evaluative pressure.

This evaluative pressure can be caused by negative stereotypes about girls’ maths

performance (Study 1 and 2) or achievement goals, and performance-approach goals in

particular (Study 3 and 4). Whilst there are various other situation-induced pressure

situations, the current programme of research focused on negative stereotypes and

achievement goals because both of these pressure situations may contribute to the same type

of cognitive mechanisms when it comes to depleting working memory capacity caused by a

stressful situation. In order to address these questions, this thesis had the following three

research objectives: 1) to examine the impact of interactivity on mental arithmetic

performance, 2) to examine how working memory and maths performance are affected by

situation-induced stress caused by priming (a) negative gender-related stereotypes (girls and

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mathematics) or (b) achievement goals (performance-approach goals and mastery-approach

goals), and 3) to examine the role of interactivity on maths performance and maths anxiety in

evaluative pressure situations caused by stereotype threat or achievement goals. The

following section will focus on presenting the findings of the four studies that contributed to

this thesis. We will begin by presenting a summary of the findings followed by a detailed

discussion based on the similarities and differences of the studies and limitations. This

section will conclude with theoretical and practical contributions of the findings and

recommendations for future studies.

1.1 Summary of the Findings

The purpose of this PhD programme of research was to investigate the role of

distributed cognition in mathematical problem solving, in evaluative pressure situations (i.e.,

stereotype threat and achievement goals in mathematical problem solving). As expected,

interactivity increased maths accuracy and reduced solution latencies (Study 1) confirming

existing findings (Guthrie, Harris, & Vallée-Tourangeau, 2015; Guthrie, Mayer, & Vallée-

Tourangeau, 2014). When girls were negatively primed about their maths performance, there

was a reduction in their working memory performance. However, the priming did not reduce

mental arithmetic performance. This study also found that participants’ maths anxiety levels

were not affected by the priming of negative stereotypes about girls’ maths performance.

As before, in the second study, interactivity increased accuracy in all of the three

different maths tasks. However, there were more benefits of interactivity for the tasks

requiring more working memory (i.e., MA tasks). Additionally, the individuals became

slower with the more demanding, novel modular arithmetic tasks. Participants spent more

time in getting the tasks correct at the expense of time (speed-accuracy trade-off). Unlike the

first study, this study found no effects of stereotype threat on working memory. There were

no effects of stereotype threat on the maths performance of the female university students.

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Finally, combining the internal and external resources of the reasoner allowed the participants

to feel less state maths anxiety when the difficulty level of the maths tasks was high and

when maths anxiety was measured straight after the primed maths tasks.

As predicted, the third study found that the individuals in the performance-approach

goal setting had a drop in their MA performance compared to participants in the mastery-

approach goal condition. Whilst it was not measured as part of the investigation, it is possible

that the drop in the performance was due to additional concerns about outperforming the

other participants (Crouzevialle & Butera, 2013; Crouzevialle et al., 2015). Perhaps also there

was less taxation of the working memory because of the strategies employed by the

participants in the performance-approach condition (implicit processing) to compute the

maths tasks compared to participants in the mastery-approach goal condition. As a

consequence of the implicit processing, more space in working memory was used to

concentrate on competing with others. Another explanation for the impaired maths

performance of the participants in the performance-approach condition could be that there is

impaired working memory processing of the performance-focused participants suggested by

Avery and Smillie (2013), resulting in impaired cognitive performance. An unexpected

finding was that the maths performance of the mastery-approach goal participants was

hampered with the interaction of external artefacts (with the use of pen and paper). Clearly,

the working memory of the participants in the mastery-approach goal condition was not

negatively affected because of the pursuit of the mastery-approach goal and therefore there

was no cognitive need to interact with the external artefacts to reduce the overall cognitive

load, confirming existing findings (Cox, 1999; Kirsh, 1995; Vallée-Tourangeau &

Wrightman, 2010; Webb & Vallée-Tourangeau, 2009).

Finally, Study 4 replicated the findings of the performance drop of the mastery-

approach goal participants. In contrast to Study 3, however, individuals in performance-

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approach goal condition benefited from the use of distributed cognition. We found that the

individuals in the performance-approach goal condition showed higher levels of state maths

anxiety at the end of the experiment than the individual in the mastery-approach goal

condition. However, after conducting a mediation analysis, we found that state maths anxiety

levels did not mediate the maths performance when interactivity was not employed

suggesting that interactivity had allowed the individuals in the performance-approach

condition to increase maths performance but not because of reduced anxiety levels as

originally thought. Whilst not measured as part of the investigation, it is possible that the

maths performance of the participants in the performance-approach goal condition was

elevated because interactivity allowed improved working memory processing required to

solve mental arithmetic tasks. Clearly, concerns about outperforming others had made the

participants more maths anxious as shown with the significant main effect of interactivity of

performance-focused individuals. However, there were no effects of increased interactivity

on state maths anxiety levels after priming of the participants. Hence, it looks like the

participants of the performance-approach goal condition may have benefited from

interactivity by allowing the participant with the reduced working memory processing to

increase their maths performance.

1.2 The Effects of Interactivity on Maths Performance

Across the two first studies, the accuracy of the mental arithmetic tasks was markedly

improved with increased interactivity, addressing the first research objective. Similar findings

have been made before (Carlson, Avraamides, Cary, & Strasberg, 2007; Kirsh, 1995; Vallée-

Tourangeau, 2013). Individuals who had the opportunity to externalize their internal

cognitive process benefited vastly in doing so. Recruiting external artefacts (the use of pen

and paper in this case) allowed the participants to transform their mental arithmetic

performance. The task difficulty level of the mental arithmetic tasks of the two first studies

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was high enough to clearly experience the benefits of employing distributed cognition. If a

task is too easy and there are no benefits of externalising the process, individuals will rely on

the internal processes only (Kirsh, 2010). Additionally, participants might be more accurate

and faster when relying on their own internal cognitive abilities. This same pattern of

increased accuracy could be found when the modular arithmetic tasks were employed during

the second study. When looking at the means of the modular arithmetic tasks with

interactivity, there was a higher percentage increase for the high WM load modular arithmetic

tasks than the lower WM load modular arithmetic tasks. For the low load tasks, interactivity

increased the performance by 5.70% and for the high load tasks, interactivity allowed an

increase of 11.30%. The high load tasks benefited more from the endorsement of distributed

cognition.

When it came to solution latencies, the participants in the interactive conditions of

Study 1 were quicker than participants in the non-interactive conditions. However,

interactivity made the participants slower when modular arithmetic tasks (both the low WM

load and high WM load tasks) were completed during Study 2. There was a speed-accuracy

trade-off with novel and more working memory dependent tasks. The participants’ focus on

increasing maths accuracy resulted in increased solution latencies. In other words, the cost of

improving accuracy was the increased latency to solution when novel tasks were computed.

1.3 The Impact of Stereotype Threat on Mental Arithmetic Performance

Across the two studies, it was found that there were no significant main effects of

stereotype threat on mental arithmetic performance (accuracies and latencies), addressing the

second research objective. Thus, negative stereotyping about women’s maths performance

did not hamper the participants’ maths performance in terms of accuracy and how quickly the

participants completed the tasks. Whilst there were similar findings made about the effects of

stereotype threat on maths performance in the first two studies, the statistically non-

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significant results of these studies may have resulted from different reasons. Participants in

the first study were Year 12 students who had recently completed the General Certificate of

Secondary Education (GCSE) maths assessment where mental arithmetic is one of the

mandatory sections of the maths syllabus. Thus, they were well-rehearsed in mental

arithmetic tasks and the processes of computing these tasks in an efficient manner due to

extensive preparations for the GCSE maths assessment. The girls had the required skill and

experience to manage the type of mental arithmetic tasks that were utilised in the Study 1 and

were not affected by the negative stereotyping while completing these difficult mental

arithmetic tasks.

While completing the mental arithmetic tasks, the participants of the first study were

clearly utilising strategies that did not rely too heavily on existing working memory

resources. They were following automated processes that did not put additional pressure on

the working memory. This was in line with Beilock et al., (2007) who reported that

stereotype threat about females’ maths performance harmed maths performance (high WM

load modular arithmetic tasks) that relied heavily on working memory resources and the

phonological parts of the system in particular. However, it was found that by heavily

practising the mental arithmetic tasks, the negative effects of stereotype threat could be

alleviated. There is less pressure on the working memory resources when the tasks have been

actively rehearsed. When the tasks are heavily practiced, they are retrieved from the long-

term memory rather than from the working memory (Beilock et al., 2007). A good example

of this type of memory retrieval would be multiplication tasks. When multiplication tasks are

computed, the process is fully automated.

Although the university students in Study 2 were not as trained on the quick mental

maths strategies as the participants of the first study because of not having the same

immediate need to use these quick strategies, the university sample was a highly selected

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sample in relation to their academic achievements. When comparing the pre-testing data of

these two samples, the university students had considerably higher levels of basic arithmetic

skills (M = 27.60, SD = 10.70) compared to the school sample where the same average

figures were much lower (M = 23.10, SD = .97). The high levels of basic arithmetic skills

could be seen as a level of confidence in the participants’ maths performance. The existing

mental arithmetic skills were high enough to deal with the extra pressures of negative

stereotyping about the maths performance. The basic arithmetic skills test is a beneficial task

as it allows the participants to complete as many simple mental arithmetic tasks during a 60-

second period as they can. The participants are scored on the number of correct answers

provided in the required time frame. Being able to be both accurate and quick when

completing the mental arithmetic tasks, can be seen as evidence to show that the individual is

also able to deal with the additional anxiety caused by the gender related stereotype threat

about maths performance. It is possible that the effects of negative stereotyping endorsement

were felt but as the mental arithmetic skills were high enough, it did not affect students’

overall maths performance. Furthermore, previous studies have shown that maths accuracy

deteriorates when individuals are timed. Additionally, maths anxiety can be induced by

regular arithmetic problems presented in timed tasks (Ashcraft, 2002). Finally, there were no

variations when it came to maths self-efficacy between the two samples confirming that the

two groups felt similarly about maths as a topic. Hence, it was concluded that the level of

maths self-efficacy did not heighten the individuals’ susceptibility to stereotype threat.

Another explanation is that the university students believed that females and males

performed at the same level on the required tasks (working memory task and maths tasks). In

other words, students in the stereotype threat condition might have doubted the accuracy of

the stereotype of women performing worse than men on the various maths related tasks and

this may have masked any possible performance differences in the maths performance or

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working memory performance. Pennington et al., (2019) made similar findings with

stereotype threat not impairing women’s inhibitory control or maths performance in the form

of modular arithmetic performance (Pennington, Litchfield, McLatchie, & Heim, 2018).

The two first studies of this thesis confirmed that there were no statistically significant

findings of stereotype threat on mental arithmetic performance using tasks that were in a

recognizable format and hence not relying heavily on working memory resources.

Furthermore, the 10 mental arithmetic tasks in known format might not have been enough to

show the effects of stereotype threat of girls’ maths performance. The reason for the 10 tasks

only was time as the first study was conducted at an educational setting and required the girls

to not miss too much of the time for teaching. Additionally, the fact that there was no effect

of stereotype threat on the modular arithmetic performance (used during the second study)

that were in a novel format, is a strong indicator that the students in the stereotype threat

condition might not have believed that there were any gender related maths performance

differences.

Finally, after careful examination of the wording of the control condition of the two

first studies (when the control participants were told that the experiment measured their

working memory capacity rather than being advised that the test was diagnostic of their

maths ability) suggests that the control condition may not have functioned as a neutral control

condition as originally anticipated. Instead, the control condition of the first two studies

might have unintentionally primed for performance-approach goals and particularly to the

idea that an individual’s working memory capacity is fixed (Dweck, 1986). Hence, pursuing

an entity theory of intelligence could lead to performance-approach goals. Indeed, this might

serve as an alternative explanation for the lack of a significant difference in maths

performance between the stereotype threat condition and the control condition of the two first

studies.

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1.4 Stereotype Threat and State Maths Anxiety

Across the two studies, it was found that maths anxiety was not affected by the

manipulation of the experimental condition (stereotype threat or control). In other words, the

participants’ maths anxiety levels were not elevated after being told that females were

expected to do worse than males in maths tasks. However, individuals in the first study

conformed to social expectations about their maths abilities and thus, their working memory

capacity was reduced compared with the control group. Nevertheless, this depletion in

working memory capacity was not because of elevated levels of maths anxiety. There may

not have been statistically significant effects of stereotype threat on maths anxiety during the

first two studies because the type of maths anxiety measure that was utilised only comprised

of statements that related to everyday situations with a mathematics component rather than

the actual task in hand. The maths anxiety measure is a self-reported measure and as such, it

does not always capture the exact feelings of the participants, and particularly if the questions

are not directly linked to the task. Perhaps, as the maths anxiety measure was taken last (after

priming, mental arithmetic tasks, and working memory measure), the effects of stereotype

threat were not felt anymore. The effects may not last that long, maybe until the next task but

not after several tasks. So rather than measuring the effects of priming into stereotype threat,

it measures the participants’ maths anxiety levels after completing the maths tasks and

working memory measure.

1.5 The Role of Interactivity on State Maths Anxiety

Study 1 found no carry-over effects of interactivity on maths anxiety. The participants

in the interactive condition (while doing the mental arithmetic tasks) did not feel less maths

anxious at the end of the experiment. One possible reason for this finding is the order of the

tasks; the maths anxiety measure was taken after the mental arithmetic tasks and working

memory measure which did not involve interactivity. The positive effects of interactivity may

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not have been felt at the end of the experiment any more. Additionally, the tasks that the

study employed did not tax working memory heavily due to being heavily practiced.

However, there was reduced state maths anxiety for the participants in the second

study who were allowed to externalize their internal cognitive process by using pen and

paper. Allowing the participants to make use of external artefacts while computing the maths

tasks reduced the effects of state maths anxiety that was measured at the end of the

experiment. There were strong carry-over effects of distributed cognition. The interactive

participants were allowed to externalise their internal cognitive process during the mental

arithmetic tasks and modular arithmetic tasks. The positive effects of interactivity carried on

to the subsequent task, to state maths anxiety. According to Ashcraft and Kirk (2001) there is

a negative association between working memory and maths anxiety. Increased maths anxiety

reduces the available working memory resources (Ashcraft & Kirk, 2001). The reasoning

agent did not need to fight for the same working memory resources, the elevated interactivity

had provided the additional cognitive resource, and as a consequence the participant was less

maths anxious. To our knowledge, this is the first study that has measured maths anxiety

(state), after allowing the participants to complete a maths tasks in an interactive setting.

There is a wealth of studies that have looked at how distributed cognition can be employed to

elevate the maths performance of highly maths anxious participants (Allen & Vallée-

Tourangeau, 2016; Guthrie & Vallée-Tourangeau, 2018; Vallée-Tourangeau, 2013).

However, these studies have not measured state maths anxiety. The studies have measured

trait maths anxiety of the participants during the experiment and investigated the maths

performance according to the participant’s trait maths anxiety levels (high maths anxious vs.

low maths anxious). The study explained here has measured maths anxiety after the

experimental session and has showed reduced maths anxiety in the interactive condition.

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Whilst it was not measured as part of the Study 2, when the participants were allowed

to employ the pen and paper option to compute the maths tasks, the participants wrote down

the required steps of the modular arithmetic tasks to come to the solution and not just the

interim totals of the individual tasks. This pattern could not be found for the mental

arithmetic tasks that were in the known format. Additionally, there were some candidates that

chose not to fully utilise the interactive option for the calculations but as a minimum,

generally opted for the writing down of the instructions. It is also important to mention that

for the high WM load tasks (this study used up to three-digit numbers), there were large

benefits of employing external artefacts to come to the solution (with a large effect size, ŋp2

= .16). The second experiment had a much larger maths component as part of the study

comprising of mental arithmetic tasks similar to the first study and modular arithmetic tasks

(high WM load). Additionally, the modular arithmetic tasks were in a novel format that

required the participant to learn the required computation first and then hold this information

in working memory to be used later on. It is therefore easy to understand that why the

participants in the interactive condition would feel less maths anxious compared to the

individuals in the control condition.

In Study 1, this similar effect could not be found as the tasks were in an easily

recognisable format with four operands of maths (up to three-digit numbers). Additionally,

the participants in the first study had learned quick strategies to compute the mental

arithmetic tasks due to extensive GCSE revision practice. The process was automated and

therefore it was assumed that it did not affect the maths anxiety levels of the participants

either. We argued that interactivity did not allow the participants to feel less maths anxious,

as there was no need for this during the first experiment. Finally, it is of importance to

remember that there was a difference in the order of the tasks between the two studies. The

state maths anxiety was measured straight after the required maths tasks (that allowed

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interactivity or control) in the second experiment and might therefore explain the statistically

significant result of reduced maths anxiety in the interactive condition, unlike Study 1 where

it was measured after the working memory measure.

1.5 Stereotype Threat and Working Memory

Stereotype threat affected the working memory capacity of the participants of Study 1

and Study 2 differently, focusing on the second research objective. The statistically

significant effect of stereotype threat on working memory capacity during the first study

showed evidence that the participants endorsed the primed stereotypes to the point that it had

an effect on their existing cognitive resources, and working memory in particular. Similar

findings have been made by Schmader and Johns (2003) who found that stereotype threat

reduced the capacity of working memory available to complete mathematical computations

(e.g., mental arithmetic tasks) for women and Latinx participants but not for groups that were

not targeted by stereotype threat (e.g., men and European-Americans). Additionally, the same

authors reported that reduced working memory capacity under stereotype threat mediated the

reductions in performance on standardized tests (e.g., quantitative section of GRE). Taken

together, these findings suggest that when the negative stereotype has been made salient,

members of stigmatized groups perform poorly on cognitive tests because this added

information about their maths performance interferes with their working memory resources

and the attentional resources in particular (Schmader & Johns, 2003).

We suspected that during the first study, working memory was mainly utilised for

storing the interim totals and for borrowing and carrying over of numbers that were required

for later on due to the familiar format of the tasks. In other words, working memory was not

used to store complicated instructions or difficult steps of the calculations. When a

computational task is in a novel format, there is additional taxation of the working memory as

the new instructions need to be stored in the working memory. The type of tasks that were

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used as part of Study 1 did not require the level of processing that required more of these

cognitive resources. The mental arithmetic tasks in Study 1 used the four operands of

mathematics (i.e., addition, subtraction, multiplication and division) that were known to the

participant. The tasks were made more demanding by increasing the size of the expressions;

there were up to 3-digit-numbers. In other words, the difficulty of the problem was not made

greater with the help of increasing the number of steps required. A good example of tasks that

require multiple steps are modular arithmetic tasks where the calculations are based on

common concepts of mathematics but are in a novel format and require multiple steps to

completion. Additionally, modular arithmetic tasks require the individual to remember the

steps of the calculations as the initial format is new to the participant and has to be learned

first. Clearly, the strategies that are part of the GCSE syllabus make the students quick and

confident with the responses to allow a high level of achievement in the mental arithmetic

part of the GCSE curriculum.

The working memory test did not follow the expected format of testing (compared to

the mental arithmetic tasks in a known format) and it is therefore assumed that the candidates

of the first study felt the extra burden of not being expected to succeed (stereotype threat).

Whilst the actual calculations of the computation span were in an easily recognisable format

(e.g., 8 - 5 = 3), the fact that the participant had to remember the second digit of each

equation made it more challenging for the participants. Additionally, the working memory

assessment was in an oral format, and as such there was additional pressure of not forgetting

anything and not making any mistakes. The participants were not allowed to use any external

artefacts to come to the solution. The researcher conducted the working memory assessment

together with the participant. This is a dual-task working memory task whereby the

participant is expected to use working memory processing and storage simultaneously.

Additionally, both the processing and storing parts of the computation span involved

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mathematical equations. Clearly, when stereotype threat was made salient, the participants’

working memory capacity suffered as there were a multitude of aspects to be remembered at

the same time. The format of the working memory assessment was novel to the girls, and

therefore required more internal cognitive resources. This format of assessment could not

have been heavily practiced and therefore not automated as a process. It is therefore possible

that the effects of stereotype threat were felt as the format and the requirement of the working

memory assessment was hard.

Unlike the earlier experiment, the second study failed to report depleted working

memory capacity resources when stereotype threat was made salient, focusing on the second

research objective. The university students were not affected by the negative stereotyping of

women’s maths performance when the working memory measurement was taken. Clearly,

this is in contrast with existing empirical findings by Schmader and Johns (2003) and with

the findings of the earlier study. Operation Span Test (OSPAN), developed by Turner and

Engle (1989) was employed to measure working memory by Schmader and colleagues

(2013). This task requires the participant to evaluate simple mathematical equations (the

correctness of the answer) while simultaneously memorizing simple words to be recalled

later. After each mathematical equation, a word is presented for later recall (the mathematical

equation and the word at the end is seen as a set). At the end of each set of equations, the

participant is expected to verbally recall each of the words from the set in the correct order.

However, the maths equations were solely employed to make the participants to use certain

amount of internal cognitive processing. The actual working memory part of the operation

span test was measured with the number of words recalled correctly from each equation and

word set. Interestingly, when Schmader and colleagues (2003) looked at the maths

performance of the operations span test separately, there were no significant results of the

negative stereotype about females’ maths performance. In other words, there were no maths

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performance differences after the priming of students into stereotype threat condition or

control. The statistically significant results that were found, were the number of correctly

remembered words as part of the operation span test.

Study 2 found that the working memory capacity of the participants was predicted by

the participant’s basic arithmetic skills rather than stereotype threat priming. This indicates

that it was the arithmetic skill that contributed to working memory capacity rather than the

stereotype threat priming used during the experiment. Due to strong maths skills (measured

with the help of basic arithmetic skills test), the participants may not have felt the stereotype

threat being strong enough. It was assumed that the priming of the students into stereotype

threat did not make them feel doubtful about their maths performance. In other words, the

participants did not need to worry about their maths abilities and performance in the

stereotype threat condition.

Finally, the participants of the original Steel and Aronson (1995) study also tested

high performing university students who demonstrated decrements in performance (the test

comprised of items from the verbal Graduate Record Examination, GRE) so there may be

others reasons why the stereotype threat manipulation of the two first studies of this thesis did

not work. Many studies have failed to find effects of stereotype threat and there may be

publication bias in this literature (Nguyen & Ryan, 2008).

1.6 Achievement Goals

After concluding that the control condition of the first two studies might have

unintentionally primed for performance-approach goals, the following two studies (Study 3

and 4) concentrated on furthering our understanding of achievement goals and their effects on

working memory. These studies sought to explore motivational approach goals (i.e.,

performance-approach goals and mastery-approach goals) and how they differentially impact

upon working memory resources. As before, we aimed to further investigate how interactivity

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influenced the effects of achievement goals on modular arithmetic performance. We wanted

to further understand whether distributed cognition could be employed to reduce any of the

detrimental effects of performance-approach goals on mental arithmetic performance.

Additionally, we wanted to further our understanding of the benefits in utilising distributed

cognition for the mastery-focused individual. Study 3 found that the participants in the

performance-approach goal condition had a reduced modular arithmetic performance

compared to the mastery-approach group. However, this performance drop was improved

with the help of interactivity in the Study 4. The modular arithmetic performance of the

participants in the mastery-approach goal condition was reduced when allowed to interact

with the external resources (with the use of pen and paper) in Study 3 and 4, suggesting that

these two achievement goals differently impact upon working memory resources.

The goals of Study 4 were replicated and extended from Study 3. Hence, the purpose

of the fourth study was to further explore on the impact of distributed cognition on the maths

performance of the mastery-approach goal individual. Additionally, we investigated whether

the adverse effects of performance-approach goals on mental arithmetic performance could

be alleviated with the use of interactivity. We also considered the role of state maths anxiety

and whether interactivity could be used as a creative way of defusing the possible impact of

maths anxiety on the modular arithmetic performance. We argued that if there was elevated

maths anxiety in the performance-approach goal condition then there should be more benefits

of externalizing the internal cognitive process to the outside world. Finally, we looked at

whether participants experience positive and negative effects after being allowed to use

interactivity to compute the modular arithmetic tasks. Some of the participants computed the

tasks without the help of interactivity and that is why that we argued that even the thought of

knowing that the option of writing things down could make the participants feel more

positive about the task.

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1.7 The Impact of Interactivity on Maths Performance

Across the two final studies, there were no significant main effects of interactivity on

modular arithmetic performance, addressing the first research question. These findings are in

line with Vallée-Tourangeau (2013) who confirmed that when participants are allowed to

interact with the external world, there is elevated maths performance for the longer sums (11

single-digit numbers) but not for the shorter sums comprised of 7 single-digit numbers.

Additionally, an interesting observation was made, whereby the participants performed

marginally better when they only relied on their internal cognitive resources (non-interactive

condition). These findings suggest that the degree to which the design of an extended

cognitive system can increase cognitive performance is clearly relative to the actual degree of

task difficulty. In other words, there was no need for the participants to rely on the external

resources when calculating shorter sums as they were clearly more efficient when relying on

their own internal cognitive resources and working memory only. Additionally, there seemed

to be less effort required to complete the mental arithmetic task in the head alone (Vallée-

Tourangeau, 2013). The same way, the modular arithmetic tasks of the two final studies were

easy enough to be computed without the assistance of the external artefacts (the use of pen

and paper). Earlier, however, the second study reported a statistically significant main effect

of interactivity on modular arithmetic performance. However, the modular arithmetic tasks

that were employed as part of the second study had a much higher difficulty level. The

numbers were either double-digit or triple-digit numbers and were presented in a horizontal

format as opposed to the vertical format. Increased interactivity allowed the participants of

Study 2 to reach higher maths accuracy and efficiency when computing the required tasks

confirming existing findings by Kirsh (2010).

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1.8 Interactivity and the Impaired Maths Performance of the Participants in the

Mastery-Approach Goal Condition

An interesting finding was made across the two final studies of this thesis (addressing

the third research objective), the participants in the mastery-approach goal condition had a

performance drop when allowed to utilise the external artefacts to compute the maths task.

Clearly, there was no need to for the mastery-focused individual to extend their current

working memory resources. They had the required cognitive resources to deal with the task.

One explanation for this finding is that there was lack of outcome related thoughts and

anxiety as suggested by Butera and Crouzevialle (2013). Evidently, as the participants in the

mastery-approach goal condition focus on the benefits of their own learning and do not worry

about outperforming other people, their working memory is not as heavily taxed as the

performance-focused individuals’ working memory. In other words, there is no dual-task set-

up of completing the maths task combined with additional anxiety for the mastery-focused

individual, allowing high cognitive performance. Another explanation for the reduced maths

performance of the interactive mastery-focused participants might be linked to working

memory processing. Avery and Smillie (2013) suggested that the pursuit of performance-

approach goals might hamper the working memory processing that is required for successful

computation of simple mental arithmetic tasks. If this process is disrupted, cognitive

processing of the maths tasks is impaired and accuracy reduced. However, this reduced

working memory processing does not seem to affect the mastery-focused individuals and

therefore it seems that there are limited benefits of externalising the internal cognitive process

to this group of individuals.

In a similar vein, in another study, dyslexic children who were aged between 9 – 11

years benefited the most from rearranging the letter tiles (interactive condition) in a word

production task compared to a control group of typically developing children (Webb &

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Vallée-Tourangeau, 2009). Developmental dyslexics demonstrate impairments of working

memory and phonological processing difficulties in particular (Snowling, 1998). By

reshaping the physical presentation of the letters, the less efficient working memory

capabilities of the dyslexic participants could be compensated. The typically developing

children did not experience the same benefits from interacting with the external artefacts. In

fact, their task performance with the easy set of letters was poorer when they manipulated the

word tiles to produce words clearly demonstrating that the effectiveness of the manipulation

of the physical problem space is relative to the task difficulty as well as the cognitive abilities

of the reasoner (Webb & Vallée-Tourangeau, 2009).

Similarly, Cox (1999) introduced the notion of cognitive differences between

reasoning with self-constructed external representations and reasoning with presented

representations (e.g., textbook diagrams). Cox (1999) argued that there are three elements

that contribute to effective reasoning with the help of external representations. Interacting

with external representations is a three-way interaction between the cognitive properties of

the representation, the demands of the tasks and the effects of prior knowledge and cognitive

style of the reasoner (Cox, 1999). According to Kirsh (1995), it has to be cognitively cost

effective for the individual to interact with the external representations. If it is easier to solve

the problem mentally then this is clearly what the individual will do (Kirsh, 1995). A good

example of this is when a primary school aged child uses fingers to compute simple mental

arithmetic tasks. When the individual is older, this way of computing is not beneficial for the

reasoner anymore. It is quicker to compute the tasks in the head alone (Vallée-Tourangeau &

Wrightman, 2010).

1.9 The Maths Performance of the Performance-Approach Goal Participants

Study 3 found reduced maths performance of the performance-approach goal

participants in the non-interactive condition compared with the mastery-approach goal

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participants (addressing the second research objective). Whilst state maths anxiety was not

measured as part of Study 3, Study 4 found that the participants in the performance-approach

goal condition were more maths anxious than the mastery-focused individuals when

measured at the end of the experiment. It is possible that lower maths performance of the

performance-focused individuals is because of outcome related concerns about maths

performance that might reduce the existing working memory capacity available to compute

the task. Evidently, the performance-focused learning encourages the individual to focus on

social comparison and to outperform others leading to anxiety and lower maths performance.

And as a consequence, together with the high-load working memory tasks, working memory

resources may be further compromised by performance-focused goals (Crouzevialle &

Butera, 2013).

Poor working memory processing (measured with the help of an N-Back WM task) of

the performance-focused individuals might lead to impaired maths performance, (Avery &

Smillie, 2013). Working memory processing and central executive in particular, is an

important component when completing mental arithmetic tasks (Imbo & Vandierendonck,

2007). It has been suggested that under high working memory load, when a performance-

approach goal has been endorsed, there is poorer working memory processing available than

in the mastery-approach goal group or when there is no go-goal control, leading to a

cognitive performance drop (Avery & Smillie, 2013). N-Back task is a continuous WM

processing task rather than a mere WM storage task. N-Back is a task where a participant is

asked to confirm whether or not the position of a currently presented stimulus matches the

position on which a previous stimulus was shown. The load of the task is varied by increasing

the number of positions between the current and previous stimulus. Finally, when the N-Back

load increases, there is a bigger load on the central executive of the working memory (Kane,

Conway, Miura, & Colflesh, 2007). Finally, there was no measurement of working memory

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processing as part of the final two studies but it is possible that the reduced maths

performance of the more performance-focused individuals was due to reduced WM

processing as suggested by Avery and Smillie, 2013.

There are differing processing strategies of maths tasks for performance-focused

participants and mastery-focused individuals (Avery et al., 2013). Based on these differing

strategies of dealing with the maths tasks, Avery et al., (2013) suggested that it is the

mastery-approach goal individuals who have reduced maths performance compared to the

performance-approach goal individuals. The authors explained these results with the type of

strategies that the mastery-approach goal participants employed to come to the solution. A

motivated focus on developing self-referential skill of the mastery-approach goal individual

relied extensively on the existing working memory resources. This is caused by the use of

deliberative and step-by-step strategies during the achievement goal pursuit and as a

consequence, their cognitive performance is deteriorated. On the contrary, a focus on

demonstrating normative skill of the more performance-focused individual is less dependent

on working memory resources. These strategies are more heuristic and rely on short-cut

strategies and therefore do not tax the working memory as much as the deliberate strategies

employed by the mastery-focused individuals (Avery et al., 2013). However, our findings run

contrary to the existing findings by Avery et al., 2013. The individuals in the mastery-

approach goal condition demonstrated a higher maths performance than those in the

performance-approach goal condition (Study 3) when interactivity was not employed and

therefore does not support the findings of Avery et al., (2013). However, it is possible that

there might be more working memory capacity available to deal with the distractive thoughts

of the performance-focused individuals which reduce task focus and overall cognitive

performance when endorsing performance-approach goals. Performance anxiety may have a

more detrimental effect on working memory resources than the reduced processing of

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working memory. However, the third study of this programme of research failed to measure

maths anxiety and therefore we have limited knowledge of the anxiety levels of the

participants.

Additionally, written protocols of the non-interactive participants were not taken as

part of Study 3 and therefore, we currently have little evidence to suggest that the participants

in the performance-approach goal condition of Study 3 utilised the implicit processing of the

modular arithmetic tasks as suggested by Avery et al., (2013). It should also be noted here

that as half of the participants of the Study 3 were allowed the use of pen and paper

(interactive condition), we have written protocols of the way the modular arithmetic tasks

were computed for this group of participants. However, this information is not useful in this

part of the analysis as most of the participants seemed to employ explicit processing only,

regardless the achievement goal endorsement. Interactivity allowed the participants to extend

the current working memory resources and therefore explicit processing was possible for both

of the participant groups. This is similar to existing findings where it has been reported that

interactivity allows deeper and more efficient processing of maths tasks (Kirsh, 2010).

Finally, different strategies to solve the modular arithmetic tasks would be used depending

whether the task was computed relying on the internal resources only as in the original study

by Avery et al., (2013).

The pursuit of performance-approach goals (the goal to attain normative superiority

over peers) is particularly distractive for the students with high working memory capacity

(Crouzevialle et al., 2015). These are students who are used to being academic high achievers

because of their higher cognitive abilities to deal with demanding cognitive tasks. However,

the higher-level cognitive abilities might actually become a burden under performance-

approach goal pursuit as the high achievers aim to raise above others. This may represent an

opportunity to reaffirm their positive status of being the high academic achievers and

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therefore trigger disruptive outcome concerns that interfere with task processing. With

performance-approach goals as compared to mastery-approach goals (with no emphasis on

social comparison), the higher the individual’s working memory capacity, the lower their MA

performance. As part of their investigation, uncertainty was manipulated by providing bogus

feedback about score and ranking just before the completion of the evaluative modular

arithmetic block. The feedback was either very positive stating high score and ranking or

average which meant medium score and ranking. The feedback was designed to generate

confidence or uncertainty regarding the chance of getting a high score and outperform peers.

The increased uncertainty of outperforming the peers, reduced the MA performance of the

performance-approach goal individuals with high working memory capacity (Crouzevialle et

al., 2015).

Whilst the level of working memory capacity was outside the scope of the two

studies, some of the performance decrements of the performance-approach goal individuals

may have been caused because of increased levels of uncertainty of outperforming others.

The participants in the final two studies were psychology undergraduate students and as such

they represented a highly selective group of participants. It could be assumed that this group

of individuals demonstrate higher levels of working memory capacity and therefore a

stronger sense to attain normative superiority over other students. Thus, there might be an

even larger performance drop for this group of students due to increased uncertainty to

outclass others.

1.10 The Endorsement of Performance-approach Goals and Interactivity

As expected, the individuals in the performance-approach goal condition elevated

their maths performance in the interactive condition in Study 4, extending the finding that

was made in Study 3 (addressing the research objective 3). The earlier study found that the

maths performance of the performance-focused individuals was reduced without the use of

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interactivity. Study 4 has shown that there was clearly a cognitive need for this group of

participants to externalise the internal cognitive process to be able to deal with the task and

additional taxation of the working memory. Interacting with the external resources allowed

the individual in the performance-focused condition to increase their cognitive performance

of completing the modular arithmetic tasks. Working memory was adversely affected by the

pursuit of performance-approach goals and that is why there were clear benefits of

interactivity for the participants to come to the solution.

Whilst the two final studies did not measure working memory processing, it is

possible that the WM processing of the participants was impaired and therefore interactivity

allowed increased maths performance. Impaired central executive functioning can have

detrimental effects on maths performance. Central executive is responsible for planning and

sequencing of activities to complete the maths task (e.g., 34 + 56). It keeps track of which

parts of the calculation have been done and where to go next. It has executive functioning

responsibilities in deciding where to go next (DeStefano & LeFevre, 2004). Clearly, by

externalising some of these functions to the outside world, the individual can gain back some

of the lost processing required to complete the task. Finally, extending this research to

examine the impact of achievement goals on working memory processing and examining the

effects of distributed cognition, increase our understanding of how motivation drives

performance and how interactivity can be used to assist with this. This is an interesting

finding as distributed cognition is normally associated with working memory capacity which

is measured with the help of a computation span task rather than working memory

processing. However, more research is required in the area.

1.11 State Maths Anxiety

As expected, Study 4 found that the individuals in the performance-approach goal

condition felt higher levels of state maths anxiety after completing the maths tasks than the

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mastery-approach goal participants. This finding is not in line with Avery and Smillie (2013)

study where it was reported that there were no heightened state anxiety levels in the

performance-approach goal condition. The endorsement of performance-approach goals

resulted in poorer working memory processing under high load (N-Back working memory

task) than the pursuit of mastery-approach goals or no-goal condition. The adverse effects on

working memory processing were only felt under high executive load (3-back) but not under

the less demanding tasks (1-back or 2-back), (Avery & Smillie, 2013). Additionally, there

was no direct measure of state maths anxiety in the Butera and Crouzevialle (2013) study.

There was a performance drop of the performance-approach goal individuals because of

distractive thoughts that were due to the activation of performance-approach goal related

thoughts during the task solving rather than increased state anxiety levels as in the study

reported here. The authors used thought suppression manipulation to investigate the reduced

levels of performance. When an individual tries to suppress a particular thought, an opposite

reaction happens and there can be an increase in its accessibility (Wegner, 1994). The

activation of performance-approach goal-related content was actively responsible for the

distractive effect reported in the study (Crouzevialle & Butera, 2013).

1.12 State Maths Anxiety and Distributed Cognition

The final study predicted that there would be a two-way interaction of instruction

(performance-approach goal or mastery-approach goal) and interactivity. And in particular, it

was predicted that the performance-focused individuals would feel more maths anxious

because of their anxiety about outperforming others in the mathematical domain. This study

did not find a two-interaction between the achievement goal endorsements and interactivity,

on state maths anxiety. The pursuit of performance-approach goals allowed the participants

feel higher levels of maths anxiety, however, there was no evidence to suggest that the

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anxiety levels were reduced with the help of interactivity leading to extended working

memory and enhanced maths performance.

Clearly, the pursuit of the achievement goals was still felt post-priming but not the

distributed cognition that was utilized during the mental arithmetic tasks. Performance-

focused individuals showed higher levels of maths anxiety after the experiment but this

anxiety was not reduced with the externalisation of the internal cognitive process. Similarly,

to Study 1, the maths anxiety of the fourth study was not measured straight after the maths

tasks. The PANAS questionnaire was measured after the mental arithmetic tasks in primed

conditions, this was then followed by the state maths anxiety measure. It is possible that the

effects of interactivity could not be felt after the PANAS questionnaire any more. It was clear

that the priming instructions of performance-approach goals presented stronger carry-over

effects as they could still be experienced after the priming of the mental arithmetic tasks and

the PANAS measurement which was evidenced with a significant result of instruction

(performance-approach goal or mastery-approach goal) on state maths anxiety.

Unlike the fourth study, Study 2 found that there were strong carry-over effects of

interactivity on state maths anxiety after completing the required maths tasks in primed

conditions. The participants who were allowed to extend their existing working memory

resources felt less maths anxious after the experiment than before. However, there were clear

differences between Study 2 and Study 4 and how and when the maths anxiety was measured.

First, Study 2 utilized a higher level of difficulty of maths tasks (modular arithmetic tasks up

to three-digit numbers) than Study 4 (up to two-digit numbers). This might explain the

significant main effect of interactivity on state maths anxiety in the Study 2. Additionally, the

order of the tasks was different. The maths anxiety questionnaire was straight after the maths

tasks under primed conditions during the Study 2 unlike the Study 4 where the maths anxiety

was measured after the PANAS measurement.

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Finally, we conducted a mediation analysis to further explore the role of state maths

anxiety on the modular arithmetic performance. We found that achievement goals did not

have a direct or indirect mediation effect of state maths anxiety on the maths performance

when participants did not externalise the internal cognitive process. In other words, the

change in the state maths anxiety levels did not mediate the maths performance when the

maths tasks were computed without interactivity. Thus, increased levels of maths state

anxiety levels are not mediating the maths performance in the non-interactive condition. We

had argued that in the non-interactive condition, the achievement goals would affect the state

maths anxiety differently which would mediate the maths performance. We had also

predicted that this pattern could not be found in the interactive condition because interactivity

would have extended the diminished working memory resources needed to complete the task.

More research is required to fully understand the reasons for the performance drop of the

performance-approach goal participants, and why there is an increase with the performance

when interactivity is used.

2 Limitations and Future Studies

Whilst this PhD programme of research has made strong empirical findings in relation

to the impact of achievement goals on working memory and the role of distributed cognition,

there are limitations. We based our analysis on existing findings by Avery and Smillie (2013)

who reported reduced working memory processing for the more performance-focused

individual, causing impaired MA performance. Hence, any future studies on achievement

goals and the role of interactivity would benefit in measuring working memory processing in

performance-approach goal or mastery-approach goal environment, crossed with interactivity

or control to fully understand the role of working memory processing and interactivity.

Additionally, it would also be of interest to further explore achievement goals and the impact

of interactivity in an educational setting.

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3 Contributions of the Findings

When the literature review of the thesis was conducted a number of clear gaps in the

research were observed. The following paragraph will give an overview of these gaps and

how they have been dealt within the thesis. This paragraph is then followed by a section on

more detailed theoretical and practical implications of the findings. First, it was confirmed

that most of the research in the field of distributed cognition and the work of Kirsh in

particular, was based on research that mainly focused on everyday observations (Kirsh,

1995b; Kirsh, 2009; Kirsh 2010). With the help of experimental manipulations, this program

of study has shown clear evidence of the positive effects (increased accuracy and latencies

with a known task format) of transferring the internal cognitive process to the outside world

when computing mental arithmetic tasks. On the contrary to the findings of Kirsh (2010), the

current study also found evidence of speed-accuracy trade-off. When the maths tasks were in

a novel format (modular arithmetic tasks), the participants of the study became slower

because of speed-accuracy trade-off. It was also noted in the beginning of this research that

maths anxiety had not been measured directly (in relation to interactivity) in the work of

Vallée-Tourangeau (e.g., Allen & Vallée-Tourangeau, 2016; Vallée-Tourangeau et al., 2016).

Hence, the current study investigated the effects of interactivity on maths anxiety and found

that the interactive participants of the Study 2 had lower maths anxiety levels compared to the

control participants. When looking at the effects of stereotype threat, Steele and Aronson

(1995) stated that the African-American participants’ academic performance was negatively

affected by negative stereotyping and this was partly explained by reduced processing whilst

this was not actually measured. The current study therefore measured the levels of working

memory as one of the measures of the study to explain any possible performance decrements

caused by stereotype threat (girls and mathematics). Additionally, it can be difficult to draw

comparable conclusions of the stereotype threat effects because performance has been tested

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in various circumstances (Nguyen, 2008). Consequently, this study focused on understanding

the underlying mechanisms of stereotype threat instead. Hence, the research reported here is

focused on these mechanisms, and particularly on the effects of stereotype threat on working

memory. Finally, whilst there is ample evidence of four different achievement goals (e.g.,

Grant & Dweck, 2003; Harackiewicz & Barron, 2002), the current study employed two

achievement goals (performance-approach goals and mastery-approach goals) to further

investigate the effects of interactivity on maths performance. By employing these two

achievement goals only, allowed us to replicate the findings of Crouzevialle and Butera

(2013). Additionally, it added to the existing findings about the varying effects of

interactivity on achievement goals.

This thesis contributes to the research area of achievement goals and the role of

distributed cognition substantially. To our knowledge, this is the first programme of research

that has looked at this area. The following section will present theoretical and practical

implications of the findings. First, we started by investigating how motivational achievement

goals differently affect working memory resources, addressing the second research objective.

We confirmed existing findings of an impaired maths performance for the performance-

focused individual because of possible worries about outperforming peers (Crouzevialle &

Butera, 2013; Crouzevialle et al., 2015) or because of reduced working memory processing

(Avery & Smillie, 2013). We then extended this finding to show that this performance drop

could be reduced with the help of interactivity, addressing the third research question.

Interactivity encouraged the coupling of internal and external resources to create a cognitive

system that allowed the maths performance to get augmented for the performance-approach

goal individual. This is a substantial finding as it has not been investigated before.

We also found that maths anxiety levels of the performance-focused individuals were

elevated after the experiment compared to the mastery-approach goal individuals. However,

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maths anxiety was not reduced through distributed cognition. Interactivity allowed the

participant in the performance-approach goal condition to have a higher maths performance

compared to the control condition, however, this was not caused through reduced maths

anxiety levels. Past research has found that interactivity transformed working memory

capacity and increased its capacity and as a consequence, the resource drain that was caused

by maths anxiety, was diffused (Vallée-Tourangeau et al., 2013). The findings of this thesis

do not support these findings. We suggest that interactivity improves maths performance for

the participant who is focused on the academic performance but not through reduced anxiety

levels. It is possible that interactivity is supporting reduced working memory processing of

the individuals in the performance-approach condition. If the working memory processing of

computing maths tasks is disrupted then allowing the reasoning agent to externalise the

external cognitive process to compute the tasks, can lead to increased maths performance.

This thesis made an unexpected finding in relation to mastery-approach goal

participants’ maths performance (Study 3 and 4). These studies found that the mastery-

focused individuals’ maths performance was lower when permitted to reconfigure the

mathematical problem through using pen and paper when compared to the control condition,

addressing the third research objective. The mastery-approach goal individuals showed lower

levels of state maths anxiety compared to performance-focused participants in the final study

indicating that their working memory was not taxed with additional maths related worries.

According to Avery and Smillie (2013) the mastery-focused participants’ working memory

processing is not impaired by the endorsement of this achievement goal. Hence, it can be

concluded that their working memory was not affected and therefore there were no additional

benefits to interact with the external artefacts. As mentioned earlier, there needs to be a

cognitive need to combine the internal cognitive resources with the external resources. Thus,

there are opposite effects in which interactivity may cause performance decrements, like in

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the studies reported here and like existing research in the area (Webb & Vallée-Tourangeau,

2009). In order to create a beneficial distributed design of cognition we must understand the

full requirement of the task, the individuals who perform the task, as well as the nature of the

interaction with the external world (Cox, 1999; Kirsh, 1995; Vallée-Tourangeau &

Wrightman, 2010; Webb & Vallée-Tourangeau, 2009).

Another important finding was made in relation to state maths anxiety. We found that

interactivity allowed reduced state maths anxiety when novel and more working memory

dependent tasks were computed. There are currently no other studies that have made a similar

finding. As mentioned earlier, the existing studies have measured trait maths anxiety only and

therefore found that there are more benefits of interactivity for the more maths anxious

individual. The study reported here has concluded that state maths anxiety can be reduced

with the help of interactivity which is an important finding as it allows the more maths

anxious individual to have improved maths performance.

These findings have extended our understanding about achievement goals and their

differing effects of working memory, addressing the second research objective. Additionally,

we have found that the detrimental effects of performance-approach goals on maths

performance can be alleviated with the help of interactivity (addressing the third research

objective). These findings can contribute to practice, predominantly by providing evidence-

based guidance for policy-makers and teaching professionals. One suggestion would be that

maths education could utilise interactivity for more performance-focused individuals. By

allowing the individual to reconfigure the maths task by externalising the cognitive process,

their maths performance may be augmented. But equally for the participant who does not

have the same cognitive need to employ interactivity, it is acceptable to rely on the internal

cognitive resources only to compute the task. As individuals possess different motivational

achievement goals that lead to varying effects on the working memory, the distributed

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cognitive system needs to be tailored to suit the individual needs of the reasoner in order for

them to be able to reach their full academic potential in an educational setting. As the current

educational system is focused on exam results and therefore heavily endorsing performance-

approach goals, these findings have implications for teaching and learning and in particular,

for mathematical education.

Finally, the findings of this PhD programme of research have shown strong empirical

evidence of the benefits of utilising interactivity in a mathematical domain when the reasoner

is feeling additional concerns about completing the task. The performance drop that has been

caused by performance-approach goal priming can be improved by using pen and paper

allowing the participant to gain higher maths performance. By allowing the participant to use

these relatively simple strategies (i.e., using pen and paper), maths performance can be

improved. In an educational setting, pupils should be allowed to utilise both the internal and

external cognitive resources depending on the level of their cognitive needs to solve a maths

task.

As mentioned earlier, this study has clearly shown that there are clear benefits of

using distributed cognition as a cognitive framework, in an academic setting. Whilst the work

of Kirsh is highly criticized for employing everyday observations only to show the benefits of

distributed cognition, the current study supports these original findings by using experimental

manipulations. The current study has allowed the participants to externalise their internal

cognitive process and by doing so the ability to think and to compute maths tasks has been

enhanced. This is clear evidence to show that people think with objects and with people

around them. Clearly, it is not an internal cognitive process only. People’s capacity to think

and reason well is clearly not only based on the cognitive abilities of the reasoner but also on

the artefacts that are used to support the thinking and decision making. As a consequence, the

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school of distributed cognition should be supported when cognitive tasks are computed and

not only in an educational setting but in any everyday task requiring cognitive resources.

References

Allen, M., & Vallée-Tourangeau, F. (2016). Interactivity Defuses the Impact of Mathematics

Anxiety in Primary School Children. International Journal of Science and Mathematics

Education, 14(8), 1553–1566. https://doi.org/10.1007/s10763-015-9659-9

Aronson, J., Quinn, D. M., & Spencer, S. J. (1998). Stereotype Threat and the Academic

Underperformance of Minorities and Women. In Prejudice (pp. 83–103). Elsevier.

https://doi.org/10.1016/B978-012679130-3/50039-9

Ashcraft, M. H. (1995). Cognitive psychology and simple arithmetic: A review and summary

of new directions. Mathematical Cognition.

Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences.

Current Directions in Psychological Science, 11(5), 181–185.

https://doi.org/10.1111/1467-8721.00196

Ashcraft, M. H., & Kirk, E. P. (2001). The Relationships Among Working Memory, Math

187

Anxiety, and Performance. Journal of Experimental Psychology: General, 130(2), 224–

237. https://doi.org/10.1037//0096-3445.130.2.224

Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math

anxiety. Psychonomic Bulletin & Review, 14(2), 243–248.

https://doi.org/10.3758/BF03194059

Ashcraft, M. H., & Moore, A. M. (2009). Mathematics Anxiety and the Affective Drop in

Performance. Journal of Psychoeducational Assessment, 27(3), 197–205.

https://doi.org/10.1177/0734282908330580

Avery, R. E., & Smillie, L. D. (2013). The impact of achievement goal states on working

memory. Motivation and Emotion, 37(1), 39–49. https://doi.org/10.1007/s11031-012-

9287-4

Avery, R. E., Smillie, L. D., & De Fockert, J. W. (2013). The role of working memory in

achievement goal pursuit. Acta Psychologica, 144(2), 361–372.

https://doi.org/10.1016/j.actpsy.2013.07.012

Baddeley, A. D., & Hitch, G. (1974). Working memory. The Psychology of Learning and

Motivation Advances in Research and Theory. https://doi.org/10.1016/S0079-

7421(08)60452-1

Beilock, S., & Carr, T. (2005). When high-powered people fail: Working memory and

“choking under pressure” in math. Psychological Science, 16(2), 101–105. Retrieved

from http://www.jstor.org/stable/40064185

Beilock, S. L. (2008). Math performance in stressful situations. Current Directions in

Psychological Science. https://doi.org/10.1111/j.1467-8721.2008.00602.x

Beilock, S. L., & Carr, T. H. (2001). On the fragility of skilled performance: What governs

choking under pressure? Journal of Experimental Psychology: General, 130(4), 701–

725. https://doi.org/10.1037/0096-3445.130.4.701

Beilock, S. L., & DeCaro, M. S. (2007). From poor performance to success under stress:

Working memory, strategy selection, and mathematical problem solving under pressure.

Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(6), 983–

998. https://doi.org/10.1037/0278-7393.33.6.983

Beilock, S. L., Holt, L. E., Kulp, C. A., & Carr, T. H. (2004). More on the fragility of

performance: Choking under pressure in mathematical problem solving. Journal of

188

Experimental Psychology: General, 133(4), 584–600. https://doi.org/10.1037/0096-

3445.133.4.584

Beilock, S. L., Rydell, R. J., & McConnell, A. R. (2007). Stereotype threat and Working

memory: Mechanisms, Alleviation, and Spillover. Journal of Experimental Psychology.

General, 136(2), 256–76. https://doi.org/10.1037/0096-3445.136.2.256

Blascovich, J., Spencer, S. J., Quinn, D., & Steele, C. (2001). African Americans and high

blood pressure: The Role of Stereotype Threat. Psychological Science.

https://doi.org/10.1111/1467-9280.00340

Bong, M. (2009). Age-related differences in achievement goal differentiation. Journal of

Educational Psychology, 101(4), 879–896. https://doi.org/10.1037/a0015945

Bosson, J. K., Haymovitz, E. L., & Pinel, E. C. (2004). When saying and doing diverge: The

effects of stereotype threat on self-reported versus non-verbal anxiety. Journal of

Experimental Social Psychology, 40(2), 247–255. https://doi.org/10.1016/S0022-

1031(03)00099-4

Broekkamp, H., Hout-Wolters, B. van, & Van Hout-Wolters, B. (2007). The gap between

educational research and practice: A literature review, symposium, and questionnaire.

Educational Research and Evaluation, 13(3), 203–220.

https://doi.org/10.1080/13803610701626127

Brophy, J. (2005). Goal Theorists Should Move on From Performance Goals. Educational

Psychologist, 40(3), 167–176. https://doi.org/10.1207/s15326985ep4003_3

Butler, R. (2013). An achievement goal perspective on student help seeking and teacher help

giving in the classroom: Theory, research, and educational implications. In Help Seeking

in Academic Settings: Goals, Groups, and Contexts (pp. 15–44).

https://doi.org/10.4324/9780203726563

Cadinu, M., Maass, A., Rosabianca, A., & Kiesner, J. (2005). Why Do Women

Underperform Under Stereotype Threat?: Evidence for the Role of Negative Thinking.

Psychological Science, 16(7), 572–578. https://doi.org/10.1111/j.0956-

7976.2005.01577.x

Carlson, R. A., Avraamides, M. N., Cary, M., & Strasberg, S. (2007). What do the hands

externalize in simple arithmetic? Journal of Experimental Psychology: Learning,

Memory, and Cognition, 33(4), 747–756. https://doi.org/10.1037/0278-7393.33.4.747

189

Carpenter, S. M., Peters, E., Västfjäll, D., & Isen, A. M. (2013). Positive feelings facilitate

working memory and complex decision making among older adults. Cognition &

Emotion, 27(1), 184–192. https://doi.org/10.1080/02699931.2012.698251

Chang, H., & Beilock, S. L. (2016). The math anxiety-math performance link and its relation

to individual and environmental factors: A review of current behavioral and

psychophysiological research. Current Opinion in Behavioral Sciences.

https://doi.org/10.1016/j.cobeha.2016.04.011

Chi, N., Yeung, J., & Von Hippel, C. (2008). Stereotype threat increases the likelihood that

female drivers in a simulator run over jaywalkers. Accident Analysis and Prevention, 40,

667–674. https://doi.org/10.1016/j.aap.2007.09.003

Church, M. A., Elliot, A. J., & Gable, S. L. (2001). Perceptions of classroom environment,

achievement goals, and achievement outcomes. Journal of Educational Psychology,

93(1), 43–54. https://doi.org/10.1037/0022-0663.93.1.43

Cowley, S. J., & Vallée-Tourangeau, F. (2017). Thinking, Values and Meaning in Changing

Cognitive Ecologies. In S. J. Cowley & F. Vallée-Tourangeau (Eds.), Cognition Beyond

the Brain: Computation, Interactivity and Human Artifice (pp. 1–17). Cham: Springer

International Publishing. https://doi.org/10.1007/978-3-319-49115-8_1

Cox, R. (1999). Representation construction, externalised cognition and individual

differences. Learning and Instruction (Vol. 9). Retrieved from

http://citeseerx.ist.psu.edu/viewdoc/download?

doi=10.1.1.490.6719&rep=rep1&type=pdf

Croizet, J.-C., & Claire, T. (1998). Extending the Concept of Stereotype Threat to Social

Class: The Intellectual Underperformance of Students From Low Socioeconomic

Backgrounds. PSPB, 24(6), 588–594.

Crouzevialle, M., & Butera, F. (2013). Performance-approach goals deplete working memory

and impair cognitive performance. Journal of Experimental Psychology: General,

142(3), 666–678. https://doi.org/10.1037/a0029632

Crouzevialle, M., & Butera, F. (2017). Performance Goals and Task Performance. European

Psychologist, 22(2), 73–82. https://doi.org/10.1027/1016-9040/a000281

Crouzevialle, M., Smeding, A., & Butera, F. (2015). Striving for excellence sometimes

hinders high achievers: Performance-approach goals deplete arithmetical performance in

190

students with 68high working memory capacity. PLoS ONE, 10(9).

https://doi.org/10.1371/journal.pone.0137629

Darnon, C., Butera, F., Mugny, G., Quiamzade, A., & Hulleman, C. S. (2009). “Too complex

for me!” Why do performance-approach and performance-avoidance goals predict exam

performance? European Journal of Psychology of Education, 24(4), 423–434.

https://doi.org/10.1007/BF03178759

Darnon, C., Harackiewicz, J. M., Butera, F., Mugny, G., & Quiamzade, A. (2007).

Performance-approach and performance-avoidance goals: When uncertainty makes a

difference. Personality and Social Psychology Bulletin, 33(6), 813–827.

https://doi.org/10.1177/0146167207301022

Darnon, C., Muller, D., Schrager, S. M., Pannuzzo, N., & Butera, F. (2006). Mastery and

performance goals predict epistemic and relational conflict regulation. Journal of

Educational Psychology. https://doi.org/10.1037/0022-0663.98.4.766

DeStefano, D., & LeFevre, J. (2004). The Role of Working memory in Mental arithmetic.

European Journal of Cognitive Psychology, 16(3), 353–386.

https://doi.org/10.1080/09541440244000328

Dowker, A., Sarkar, A., & Looi, C. Y. (2016). Mathematics anxiety: What have we learned in

60 years? Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2016.00508

Dweck, C. S. (1986). Motivational processes affecting learning. American Psychologist,

41(10), 1040–1048. https://doi.org/10.1037/0003-066X.41.10.1040

Elliman, N. A., Green, M. W., Rogers, P. J., & Finch, G. M. (1997). Processing-efficiency

theory and the working-memory system: Impairments associated with sub-clinical

anxiety. Personality and Individual Differences. https://doi.org/10.1016/S0191-

8869(97)00016-0

Elliot, A. J., & Church, M. A. (1997). A hierarchical model of approach and avoidance

achievement motivation. Journal of Personality and Social Psychology, 72(1), 218–232.

https://doi.org/10.1037//0022-3514.72.1.218

Elliot, A. J., & Dweck, C. (2005). A conceptual history of the achievement goal construct.

Handbook of Competence and Motivation.

Elliot, A. J. J., McGregor, H. A. A., Elliott, Elliot, A. J. J., & McGregor, H. A. A. (2001). A 2

x 2 achievement goal framework. Journal of Personality and Social Psychology, 80(3),

191

501–519.

Elliott, A. J., Shell, M. M., Henry, K. B., & Maier, M. A. (2005). Achievement goals,

performance contingencies, and performance attainment: An experimental test. Journal

of Educational Psychology. https://doi.org/10.1037/0022-0663.97.4.630

Elliott, E. S., & Dweck, C. S. (1988). Goals: An Approach to Motivation and Achievement.

Journal of Personality and Social Psychology. https://doi.org/10.1037/0022-3514.54.1.5

Elzinga, B. M., & Roelofs, K. (2005). Cortisol-Induced Impairments of Working Memory

Require Acute Sympathetic Activation. Behavioral Neuroscience, 119(1), 98–103.

https://doi.org/10.1037/0735-7044.119.1.98

Engle, R. W. (2002). Working Memory Capacity as Executive Attention. Current Directions

in Psychological Science, 11(1), 19–23. https://doi.org/10.1111/1467-8721.00160

Entwistle, N. (1988). Motivational factors in students’ approaches to learning. In Learning

strategies and learning styles: Perspectives on individual differences (pp. 21–51).

https://doi.org/10.1007/978-1-4899-2118-5

Eysenck, M. W., & Calvo, M. G. (1992). ANXIETY AND PERFORMANCE - THE

PROCESSING EFFICIENCY THEORY. Cognition & Emotion, 6(6), 409–434.

https://doi.org/10.1080/02699939208409696

Faust, M. W., Ashcraft, M. H., & Fleck, D. E. (1996). Mathematics Anxiety Effects in

Simple and Complex Addition. Mathematical Cognition, 2(1), 25–62.

https://doi.org/10.1080/135467996387534

Forbes, C. E., Schmader, T., & Allen, J. J. B. (2008). The role of devaluing and discounting

in performance monitoring: a neurophysiological study of minorities under threat.

Social Cognitive and Affective Neuroscience, 3(3), 253–261.

https://doi.org/10.1093/scan/nsn012

Goldin-Meadow, S. (2006). Talking and Thinking With Our Hands. Retrieved from

http://journals.sagepub.com/doi/pdf/10.1111/j.0963-7214.2006.00402.x

Goldin-Meadow, S., Nusbaum, H., Kelly, S. D., & Wagner, S. (2001). Explaining Math:

Gesturing Lightens the Load, 12(6), 516–522. https://doi.org/10.1111/1467-9280.00395

Goldin-Meadow, S., & Wagner, S. M. (2005). How our hands help us learn. Trends in

Cognitive Sciences. https://doi.org/10.1016/j.tics.2005.03.006

192

Good, C., Rattan, A., & Dweck, C. S. (2012). Why do women opt out? Sense of belonging

and women’s representation in mathematics. Journal of Personality and Social

Psychology, 102(4), 700–717. https://doi.org/10.1037/a0026659

Graham, S., & Golan, S. (1991). Motivational Influences on Cognition: Task Involvement,

Ego Involvement, and Depth of Information Processing. Journal of Educational

Psychology. https://doi.org/10.1037/0022-0663.83.2.187

Grant, H., & Dweck, C. S. (2003). Clarifying Achievement Goals and Their Impact. Journal

of Personality and Social Psychology. https://doi.org/10.1037/0022-3514.85.3.541

Guthrie, L. G., & Vallée-Tourangeau, F. (2015). Interactivity and mental arithmetic:

Coupling mind and world transforms and enhances performance. Studies in Logic,

Grammar and Rhetoric, 41(54), 41–59. https://doi.org/10.1515/slgr-2015-0019

Guthrie, L. G., & Vallée-Tourangeau, F. (2018). Numbers in Action: Individual Differences

and Interactivity in Mental arithmetic. Cognitive Processing, 1–10.

https://doi.org/10.1007/s10339-018-0856-7

Guthrie, L., Mayer, J., & Vallée-Tourangeau, F. (2014). The hands that guide the thinking:

Interactivity in mental arithmetic. In Proceedings of the Annual Meeting of the

Cognitive Science Society 36 (pp. 3014–3019). Cognitive Science Society.

Guthrie, L., & Vallée-Tourangeau, F. (2015). Interactivity, Expertise, and Individual

Differences in Mental Arithmetic. In Proceedings of the Annual Meeting of the

Cognitive Science Society 37. Retrieved from

https://www.researchgate.net/publication/280920393

Halpern, D. F., & Wai, J. (2007). The world of competitive Scrabble: Novice and expert

differences in visuopatial and verbal abilities. Journal of Experimental Psychology:

Applied, 13(2), 79–94. https://doi.org/10.1037/1076-898X.13.2.79

Harackiewicz, J. M., & Barron, K. E. (2002). Revision of Achievement Goal Theory:

Necessary and Illuminating. Article in Journal of Educational Psychology.

https://doi.org/10.1037/0022-0663.94.3.638

Harackiewicz, J. M., Barron, K. E., Carter, S. M., Lehto, A. T., & Elliot, A. J. (1997).

Predictors and consequences of achievement goals in the college classroom. Journal of

Personality and Social Psychology, 73(6), 1284–1295.

Harackiewicz, J. M., Barron, K. E., Tauer, J. M., Carter, S. M., & Elliot, A. J. (2000). Short-

193

term and long-term consequences of achievement goals: Predicting interest and

performance over time. Journal of Educational Psychology.

https://doi.org/10.1037/0022-0663.92.2.316

Harackiewicz, J. M., & Linnenbrink, E. A. (2005). Multiple Achievement Goals and Multiple

Pathways for Learning: The Agenda and Impact of Paul R. Pintrich. Educational

Psychologist. https://doi.org/10.1207/s15326985ep4002_2

Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety. Journal for

Research in Mathematics Education, 21(1), 33–46. https://doi.org/10.2307/749455

Hollan, J., Hutchins, E., & Kirsh, D. (2000). Distributed Cognition: Toward a New

Foundation for Human-Computer Interaction Research. ACM Transactions on

Computer-Human Interaction, 7(2), 174–196. Retrieved from

http://delivery.acm.org/10.1145/360000/353487/p174-hollan.pdf?

ip=131.227.186.94&id=353487&acc=ACTIVE

SERVICE&key=BF07A2EE685417C5.B226837D415D06CF.4D4702B0C3E38B35.4D

4702B0C3E38B35&CFID=993885512&CFTOKEN=62278892&__acm__=150771149

6_c5a44aaf0ba2863cde33a18

Hopko, D. R., Ashcraft, M. H., Gute, J., Ruggiero, K. J., & Lewis, C. (1998). Mathematics

Anxiety and Working Memory: Support for the Existence of a Deficient Inhibition

Mechanism. Journal of Anxiety Disorders, 12(4), 343–355. Retrieved from

https://ac.els-cdn.com/S088761859800019X/1-s2.0-S088761859800019X-main.pdf?

_tid=a1f937a2-a385-11e7-8b27-

00000aacb360&acdnat=1506518182_29fb8496685d0e6e33b41f6c0cfe42d8

Hornbaek, K., & Oulasvirta, A. (2017). What Is Interaction? In CHI ’17 Proceedings of the

2017 CHI Conference on Human Factors in Computing Systems (pp. 5040–5052).

https://doi.org/10.1145/3025453.3025765

Hulleman, C. S., Durik, A. M., Schweigert, S. A., & Harackiewicz, J. M. (2008). Task

Values, Achievement Goals, and Interest: An Integrative Analysis. Journal of

Educational Psychology, 100(2), 398–416. https://doi.org/10.1037/0022-0663.100.2.398

Hunt, T. E., Clark-Carter, D., & Sheffield, D. (2011). The Development and Part Validation

of a U.K. Scale for Mathematics Anxiety. Journal of Psychoeducational Assessment,

29(5), 455–466. https://doi.org/10.1177/0734282910392892

194

Hutchins, E. (1995). Cognition in the Wild. MIT Press.

https://doi.org/10.1023/A:1008642111457

Hyde, J. S., Fennema, E., & Lamon, S. J. (1990). Gender Differences in Mathematics

Performance - a Metaanalysis. Psychological Bulletin, 107(2), 139–155.

https://doi.org/10.1037//0033-2909.107.2.139

Imbo, I., & Vandierendonck, A. (2007). The role of phonological and executive working

memory resources in simple arithmetic strategies. European Journal of Cognitive

Psychology, 19(6), 910–933. https://doi.org/10.1080/09541440601051571

Kane, M. J., Conway, A. R. A., Miura, T. K., & Colflesh, G. J. H. (2007). Working Memory,

Attention Control, and the N-Back Task: A Question of Construct Validity. Journal of

Experimental Psychology: Learning Memory and Cognition, 33(3), 615–622.

https://doi.org/10.1037/0278-7393.33.3.615

Kane, M. J., & Engle, R. W. (2000). Working-memory capacity, proactive interference, and

divided attention: Limits on long-term memory retrieval. Journal of Experimental

Psychology: Learning, Memory, and Cognition, 26(2), 336–358.

https://doi.org/10.1037/0278-7393.26.2.336

Kane, M. J., & Engle, R. W. (2002). The role of prefrontal cortex in working-memory

capacity, executive attention, and general fluid intelligence: An individual-differences

perspective. Psychonomic Bulletin and Review. https://doi.org/10.3758/BF03196323

Katz, I., Roberts, S. O., & Robinson, J. M. (1965). Effects of Task Difficulty, Race of

Administrator, and Instructions on Digit-Symbol Performance of Negroes. Journal of

Personality and Social Psychology, 2(1), 53–59. https://doi.org/10.1037/h0022080

Kirschbaum, C., Wolf, O. ., May, M., Wippich, W., & Hellhammer, D. . (1996). Stress- and

treatment-induced elevations of cortisol levels associated with impaired declarative

memory in healthy adults. Life Sciences, 58(17), 1475–1483.

https://doi.org/10.1016/0024-3205(96)00118-X

Kirsh, D. (1995). Complementary Strategies : Why we use our hands when we think.

Seventeenth Annual Conference of the Cognitive Science Society, 212–217.

Kirsh, D. (1995). The intelligent use of space. Artificial Intelligence, 73(1–2), 31–68.

https://doi.org/10.1016/0004-3702(94)00017-U

Kirsh, D. (1997). Interactivity and multimedia interfaces. Instructional Science, 25, 79–96.

195

Retrieved from https://link.springer.com/content/pdf/10.1023%2FA

%3A1002915430871.pdf

Kirsh, D. (2010). Thinking with External Representations. AI and Society, 25(4), 441–454.

https://doi.org/10.1007/s00146-010-0272-8

Kirsh, D. (2013). Embodied cognition and the magical future of interaction design. ACM

Transactions on Computer-Human Interaction, 20(1), 1–30.

https://doi.org/10.1145/2442106.2442109

Klein, K., & Boals, A. (2001). The Relationship of Life Event Stress and Working Memory

Capacity. Applied Cognitive Psychology. https://doi.org/10.1002/acp.727

Koole, S. L., & Dijksterhuis, A. (1999). The cessation of rumination through self-affirmation

Stereotypes View project Stress recovery during exposure to natural and urban

environments: A multi-lab replication View project. Article in Journal of Personality

and Social Psychology. https://doi.org/10.1037/0022-3514.77.1.111

Kray, L. J., Galinsky, A. D., & Thompson, L. (2002). Reversing the Gender Gap in

Negotiations: An Exploration of Stereotype Regeneration. Organizational Behavior and

Human Decision Processes, 87(2), 386–410. https://doi.org/10.1006/obhd.2001.2979

Lee, J. (2009). Universals and Specifics of Math self-concept, Math self-efficacy, and Math

anxiety across 41 PISA 2003 Participating Countries. Learning and Individual

Differences, 19(3), 355–365. https://doi.org/10.1016/j.lindif.2008.10.009

Lee, K., Ning, F., & Goh, H. C. (2014). Interaction between cognitive and non-cognitive

factors: The influences of academic goal orientation and working memory on

mathematical performance. Educational Psychology.

https://doi.org/10.1080/01443410.2013.836158

Lewis, B. P., & Linder, D. E. (1997). Thinking about Choking? Attentional Processes and

Paradoxical Performance. Personality and Social Psychology Bulletin, 23(9), 937–944.

https://doi.org/10.1177/0146167297239003

Linnenbrink, E. A. (2005). The Dilemma of Performance-Approach Goals: The Use of

Multiple Goal Contexts to Promote Students’ Motivation and Learning. Journal of


Linnenbrink, E. A., Ryan, A. M., & Pintrich, P. R. (1999). The role of goals and affect in

working memory functioning. Learning and Individual Differences, 11(2), 213–230.

196

https://doi.org/10.1016/S1041-6080(00)80006-0

Lyons, I. M., & Beilock, S. L. (2012a). Mathematics anxiety: Separating the math from the

anxiety. Cerebral Cortex, 22(9), 2102–2110. https://doi.org/10.1093/cercor/bhr289

Lyons, I. M., & Beilock, S. L. (2012b). When Math Hurts: Math Anxiety Predicts Pain

Network Activation in Anticipation of Doing Math. PLoS ONE, 7(10), e48076.

https://doi.org/10.1371/journal.pone.0048076

Ma, X. (1999). A Meta-Analysis of the Relationship Between Anxiety Toward Mathematics

and Achievement in Mathematics. Journal for Research in Mathematics Education,

30(5), 520–540. https://doi.org/10.2307/749772

Maglio, P., Matlock, T., Raphaely, D., Chernicky, B., & Kirsh, D. (1999). Interactive Skill in

Scrabble. The Twenty-First Annual Conference of the Cognitive Science Society, 326–

330.

Maloney, E. A., Schaeffer, M. W., & Beilock, S. L. (2013). Mathematics anxiety and

stereotype threat: shared mechanisms, negative consequences and promising

interventions. Research in Mathematics Education, 15(2), 115–128.

https://doi.org/10.1080/14794802.2013.797744

Mattarella-Micke, A., Mateo, J., Kozak, M. N., Foster, K., & Beilock, S. L. (2011). Choke or

Thrive? The Relation Between Salivary Cortisol and Math Performance Depends on

Individual Differences in Working Memory and Math-Anxiety. Emotion, 11(4), 1000–

1005. https://doi.org/10.1037/a0023224

May, D. (2009). Mathematics self-efficacy and anxiety questionnaire. Retrieved from

https://www.researchgate.net/profile/Harshvardhan_Singh7/post/Does_anyone_have_ac

cess_to_instruments_that_measure_Mathematics_Anxiety_and_Mathematics_Self-

Efficacy_for_teaching_mathematics_such_AMAS_RMARS/attachment/

59d63a5079197b80779977dd/AS:40576385291

McGregor, H. A., & Elliot, A. J. (2002). Achievement goals as predictors of achievement-

relevant processes prior to task engagement. Journal of Educational Psychology, 94(2),

381–395. https://doi.org/10.1037/0022-0663.94.2.381

Mendes, W. B., Blascovich, J., Lickel, B., & Hunter, S. (2002). Challenge and Threat During

Social Interactions With White and Black Men. Personality and Social Psychology

Bulletin, 28(7), 939–952. https://doi.org/10.1177/01467202028007007

197

Miyake, A., & Shah, P. (1999). Toward unified theories of working memory: Emerging

general consensus, unresolved theoretical issues, and future research directions. In

Models of working memory: Mechanisms of active maintenance and control (pp. 442–

481). https://doi.org/10.1017/CBO9781139174909.016

Muraven, M., & Baumeister, R. F. (2000). Self-regulation and depletion of limited resources:

Does self-control resemble a muscle? Psychological Bulletin, 126(2), 247–259.

https://doi.org/10.1037/0033-2909.126.2.247

Murphy, M. C., Steele, C. M., & Gross, J. J. (2007). Signaling Threat. Psychological Science,

18(10), 879–885. https://doi.org/10.1111/j.1467-9280.2007.01995.x

Neth, H., & Payne, S. (2011). Interactive Coin Addition: How Hands Can Help Us Think.

Proceedings of the 33rd CogSci, 279–284. Retrieved from

http://citeseerx.ist.psu.edu/viewdoc/download?

rep=rep1&type=pdf&doi=10.1.1.208.4071

Nguyen, H.-H. D., & Ryan, A. M. (2008). Does stereotype threat affect test performance of

minorities and women? A meta-analysis of experimental evidence. Journal of Applied

Psychology, 93(6), 1314–1334. https://doi.org/10.1037/a0012702

Osborne, J. W., & Jones, B. D. (n.d.). Identification with Academics and Motivation to

Achieve in School: How the Structure of the Self Influences Academic Outcomes.

https://doi.org/10.1007/s10648-011-9151-1

Pajares, F., & Graham, L. (1999). Self-Efficacy, Motivation Constructs, and Mathematics

Performance of Entering Middle School Students. Contemporary Educational

Psychology, 24(2), 123–139. https://doi.org/10.1006/ceps.1998.0991

Pennington, C. R., Litchfield, D., McLatchie, N., & Heim, D. (2018). Stereotype threat may

not impact women’s inhibitory control or mathematical performance: Providing support

for the null hypothesis. European Journal of Social Psychology.

https://doi.org/10.1002/ejsp.2540

Pintrich, P. R. (2003). A Motivational Science Perspective on the Role of Student Motivation

in Learning and Teaching Contexts. Journal of Educational Psychology, 95(4), 667–

686. https://doi.org/10.1037/0022-0663.95.4.667

Pletzer, B., Kronbichler, M., Nuerk, H. C., & Kerschbaum, H. H. (2015). Mathematics

anxiety reduces default mode network deactivation in response to numerical tasks.

198

Frontiers in Human Neuroscience, 9(April). https://doi.org/10.3389/fnhum.2015.00202

Poortvliet, P. M., & Darnon, C. (2010). Toward a More Social Understanding of

Achievement Goals. Current Directions in Psychological Science, 19(5), 324–328.

https://doi.org/10.1177/0963721410383246

Poortvliet, P. M., Janssen, O., Van Yperen, N. W., & Van De Vliert, E. (2007). Achievement

goals and interpersonal behavior: How mastery and performance goals shape

information exchange. Personality and Social Psychology Bulletin.

https://doi.org/10.1177/0146167207305536

Ramirez, G., Gunderson, E. a., Levine, S. C., & Beilock, S. L. (2013). Math Anxiety,

Working Memory, and Math Achievement in Early Elementary School. Journal of

Cognition and Development, 14(2). https://doi.org/10.1080/15248372.2012.664593

Richardson, F. C., & Suinn, R. M. (1972). The Mathematics Anxiety Rating Scale:

Psychometric data. Journal of Counseling Psychology, 19(6), 551–554.

https://doi.org/10.1037/h0033456

Rosen, V. M., & Engle, R. W. (1998). Working Memory Capacity and Suppression. Journal

of Memory and Language, 39(3). Retrieved from

https://ac.els-cdn.com/S0749596X98925906/1-s2.0-S0749596X98925906-main.pdf?

_tid=9abfa69e-b896-11e7-9b66-

00000aab0f02&acdnat=1508834444_02788b274148dfb5e1a1537b2096e90b

Rydell, R. J., McConnell, A. R., Mackie, D. M., & Strain, L. M. (2006). Of Two Minds.

Psychological Science, 17(11), 954–958. https://doi.org/10.1111/j.1467-

9280.2006.01811.x

Salthouse, T., & Babcock, R. (1990). Computation span and listening span tasks.

Unpublished manuscript. Georgia Institute of Technology, Atlanta.

Sattizahn, J. R., Moser, J. S., & Beilock, S. L. (2016). A Closer Look at Who ???Chokes

Under Pressure??? Journal of Applied Research in Memory and Cognition, 5(4), 470–

477. https://doi.org/10.1016/j.jarmac.2016.11.004

Schiefele, U. (1991). Interest, Learning, and Motivation. Educational Psychologist, 26(3–4),

299–323. https://doi.org/10.1080/00461520.1991.9653136

Schmader, T., & Johns, M. (2003). Converging Evidence That Stereotype Threat Reduces

Working Memory Capacity. Journal of Personality and Social Psychology, 85(3), 440–

199

452. https://doi.org/10.1037/0022-3514.85.3.440

Schmader, T., Johns, M., & Barquissau, M. (2004). The Costs of Accepting Gender

Differences: The Role of Stereotype Endorsement in Women’s Experience in the Math

Domain. Sex Roles, 5012(11). Retrieved from

https://link.springer.com/content/pdf/10.1023%2FB

%3ASERS.0000029101.74557.a0.pdf

Schmader, T., Johns, M., & Forbes, C. (2008). An Integrated Process Model of Stereotype

Threat Effects on Performance Toni. Psychological Review, 115(2), 336–356.

https://doi.org/10.1037/0033-295X.115.2.336.An

Seibt, B., & Förster, J. (2004). Stereotype Threat and Performance: How Self-Stereotypes

Influence Processing by Inducing Regulatory Foci. Journal of Personality and Social

Psychology, 87(1), 38–56. https://doi.org/10.1037/0022-3514.87.1.38

Senko, C., Hulleman, C. S., & Harackiewicz, J. M. (2011). Achievement Goal Theory at the

Crossroads: Old Controversies, Current Challenges, and New Directions. Educational

Psychologist, 46(1), 26–47. https://doi.org/10.1080/00461520.2011.538646

Shim, S., & Ryan, A. (2005). Changes in Self-Efficacy, Challenge Avoidance, and Intrinsic

Value in Response to Grades: The Role of Achievement Goals. The Journal of

Experimental Education, 73(4), 333–349. https://doi.org/10.3200/JEXE.73.4.333-349

Simons, J., Dewitte, S., & Lens, W. (2003). “Don’t do it for me. Do it for yourself!”;

Stressing the personal relevance enhances motivation in physical education. Journal of

Sport and Exercise Psychology, 25, 145–160. https://doi.org/10.1123/jsep.25.2.145

Skaalvik, E. M. (1997). Self-enhancing and self-defeating ego orientation: Relations with

task and avoidance orientation, achievement, self-perceptions, and anxiety. Journal of


Snowling, M. (1998). Dyslexia as a Phonological Deficit: Evidence and Implications. Child

Psychology and Psychiatry Review, 3(1), 4–11.

https://doi.org/10.1017/S1360641797001366

Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype Threat and Women’s Math

Performance. Journal of Experimental Social Psychology, 35, 4–28.

https://doi.org/10.1006/jesp.1998.1373

Stangor, C., Carr, C., & Kiang, L. (1998). Activating stereotypes undermines task

200

performance expectations. Journal of Personality and Social Psychology, 75(5), 1191–

1197. https://doi.org/10.1037/0022-3514.75.5.1191

Steele, C. M. (1997). A threat in the air: How stereotypes shape intellectual identity and

performance. American Psychologist, 52(6), 613–629. https://doi.org/10.1037/0003-

066X.52.6.613

Steele, C. M., & Aronson, J. (1995). Stereotype Threat and the Intellectual Test Performance

of African Americans. Journal of Personality and Social Psychology, 69(5), 797–811.

https://doi.org/10.1037/0022-3514.69.5.797

Stevenson, L. M., & Carlson, R. A. (2003). Information acquisition strategies and the

cognitive structure of arithmetic. Memory and Cognition.

https://doi.org/10.3758/BF03195808

Stone, J. (2002). Battling Doubt by Avoiding Practice: The Effects of Stereotype Threat on

Self-Handicapping in White Athletes. Personality and Social Psychology Bulletin,

28(12), 1667–1678. https://doi.org/10.1177/014616702237648

Stone, J., Lynch, C. I., Sjomeling, M., & Darley, J. M. (1999). Stereotype Threat Effects on

Black and White Athletic Performance. Journal of Personality and Social Psychology,

77(6), 1213–1227. Retrieved from http://content.ebscohost.com/ContentServer.asp?

T=P&P=AN&K=1999-15054-

009&S=L&D=pdh&EbscoContent=dGJyMMvl7ESeprQ4zOX0OLCmr0%2BeprNSr6a

4S7KWxWXS&ContentCustomer=dGJyMPGqr0qvp7ZOuePfgeyx44Dt6fIA

Suárez-Pellicioni, M., Núñez-Peña, M. I., & Colomé, À. (2015). Attentional bias in high

math-anxious individuals: evidence from an emotional Stroop task. Frontiers in

Psychology, 6, 1577. https://doi.org/10.3389/fpsyg.2015.01577

Tronsky, L. N. (2005). Strategy use, the development of automaticity, and working memory

involvment in complex multiplication. Memory & Cognition, 33(5), 927–940.

https://doi.org/10.1007/s13398-014-0173-7.2

Vallée-Tourangeau, F. (2013). Interactivity, Efficiency, and Individual Differences in Mental

Arithmetic. Experimental Psychology, 60(4), 302–311. https://doi.org/10.1027/1618-

3169/a000200

Vallée-Tourangeau, F., Sirota, M., & Vallée-Tourangeau, G. (2016). Interactivity mitigates

the impact of working memory depletion on mental arithmetic performance. Cognitive

201

Research: Principles and Implications, 1(1), 26. https://doi.org/10.1186/s41235-016-

0027-2

Vallée-Tourangeau, F., Sirota, M., & Villejoubert, G. (2013). Reducing the Impact of Math

Anxiety on Mental Arithmetic: The Importance of Distributed Cognition. In

Proceedings of the Annual Meeting of the Cognitive Science Society 35 (35) (pp. 3615–

3620). Cognitive Science Society.

Vallée-Tourangeau, F., & Wrightman, M. (2010). Interactive skills and individual differences

in a word production task. AI and Society. https://doi.org/10.1007/s00146-010-0270-x

Vallée-Tourangeau, G., & Vallée-Tourangeau, F. (2017). Cognition Beyond the Classical

Information Processing Model: Cognitive Interactivity and the Systemic Thinking

Model (SysTM). In S. J. Cowley & F. Vallée-Tourangeau (Eds.), Cognition Beyond the

Brain: Computation, Interactivity and Human Artifice (pp. 133–154). Cham: Springer

International Publishing. https://doi.org/10.1007/978-3-319-49115-8_7

Van Yperen, N. W., Hamstra, M. R. W., & Van Der Klauw, M. (2011). To Win, or Not to

Lose, At Any Cost: The Impact of Achievement Goals on Cheating. British Journal of

Management, 22(SUPPL. 1). https://doi.or/10.1111/j.1467-8551.2010.00702.x

Watson, D., Clark, L. A., & Tellegen, A. (1988). Development and Validation of Brief

Measures of Positive and Negative Affect: The PANAS Scales. Journal of Personality

and Social Psychology, 54(6), 1063–1070. https://doi.org/10.1037/0022-3514.54.6.1063

Webb, S., & Vallée-Tourangeau, F. (2009). Interactive Word Production in Dyslexic

Children. In The 31st Annual Conference of the Cognitive Science Society (pp. 1436–

1441).

Wegner, D. M. (1994). Ironic Processes of Mental Control. Psychological Review (Vol. 101).

Retrieved from

https://www.redirectanxiety.com/wp-content/uploads/2015/04/Wegner1994.pdf

Wolters, C. A., Yu, S. L., & Pintrich, P. R. (1996). The relation between goal orientation and

students’ motivational beliefs and self-regulated learning. Learning and Individual

Differences. https://doi.org/10.1016/S1041-6080(96)90015-1

Yang, H., Yang, S., & Isen, A. M. (2013). Positive affect improves working memory:

Implications for controlled cognitive processing. Cognition and Emotion, 27(3), 474–

482. https://doi.org/10.1080/02699931.2012.713325

202

Young, C., Wu, S., & Menon, V. (2012). The Neurodevelopmental Basis of Math Anxiety.

Psychological Science, 23(5), 492–501. https://doi.org/10.1177/0956797611429134

Zbrodoff, N. J., & Logan, G. D. (2005). What everyone finds: The problem-size effect. In

Handbook of mathematical cognition (pp. 331–345).

203

Appendix A: Ethical Approval for Study 1

204

Appendix B: SAFE for Study 2

206

Appendix C: SAFE for Study 3

209

Appendix D: SAFE for Study 4

212

Appendix E: Basic Arithmetic Skills Test (BAS), Study 1, 2, and 4

216

Appendix F: Mathematics Self-Efficacy and Anxiety Questionnaire, Study 1 and 2

Please, answer the following 7 questions.

The scale is from 1-5 where

1 = I don’t agree and 5 = I strongly agree.

Please, circle around the number.

1. I believe I am the kind of person who is good at mathematics.

1 2 3 4 5

2. I believe I am the type of person who can do mathematics.

1 2 3 4 5

3. I believe I can learn well in a mathematics course.

1 2 3 4 5

4. I feel that I will be able to do well in future mathematics courses.

1 2 3 4 5

5. I believe I can understand the content in a mathematics course.

1 2 3 4 5

6. I believe I can get an “A” when I am in a mathematics course.

1 2 3 4 5

7. I believe I can do the mathematics in a mathematics course.

1 2 3 4 5

217

Appendix G: Maths Anxiety Scale (Trait), Study 2 and 4

How anxious would you feel in the following situations?

1. Having someone watch you multiply 12 x 23 on paper?Not at all A little A fair amount Much Very much1 2 3 4 5

2. Adding up a pile of change?Not at all A little A fair amount Much Very much1 2 3 4 5

3. Being asked to write an answer on the board at the front of a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5

4. Being asked to add up the number of people in a room?Not at all A little A fair amount Much Very much1 2 3 4 5

5. Calculating how many days until a person’s birthday?Not at all A little A fair amount Much Very much1 2 3 4 5

6. Taking a maths exam?Not at all A little A fair amount Much Very much1 2 3 4 5

7. Being asked to calculate £9.36 divided by 4 in front of several people?Not at all A little A fair amount Much Very much1 2 3 4 5

8. Being giving a telephone number and having to remember it?Not at all A little A fair amount Much Very much1 2 3 4 5

9. Reading the word ‘algebra’?Not at all A little A fair amount Much Very much1 2 3 4 5

10. Calculating a series of multiplication problems on paper?Not at all A little A fair amount Much Very much1 2 3 4 5

11. Working out how much time you have left before you set off work or place of study?Not at all A little A fair amount Much Very much1 2 3 4 5

218

12. Listening to someone talk about maths?Not at all A little A fair amount Much Very much1 2 3 4 5

13. Working out how much change a cashier should have given you in a shop after buying several items?Not at all A little A fair amount Much Very much1 2 3 4 5

14. Deciding how much each person should give you after you buy an object that you are all sharing the cost of?

Not at all A little A fair amount Much Very much1 2 3 4 5

15. Reading a maths text book?Not at all A little A fair amount Much Very much1 2 3 4 5

16. Watching someone work out an algebra problem?Not at all A little A fair amount Much Very much1 2 3 4 5

17. Sitting in a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5

18. Being given a surprise maths test in a class?Not at all A little A fair amount Much Very much1 2 3 4 5

19. Being asked to memorize a multiplication table?Not at all A little A fair amount Much Very much1 2 3 4 5

20. Watching a teacher/lecturer write equations on the board?Not at all A little A fair amount Much Very much1 2 3 4 5

21. Being asked to calculate three fifths as a percentage?Not at all A little A fair amount Much Very much1 2 3 4 5

22. Working out how much your shopping bill comes to?Not at all A little A fair amount Much Very much1 2 3 4 5

23. Being asked a maths question by a teacher in front of a class?Not at all A little A fair amount Much Very much1 2 3 4 5

219

Appendix H: Computation Span (Working Memory), Study 1, 2, and 4

You will be asked to read a simple expression and announce your answer. You will also be

asked to remember the second number for each equation.

Make sure to provide a correct answer to the arithmetic task. Accurate recall will only

be recorded if you have given a correct answer to the arithmetic task.

When the page is blank, without an equation, recall the second number from each equation –

for this practice sequence, the arithmetic answers would be 1 and 11, and the numbers to

recall would be 2 and 6:

3 – 2 = 1

5 + 6 = 11

Let’s practice with another set of two equations:

8 – 5 =

7 + 1 =

220

Arithmetic answer: 3 and 8

Recall answer: 5 and 1

Because the 2 equations were:

8 – 5 = 3

7 + 1 = 8

Expect to be asked to recall more than two numbers.

The test starts now.

221

9 – 1 =

Recall

222

5 + 2 =

Recall

223

9 – 5 =

8 + 9 =

Recall

224

1 + 3 =

8 – 2 =

Recall

225

8 + 1 =

6 – 2 =

5 + 9 =

Recall

226

7 – 2 =

3 + 7 =

5 + 9 =

Recall

227

7 + 2 =

6 – 2 =

8 – 5 =

5 + 7 =

Recall

228

7 + 6 =

8 – 1 =

1 + 2 =

9 – 5 =

1 + 7 =

Recall

229

9 + 2 =

9 – 6 =

9 – 5 =

6 + 7 =

6 – 1 =

Recall

230

3 + 4 =

8 – 3 =

5 – 1 =

1 + 7 =

4 + 9 =

9 – 6 =

Recall

231

4 + 5 =

8 + 2 =

8 – 1 =

7 + 8 =

7 – 5 =

4 + 7 =

Recall

232

3 + 2 =

5 + 1 =

8 + 9 =

7 – 4 =

9 – 5 =

1 + 6 =

4 – 3 =

Recall

233

8 – 7 =

1 + 5 =

8 + 4 =

2 + 8 =

7 – 2 =

2 + 9 =

4 – 3 =

Recall

234

Appendix I: Mental Arithmetic Tasks (Known Format), Study 1 and 2

Please, complete the following tasks:

1. 433 + 288 =

2. 93 – 37 =

3. 7 x 29 =

4. 168 / 4 =

5. (66 x 3) / 2 + 5 – 8 =

6. 548 + 695 =

7. 737 – 269 =

8. 13 x 77 =

9. 18 / 2 + 23 – (3 x 5) =

10. 486 + 843 =

235

Appendix J: Modular Arithmetic Tasks, Study 2

Welcome to the second part of the test!

You will be solving a series of problems on the computer. You are going to see problems on the screen that look like the following:

17 ≡ 5 (mod 6) Your job is to judge whether the problems are "true" or "false" as quickly and as accurately as possible.

Example 1: Is the following statement true? 35 ≡ 19 (mod 2) First we subtract 19 from 35: 35 - 19 = 16 Does 2 divide into 16 with 0 as the remainder? Yes, 2 goes into 16 eight times, with a remainder of zero. Thus our statement is true.


1. 83 ≡ 27 (mod 8) =

2. 135 ≡ 69 (mod 6) =

3. 51 ≡ 19 (mod 4) =

4. 346 ≡ 229 (mod 9) =

5. 43 ≡ 27 (mod 7) =

6. 277 ≡ 139 (mod 3) =

7. 54 ≡ 36 (mod 7) =

8. 245 ≡ 59 (mod 3) =

9. 73 ≡ 37 (mod 7) =

10. 337 ≡ 149 (mod 4) =

11. 83 ≡ 35 (mod 4) =

12. 483 ≡ 297 (mod 4) =

236

13. 62 ≡ 38 (mod 6) =

14. 137 ≡ 69 (mod 8) =

15. 45 ≡ 27 (mod 4) =

16. 161 ≡ 79 (mod 6) =

17. 63 ≡ 48 (mod 4) =

18. 153 ≡ 77 (mod 6) =

19. 42 ≡ 27 (mod 3) =

20. 172 ≡ 84 (mod 8) =

21. 82 ≡ 55 (mod 8) =

22. 263 ≡ 98 (mod 8) =

23. 54 ≡ 18 (mod 6) =

24. 177 ≡ 69 (mod 4) =

25. 43 ≡ 18 (mod 3) =

26. 233 ≡ 196 (mod 9) =

27. 67 ≡ 18 (mod 6) =

28. 262 ≡ 175 (mod 9) =

29. 75 ≡ 59 (mod 4) =

30. 245 ≡ 189 (mod 6) =

237

Appendix K: Modular Arithmetic Tasks, Study 3 and 4

You will be solving a series of problems on the computer. You are going to see problems on

the screen that look like the following:

17 ≡ 5 (mod 6)

Your job is to judge whether the problems are "true" or "false" as quickly and as accurately as

possible.

Example 1: Is the following statement true?

35 ≡ 19 (mod 2)

First we subtract 19 from 35:

35 - 19 = 16

Does 2 divide into 16 with 0 as the remainder?

Yes, 2 goes into 16 eight times, with a remainder of zero. Thus our statement is true.


238

Block 1:

31. 42 ≡ 27 (mod 3) =

32. 36 ≡ 27 (mod 3) =

33. 43 ≡ 27 (mod 8) =

34. 53 ≡ 26 (mod 4) =

35. 54 ≡ 36 (mod 7) =

36. 73 ≡ 37 (mod 7) =

37. 54 ≡ 26 (mod 6) =

38. 52 ≡ 17 (mod 4) =

39. 83 ≡ 27 (mod 9) =

40. 41 ≡ 27 (mod 6) =

41. 43 ≡ 27 (mod 7) =

42. 54 ≡ 36 (mod 6) =

43. 41 ≡ 27 (mod 7) =

44. 83 ≡ 27 (mod 8) =

45. 32 ≡ 14 (mod 6) =

46. 36 ≡ 27 (mod 4) =

47. 32 ≡ 14 (mod 7) =

48. 45 ≡ 29 (mod 8) =

49. 53 ≡ 26 (mod 3) =

50. 45 ≡ 29 (mod 9) =

51. 52 ≡ 17 (mod 7) =

52. 45 ≡ 27 (mod 3) =

53. 41 ≡ 23 (mod 4) =

54. 42 ≡ 27 (mod 4) =

239

Block 2:

1. 82 ≡ 55 (mod 9) =

2. 56 ≡ 38 (mod 4) =

3. 54 ≡ 27 (mod 9) =

4. 63 ≡ 48 (mod 4) =

5. 75 ≡ 59 (mod 4) =

6. 51 ≡ 19 (mod 4) =

7. 63 ≡ 15 (mod 6) =

8. 62 ≡ 38 (mod 6) =

9. 45 ≡ 27 (mod 4) =

10. 82 ≡ 55 (mod 8) =

11. 83 ≡ 35 (mod 4) =

12. 56 ≡ 38 (mod 3) =

13. 41 ≡ 23 (mod 3) =

14. 43 ≡ 18 (mod 5) =

15. 54 ≡ 27 (mod 8) =

16. 63 ≡ 48 (mod 3) =

17. 67 ≡ 18 (mod 7) =

18. 75 ≡ 59 (mod 5) =

19. 51 ≡ 19 (mod 3) =

20. 63 ≡ 15 (mod 7) =

21. 62 ≡ 38 (mod 7) =

22. 45 ≡ 27 (mod 3) =

23. 41 ≡ 23 (mod 4) =

24. 43 ≡ 18 (mod 3) =

240

Appendix L: Positive and Negative Affect Scale (PANAS), Study 4This scale consists of a number of words that describe different feelings and emotions. Read

each item and then mark the appropriate answer in the space next to that word. Indicate to

what extent you feel this way right now, that is, at the present moment.

Use the following scale to record your answers:

1 2 3 4 5

Very slightly or not at all A little Moderately Quite a bit Extremely

1.____Interested 11.____Irritable

2.____Distressed 12.____Alert

3.____Excited 13.____Ashamed

4.____Upset 14.____Inspired

5.____Strong 15.____Nervous

6.____Guilty 16.____Determined

7.____Scared 17.____Attentive

8.____Hostile 18.____Jittery

9.____Enthusiastic 19.____Active

10.____Proud 20.____Afraid

241

Appendix M: Maths Anxiety Scale (State), Study 1, 2, and 4

How anxious would you feel NOW in the following situations?

1. Having someone watch you multiply 12 x 23 on paper?Not at all A little A fair amount Much Very much1 2 3 4 5

2. Adding up a pile of change?Not at all A little A fair amount Much Very much1 2 3 4 5

3. Being asked to write an answer on the board at the front of a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5

4. Being asked to add up the number of people in a room?Not at all A little A fair amount Much Very much1 2 3 4 5

5. Calculating how many days until a person’s birthday?Not at all A little A fair amount Much Very much1 2 3 4 5

6. Taking a maths exam?Not at all A little A fair amount Much Very much1 2 3 4 5

7. Being asked to calculate £9.36 divided by 4 in front of several people?Not at all A little A fair amount Much Very much1 2 3 4 5

8. Being giving a telephone number and having to remember it?Not at all A little A fair amount Much Very much1 2 3 4 5

9. Reading the word ‘algebra’?Not at all A little A fair amount Much Very much1 2 3 4 5

10. Calculating a series of multiplication problems on paper?Not at all A little A fair amount Much Very much1 2 3 4 5

11. Working out how much time you have left before you set off work or place of study?Not at all A little A fair amount Much Very much1 2 3 4 5

12. Listening to someone talk about maths?Not at all A little A fair amount Much Very much1 2 3 4 5

13. Working out how much change a cashier should have given you in a shop after buying several items?

242

Not at all A little A fair amount Much Very much1 2 3 4 5

14. Deciding how much each person should give you after you buy an object that you are all sharing the cost of?Not at all A little A fair amount Much Very much1 2 3 4 5

15. Reading a maths text book?Not at all A little A fair amount Much Very much1 2 3 4 5

16. Watching someone work out an algebra problem?Not at all A little A fair amount Much Very much1 2 3 4 5

17. Sitting in a maths class?Not at all A little A fair amount Much Very much1 2 3 4 5

18. Being given a surprise maths test in a class?Not at all A little A fair amount Much Very much1 2 3 4 5

19. Being asked to memorize a multiplication table?Not at all A little A fair amount Much Very much1 2 3 4 5

20. Watching a teacher/lecturer write equations on the board?Not at all A little A fair amount Much Very much1 2 3 4 5

21. Being asked to calculate three fifths as a percentage?Not at all A little A fair amount Much Very much1 2 3 4 5

22. Working out how much your shopping bill comes to?Not at all A little A fair amount Much Very much1 2 3 4 5

23. Being asked a maths question by a teacher in front of a class?Not at all A little A fair amount Much Very much1 2 3 4 5

243

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