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Prior mathematics achievement,cognitive appraisals and anxiety aspredictors of Finnish students’ latermathematics performance and careerorientationMinna Kyttälä a & Piia Maria Björn ba Department of Applied Sciences of Education , University ofHelsinki , Helsinki, Finlandb Department of Educational Sciences , University of Jyväskylä ,Jyväskylä, FinlandPublished online: 20 Jul 2010.

To cite this article: Minna Kyttälä & Piia Maria Björn (2010) Prior mathematics achievement,cognitive appraisals and anxiety as predictors of Finnish students’ later mathematics performanceand career orientation, Educational Psychology: An International Journal of ExperimentalEducational Psychology, 30:4, 431-448

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Educational PsychologyVol. 30, No. 4, July 2010, 431–448

ISSN 0144-3410 print/ISSN 1469-5820 online© 2010 Taylor & FrancisDOI: 10.1080/01443411003724491http://www.informaworld.com

Prior mathematics achievement, cognitive appraisals and anxiety as predictors of Finnish students’ later mathematics performance and career orientation

Minna Kyttäläa* and Piia Maria Björnb

aDepartment of Applied Sciences of Education, University of Helsinki, Helsinki, Finland; bDepartment of Educational Sciences, University of Jyväskylä, Jyväskylä, FinlandTaylor and FrancisCEDP_A_472971.sgm(Received 4 May 2009; final version received 23 February 2010)10.1080/01443411003724491Educational Psychology0144-3410 (print)/1469-5820 (online)Original Article2010Taylor & Francis0000000002010MinnaKyttälä[email protected]

The aim of this two-year longitudinal study was to investigate the role and impactof prior mathematics performance, cognitive appraisals and mathematics-specific,affective anxiety in determining later mathematics achievement and future careerorientation among Finnish adolescents. The basic ideas of the control-valuetheory, assumed to be culturally universal, and previous controversial resultsregarding the relationship between mathematics anxiety and mathematicsachievement were tested in the Finnish cultural context with a longitudinal design.The key premise of the control-value theory is that control and value appraisals aresignificant determinants of both activity and outcome achievement emotions. Ourresults suggest that mathematics anxiety, a prospective outcome emotion, isdetermined by outcome expectancies (success or failure) and outcome value (theimportance of performing well). They also suggest that anxiety as a negativeaffective emotion is a problem not only for those who perform poorly but probablyalso for certain pupils across all achievement levels. Compared with theperformance level and with the boys, the girls exhibited inaccurately low outcomeexpectancies in mathematics. These low expectancies connected to the negativevalue of failure are a potential cause for their higher anxiety level. The educationalimplications of the findings are discussed.

Keywords: mathematics anxiety; cognitive appraisals; outcome expectancy;outcome value; mathematics achievement

Introduction

According to Bandura’s (1986) social cognitive theory, students’ academic self-efficacy beliefs predict their subsequent academic performance. Thus, a judgement ofconfidence in a certain academic domain promotes good performance in a similardomain later on. These self-efficacy beliefs are composed of experiences of priorachievement. Self-efficacy beliefs are also assumed to act as mediators between priorand later performance and, furthermore, these self-related appraisals are assumed tobe important antecedents of human emotions (Pekrun, 2006). According to recentresearch, students experience a range of different emotions related to learning andachievement (Goetz, Frenzel, Pekrun, & Hall, 2006). Almost all common emotions,such as enjoyment, hope, pride, anger, anxiety and shame, can be experienced inacademic settings.

*Corresponding author. Email: [email protected]

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432 M. Kyttälä and P.M. Björn

Academic emotions are important for several reasons. First, because emotions arepertinent components of subjective well-being (Diener, 2000; Diener, Oishi, & Lucas,2003), they are important educational outcomes in themselves. In addition, they directboth interest development and motivation (Izard, 2009; Krapp, 2005; Pekrun, Goetz,Titz, & Perry, 2002) as well as the use of cognitive resources (Derakshan & Eysenck,1998; Easterbrook, 1959; Eysenck & Calvo, 1992; Eysenck, Derakshan, Santos, &Calvo, 2007; Humphreys & Revelle, 1984), affecting student learning and achieve-ment. Finally, academic emotions are considered to predict well future career orienta-tion; emotional attraction to a given domain (e.g. mathematics) arouses the will tochoose a career in that domain (Wigfield, Battle, Keller, & Eccles, 2002).

Academic emotions can be divided into achievement activity emotions andachievement outcome emotions (Pekrun, 2006). Anxiety, which is one of the mostinvestigated emotions in the field of academic achievement, is an outcome emotion.It is determined by both outcome expectancy and outcome value, which Pekrun(2006) refers to as cognitive appraisals. Outcome expectancy refers to the perceivedcontrollability of achievement outcomes and outcome value includes the subjectivevalue of those same outcomes. The control-value theory suggests that a lack ofcontrollability and the negative value of an outcome produce negative outcomeemotions such as anxiety (Pekrun, Elliot, & Maier, 2006). Thus, when a person simul-taneously expects a failure and would like to avoid the failure but thinks that theoutcome (failure) is hard to avoid, anxiety results. Poor outcome expectancies refer topoor self-efficacy beliefs (see Bandura, 1986); a person with poor self-efficacy in acertain domain does not have a judgement of confidence in his own skills in thatdomain. In addition, the outcome value is very important because if a person does notcare about the outcome, negative outcome expectancy alone does not cause anxiety.

Students’ academic emotions, such as anxiety, are organised in domain-specificways (Beasley, Long, & Natali, 2001; Goetz et al., 2006; Pekrun, 2006). Thus, theintensity of different emotions seems to vary depending on the academic domain.Mathematics anxiety, especially mathematics test anxiety, is an active research area inthe field of education. There is a large body of research suggesting that mathematicsanxiety (see, e.g., Ashcraft, 2002; Beilock, 2008; Hembree, 1990) may have an effecton mathematics performance. The term ‘mathematics anxiety’ refers to a state ofdiscomfort, such as fear, tension or distress, when performing mathematical tasks orwhen otherwise faced with mathematics. Simultaneously, anxiety refers to a state ofuncertainty. The object of anxiety is not a danger in itself but rather ‘the uncertaintyabout some event or state which implies a possible danger’ (Miceli & Castelfranchi,2005, p. 295). Mathematics anxiety can be considered a separate anxiety domain.Thus, it is restricted to mathematics, not to achievement in general (Ashcraft &Moore, 2009; Sepie & Keeling, 1978). Furthermore, mathematics anxiety is not just aform of domain-specific test anxiety but rather ‘a person’s negative, affective reactionto situations involving numbers, math, and mathematics calculation’ (Ashcraft &Moore, 2009, p. 197).

The effects of mathematics anxiety

Compelling evidence suggests that mathematics anxiety is connected to poor mathe-matics performance (see the meta-analysis by Ashcraft, 2002; Beilock, 2008;Hembree, 1990). Based on previous research, anxiety has both online and long-termeffects. General anxiety is often accompanied by cognitive processing impairment

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Educational Psychology 433

(e.g. Derakshan & Eysenck, 1998; Easterbrook, 1959; Eysenck & Calvo, 1992;Eysenck et al., 2007; Hopko, Ashcraft, Gute, Ruggiero, & Lewis, 1998; Humphreys& Revelle, 1984), decreasing the information processing resources available. Besidesavoiding mathematics by taking fewer mathematics courses and choosing study fieldsnot connected to mathematics (long-term effects), mathematics anxious students tendto avoid the unpleasantness of mathematics by rushing through the tasks. Thus,regardless of high error rates, they work through difficult problems very fast (onlineeffects; Faust, Aschraft, & Fleck, 1996). The overall avoidance of mathematics istypical of individuals with high mathematics anxiety levels.

Females seem to display higher mathematics anxiety levels than males (Casey,Nuttall, & Pezaris, 1997; Hembree, 1990; Ma & Cartwright, 2003; OECD, 2004;Osborne, 2001), and mathematics anxiety has been observed to be more stable acrosstime in girls than in boys (Ma & Xu, 2004). In Osborne’s (2001) results, the anxietylevel also explained gender differences in mathematics achievement to some extent.However, Hembree (1990) cited evidence suggesting that, compared with males, thehigh anxiety level of females does not always result in lower mathematics performance.

In fact, the relationship between mathematics anxiety and mathematics perfor-mance is marked by controversial results. As stated before, Hembree (1990)concluded that mathematics anxiety depresses performance in mathematics, not viceversa. He (Hembree, 1990) based his conclusion partly on the results of certain treat-ments that have been able to improve the mathematics performance of formerly high-anxious students to the level of low-anxious students. However, based on longitudinaldata, Ma and Xu (2004) showed that prior low achievement in mathematics seemed tocause later anxiety in mathematics but not the other way round. Thus, prior mathemat-ics anxiety did not relate to later low performance in mathematics. There was also asignificant gender difference in the causal pattern: while prior low achievement inmathematics caused later higher mathematics anxiety in boys across the period ofobservations, in girls, prior low achievement was related to later mathematics anxietyonly during certain critical transition points (e.g. from elementary school to juniorhigh school) (Ma & Xu, 2004).

Individuals with high levels of mathematics anxiety do not perform poorly in alldomains of mathematics (Ashcraft, 2002). Thus, it is possible that results concerningthe consequences of mathematics anxiety are strongly dependent on the way the math-ematical skills are measured. The attentional control theory of Eysenck et al. (2007)supports this notion. According to this theory, anxiety depresses performance effi-ciency by distracting the performance but does not necessarily impair performanceeffectiveness. Thus, despite the distraction, the outcome, for example, responseaccuracy, might be at a good level. Eysenck et al. (2007) suggested that the effect ofanxiety on effectiveness might be more impressive when task demands increasebecause then it becomes harder to compensate for the impaired efficiency. This meansthat the effects of anxiety on performance outcome depend simultaneously on both theskills of an anxious individual and the demands of the task to be completed.

The results of the consequences and antecedents of mathematics anxiety may alsobe highly dependent on the measured domain of anxiety (Balo[gbreve] lu & Koçak, 2006).The construct ‘mathematics anxiety’ is multidimensional and has often been separatedinto different domains such as mathematics test anxiety and numerical anxiety (Rounds& Hendel, 1980) or numerical task anxiety, mathematics test anxiety and mathematicscourse anxiety (Alexander & Martray, 1989). Wigfield and Meece (1988) managed toseparate two different components of mathematics anxiety: a negative affective reaction

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(fear, discomfort and nervousness) component and a cognitive (worry about doing well)component. Thus, depending on the measurement, the concept ‘mathematics anxiety’may contain either the affective reaction in different mathematics-related situations orthe cognitive worry about success or both. When investigating the role of mathematicsanxiety and comparing the results of previous studies, the multidimensionality of theconstruct should be taken into account. In fact, it is hard to compare the results of differ-ent studies because the results are highly dependent on the anxiety measurement, whichdiffers from study to study (Keedwell & Snaith, 1996).

In the present study, the concept ‘mathematics anxiety’ is restricted to the affectivecomponent. Beasley et al. (2001) suggested that affective mathematics anxiety is morelike a pervasive trait than a state varying occasionally. The difference between stateand trait anxiety is temporal. State anxiety refers to a momentary anxiety, while traitanxiety refers to a more general proneness to be anxious (Newbegin & Owens, 1996).From an educational perspective, a domain-specific trait anxiety that develops into aconstant negative feeling of uncontrollability can be considered a more severe prob-lem than an occasional state of anxiety. However, it is not clear how this negativeaffective trait is related to previous and later performance in mathematics since mostof the anxiety measurements used in studies concerning this issue usually tap both theaffective reaction and the cognitive worry.

The current study

The aim of this two-year longitudinal study was to investigate the role and impactof prior mathematics performance, cognitive appraisals (outcome expectancy andoutcome value) and mathematics-specific, affective anxiety in determining later math-ematics achievement and future career orientation among Finnish adolescents. Thestudy was designed to test the basic ideas of the control-value theory (Pekrun, 2006),assumed to be culturally universal, in the Finnish cultural context and previous contro-versial results regarding the relationship between mathematics anxiety and mathemat-ics achievement with a longitudinal design. Even though experimental laboratorystudies convincingly suggest that mathematics anxiety depresses performance inmathematics (see Ashcraft & Moore, 2009), the same results are not necessarilyachieved in longitudinal studies (see, e.g., Ma & Xu, 2002). As stated before, insteadof concentrating on mathematics anxiety as a multidimensional phenomenon, wefocused on affective mathematics anxiety to investigate the relations between affec-tive reactions and previous and later performance.

Compared with many other OECD countries, Finnish students form a somewhatdissimilar group. In Finland, children enter formal schooling the year they are sevenyears old, which is later than in many other countries. However, despite this late start,quite extensive international comparisons of mathematical skills among comprehen-sive school pupils have suggested that at approximately 15 years of age, Finnish pupilsappear to achieve rather high results in mathematics (OECD, 2004). Among certainother things, this success probably reflects the important role of mathematics in theFinnish curriculum. The national value of mathematics probably shapes the subjectiveoutcome values of the students, which, in addition to outcome expectancies, aresignificant determinants of academic emotions such as anxiety, according to thecontrol-value theory (see Pekrun, 2006).

In Finland, gender differences in mathematics performance are small; for example,Finnish boys and girls performed equally well in the ‘space-and-shape’ domain of

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mathematics, whereas pupils in other OECD countries exhibited the largest genderdifference in this particular domain (OECD, 2004). However, despite this internationalsuccess and gender equality at the result level, Finnish female students did show a highermathematics anxiety level than male students (OECD, 2004). Thus, in the present study,we expected to find significant gender differences in mathematics anxiety. Applyingthe control-value theory and keeping in mind the national value of achievement in math-ematics, we expected that these gender differences in mathematics anxiety would bemediated by different outcome expectancies rather than different outcome values.These self-related outcome expectancies in mathematics have been observed to besignificantly lower among girls than among boys (Hyde, Fennema, Ryan, Frost, &Hopp, 1990; McGraw, Lubienski, & Strutchens, 2006). However, according to thetheory, the causal, functional relations between emotions, self-related appraisals andachievement were assumed to be universal across genders (Frenzel, Pekrun, & Goetz,2007). Thus, despite the expected differences in the mean level, we tested the samerelations separately for boys and girls, expecting similar functional relations.

In addition to the assumptions of the control-value theory, we tested the possiblestructural relationships between prior mathematics achievement, cognitive appraisals,affective anxiety and later achievement among Finnish adolescents. Even though Maand Xu (2004) observed that prior mathematics anxiety did not relate to later low perfor-mance in mathematics, previous results concerning the effects of mathematics anxietyon performance show that anxiety can have different effects on mathematics achieve-ment in different cultural groups (see, e.g., Nasser & Birenbaum, 2005). Thus, resultsmay vary depending on the cultural group that participants represent. Results may alsovary depending on the measured domain of anxiety (Balo[gbreve] lu & Koçak, 2006).

To test the possible long-term effects of mathematics anxiety, we also tested therelationships between prior mathematics achievement, cognitive appraisals, anxietyand future career orientation. Some Finnish research data focusing on adolescentacademic skills and future career orientation are already available (e.g. Holopainen &Savolainen, 2006; Savolainen, Ahonen, Aro, & Holopainen, 2008). However, theprevious studies have mainly focused on the predictive power of language skills, notmathematical skills and mathematics anxiety.

Based on the theories and previous results, the following hypotheses were set:

H1: Negative outcome expectancy and negative outcome value are determinants ofmathematics anxiety.

H2: Gender differences in mathematics anxiety are mediated by outcome expectancies.H3: Prior low achievement in mathematics predicts later mathematics anxiety, and the

effect of previous mathematics achievement on later mathematics anxiety is medi-ated by outcome expectancies.

H4: The effect of previous mathematics achievement on later mathematics performanceis both direct and mediated by outcome expectancies.

H5: The effect of prior mathematics performance on future career orientation is medi-ated by outcome expectancies and mathematics anxiety.

H6: The functional relations between anxiety, appraisals and achievement are universalacross genders.

Methods

Participants

A total of 116 lower-secondary 13- to 14-year-old female (N = 52) and male (N = 64)students from an urban economic zone in central Finland participated in this two-year

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follow-up study. The sample was selected on the basis of the interest of the participat-ing schools after achieving permission from the school authorities. Participation in thestudy was voluntary and required parental consent. Letters of invitation and participa-tion consent forms were distributed to 121 students, 116 (96%) of whom agreed toparticipate. In the first year of our study, the participants were in the eighth grade. InFinland, the ninth year is the last year of compulsory school. The sample was homo-geneous in terms of race and cultural background. Moreover, all the children spokeFinnish as their native language.

Measures

Mathematics skills

Mathematics skills were measured using the Test for Basic Mathematical Skills forGrades 7–9 (KTLT; Räsänen & Leino, 2005). It is a Finnish paper-and-pencil testused to screen for potential mathematical difficulties. It contains calculation tasksfrom different essential realms of mathematics: addition, subtraction, multiplicationand division tasks both as numeric (e.g. ‘5.01 + 6.7 =’) and as word problems (e.g.‘New curtains will be purchased for the school. There are six classrooms with threewindows in each. There must be two curtains for every window. How many curtainswill be needed altogether?’). The tasks require knowledge of primarily wholenumbers but also fractions and decimals. There are also equation tasks (e.g. ‘Calcu-late −3x when x = 3’) and geometry problems. The test has four parallel versions (A,B, C and D). Versions A (Time 1) and C (Time 3) were used in this study (Figure 1).Each test version contains 40 calculation tasks and has a time limit of 40 minutes.The maximum score is 40. The internal reliability of both the A version and the Cversion in the normative data (N = 1157) was .88 (Räsänen & Leino, 2005). The testalso correlated significantly with other measures of mathematical skills (r = .61–.78,p < .001; Räsänen & Leino, 2005).Figure 1. Three measurement time points.

Mathematics anxiety

Mathematics anxiety was measured using part of the Math Anxiety Questionnaire(MAQ) developed by Wigfield and Meece (1988). In the MAQ, anxiety is rated on aseven-point scale. Only those seven items considered to measure the emotional worrycomponent of mathematics anxiety (negative affective reactions: fear, discomfort andnervousness; see Appendix 1; Wigfield & Meece, 1988) were chosen. The seventhitem was slightly modified to fit this study. The total score was the composite scoreof all the answers. The maximum score was 42. Cronbach’s alpha for this scale in thissample was .73.

Cognitive appraisals

Outcome expectancies were measured with three items of Marsh’s (1990) self-efficacy scale (e.g. ‘I cannot cope with mathematics’, see Appendix 1) using a seven-point scale. The total score was the composite score of all the answers. The maximumscore was 21. Cronbach’s alpha for this scale was .85. Outcome value was measuredwith three items of the cognitive worry part of the MAQ (Wigfield & Meece, 1988)with a seven-point scale. The items in the original version of the MAQ are assumed

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to measure the cognitive worry component of mathematics anxiety. However, tomeasure the experienced personal importance of success or vice versa, the experi-enced negative impact of failure, we used the verb ‘care’ instead of ‘worry’ (seeAppendix 1) when we translated the items into Finnish. Thus, we wanted to tap thepersonal importance of success instead of cognitive worry. The maximum score was21. Cronbach’s alpha for this scale was .55.

Future career orientation

Future career orientation was measured with a questionnaire with a five-point Likertscale developed for this study (see Appendix 1). It included three statements aboutinterest in mathematically oriented study fields or professions (e.g. ‘I am interested inoccupations where mathematical skills are needed’, see Appendix 1). The total scorewas the composite score of all answers. The maximum score was 15. Cronbach’salpha for this scale was .79.

Procedure

There were three separate measurement time points (Figure 1). Mathematical skillswere measured at Time 1 (during the first half of the eighth school year) and Time 3(during the second half of the ninth school year). Cognitive appraisals, mathematicsanxiety and future career orientation were measured at Time 2 (during the first half ofthe ninth school year). Thus, between Times 1 and 2, there were approximately ninemonths and between Times 2 and 3, about seven months.

A trained research assistant administered the questionnaires and the mathematicstests to the children. The participants were tested in groups in a quiet classroom in thepresence of the research assistant and the mathematics teacher or special educationteacher.

Results

Preliminary analysis

The internal consistency of the scales was acceptable (see the task descriptions).Cronbach’s alpha for the scales ranged from .55 (outcome value) to .85 (outcomeexpectancies). Table 1 displays the descriptive statistics for each of the variablesin the study. Correlations between all the variables are also presented in Table 1.Mathematics anxiety (in the ninth grade) correlated significantly and negatively with

Figure 1. Three measurement time points.

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outcome expectancies, mathematical skills in the ninth grade and future careerorientation but not with outcome value and mathematical skills in the eighth grade.One-way ANOVAs (Table 2) show that the boys were significantly more oriented tocareers related to mathematics in the future than girls (F = 4.23, p < .05) and that theyconsidered themselves to be more capable in mathematics (F = 5.01, p < .05) andexperienced less mathematics anxiety than girls (F = 4.87, p < .05). However, nodifferences were found between the boys’ and the girls’ outcome values or perfor-mance in the Test for Basic Mathematical Skills.

Path models

Our hypotheses were tested by path models using Amos 16.0. We tested the fits of allour models with the χ2 statistic and selected fit indices (comparative fit index [CFI]and root mean square error of approximation [RMSEA]). CFIs greater than .95 andRMSEAs less than .06 indicate acceptable model fit (Hu & Bentler, 1999). Only thestatistically significant paths were included in the final models. First, we tested thehypothesis that negative outcome expectancies and positive outcome values are deter-minants of mathematics anxiety (H1; Model 1). Our data support the hypothesis,showing that both outcome expectancies (standardised estimate = −.64, p < .001) andoutcome values (standardised estimate = .33, p < .001) predict the amount of experi-enced anxiety (Figure 2, Model 1). Together, they explain 39% of the variance in theanxiety level. The model is given below.

Table 1. Descriptive statistics and correlations between measured variables.

Measured variable M SD Skewness Kurtosis 1 2 3 4 5

Basic calculation 1a 21.60 6.48 −.374 .713 —Basic calculation 2b 22.82 7.60 −.037 −.622 .72*** —Future orientation 8.70 3.32 .043 −.983 .30** .30** —Outcome expectancy 7.46 4.08 .103 −1.37 .53*** .58*** .55*** —Outcome value 10.55 3.63 .144 .002 .25* .35*** .31** .32** —Mathematics anxiety 19.02 7.10 .050 −.623 −.19 −.23* −.31** −.52*** .11

Note: aTime 1; bTime 3; *p < .05; **p < .01; ***p < .001.

Table 2. Gender differences in measured variables.

Girls Boys

Measured variable M SD M SD F

Basic calculation 1a 20.57 6.23 22.43 6.60 2.25Basic calculation 2b 21.74 7.58 23.65 7.57 1.66Future orientation 7.98 2.79 9.29 3.62 4.23*Outcome expectancy 6.50 3.80 8.23 4.15 5.01*Outcome value 10.58 3.55 10.53 3.72 0.01Mathematics anxiety 20.73 6.99 17.67 6.95 4.87*

Note: aTime 1; bTime 3; *p < .05.

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Figure 2. Model 1.Second, we tested the hypothesis that gender differences in mathematics anxietyare mediated by differences in outcome expectancies (H2; Model 2). As shown by theone-way ANOVAs (Table 2), the girls were significantly more anxious than the boys(F = 4.87, p < .05) and had significantly lower outcome expectancies (F = 5.01,p < .05). Our data supported the hypothesis, showing that gender has both a directeffect on outcome expectancies (standardised estimate = −.21, p < .05) and an indirecteffect on mathematics anxiety via outcome expectancies (standardised estimate = .14)(Figure 3, Model 2). The fit of the model was good (χ2(2) = .87, p = .646, CFI = 1.00,RMSEA = .00). To confirm the mediation hypothesis, we tested an alternative modelwith a direct path from gender to mathematics anxiety. Although the fit of the alterna-tive model was good (χ2(1) = .01, p = .946, CFI = 1.00, RMSEA = .00), gender hadno direct effect on mathematics anxiety (standardised estimate = .07, p = .350),confirming our hypothesis.Figure 3. Model 2.Third, we tested the hypothesis that prior low achievement in mathematics causeslater mathematics anxiety and that the effect of previous mathematics achievement onlater mathematical anxiety is mediated by outcome expectancies (H3). To test themediation hypothesis, we constructed two different models. The first of these(Figure 4, Model 3) included no direct path from prior mathematics performance tolater anxiety. The fit of the model was good (χ2(2) = 3.37, p = .186, CFI = .99,RMSEA =.07). Prior mathematics performance predicts outcome expectancies (stan-dardised estimate = .47, p < .001), which, if taken further, predict mathematics anxiety(standardised estimate = −.64, p < .001). Prior mathematics performance had an indi-rect effect on later mathematics anxiety (standardised estimate = −.29) via outcomeexpectancies. To confirm our mediation hypothesis, an alternative model with a direct

Figure 2. Model 1.

Figure 3. Model 2.

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path from prior mathematics performance to later anxiety was tested. The results showthat the direct effect was not significant (standardised estimate = .07, p = .374), indi-cating that prior mathematics performance had only an indirect effect on later anxiety.Figure 4. Model 3.Fourth, we tested the hypothesis that the effect of previous mathematics achieve-ment on later mathematics performance is both direct and mediated by outcomeexpectancies (H4). The results showed that the fit of the model was good (Figure 5,Model 4; χ2(3) = 4.17, p = .244, CFI = .99, RMSEA = .06). The model further showedthat prior mathematics performance had both a direct effect on later mathematicsperformance and an indirect effect mediated by outcome expectancies. However, theindirect effect was quite low (standardised estimate = .09), suggesting that eventhough outcome expectancies are significant predictors of later mathematics perfor-mance, they do not mediate the influence of prior mathematical skills on later mathe-matical skills. An alternative model with a direct path from anxiety to latermathematics performance was tested. Even though the fit of the model was good(χ2(2) = 3.37, p = .186, CFI = .99, RMSEA = .08), the effect of anxiety on later math-ematics performance (standardised estimate = −.09, p = .370) was not significant.Figure 5. Model 4.Fifth, we tested the hypothesis that the effect of prior mathematics performance onfuture career orientation is mediated by outcome expectancies and mathematics anxi-ety. The fit of the model was good (Figure 6, Model 5; χ2(5) = 4.82, p = .438, CFI =1.00, RMSEA = .00). However, mathematics anxiety had no significant effect onfuture career orientation. Thus, an alternative model without the direct path from anxi-ety to career orientation was tested. The fit of the model was good (χ2(6) = 6.30, p =.390, CFI = 1.00, RMSEA = .02). The results showed that prior mathematics perfor-mance is only indirectly related to later career orientation via outcome expectancies

Figure 4. Model 3.

Figure 5. Model 4.

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(standardised estimate = .23), supporting our mediation hypothesis (H5). Contradictoryto prior assumptions, anxiety did not predict future career orientation.Figure 6. Model 5.Finally, we compared the path structure of the boys and the girls to test the genderuniversality hypothesis (H6) using the multigroup analysis (Arbuckle, 2005). Theresults showed that the common model fits the data from both groups well (χ2(10) =5.95, p = .819). Next, we compared the similarity of the regression estimates for theboys and the girls by testing a model suggesting that boys and girls have the sameregression weights. The model fitted the data well (χ2(15) = 11.49, p = .717). Thus,the regression weights for the boys and the girls did not differ. The covariance matri-ces of the two groups can also be considered to be equal (χ2(10) = 8.68, p = .563).This supports our gender universality hypothesis (H6), suggesting that even thoughgender differences at the mean level may be significant, the functional relations aresimilar.

Discussion

The aim of this two-year longitudinal study was to investigate the role and impact ofprior mathematics performance, cognitive appraisals and mathematics-specific, affec-tive anxiety in determining later mathematics achievement and future career orienta-tion among Finnish adolescents. The theoretical aim was to test the features of thecontrol-value theory among Finnish lower-secondary boys and girls.

First, we tested whether mathematics anxiety is determined by outcome expect-ancy and outcome value. This was exactly the case, supporting not only our firsthypothesis but also the cultural universality hypothesis of the control-value theory(see, e.g., Frenzel et al., 2007). The outcome expectancy was negatively related tomathematics anxiety, indicating that low mathematics outcome expectancy, that is,expecting a failure, was related to higher mathematics anxiety levels. In addition, theoutcome value (How important is it that I perform well?) was positively related toanxiety, indicating that the experienced importance of success is related to higherlevels of mathematics anxiety. Together, these two appraisals can breed a state ofuncontrollability, which is central to the arousal of anxiety (Pekrun, 2006). The fact

Figure 6. Model 5.

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that one expects a failure (I cannot do mathematics well), which, however, is not adesired outcome (it would be important to perform well), induces a negative state ofuncertainty and uncontrollability (I am not sure whether I’ll manage or not). This is inline with the suggestion that anxiety refers not only to a state of fear but rather to astate of uncertainty or dread about a possible event (Miceli & Castelfranchi, 2005).

Just as previous studies have often shown (Casey et al., 1997; Hembree, 1990;OECD, 2004; Osborne, 2001), the girls experienced significantly more anxiety thanthe boys. In fact, as we expected, the girls showed a thoroughly negative profile withlower outcome expectancies, higher mathematics anxiety and less orientation tomathematics in the future, even though they performed just as well as the boys onmathematics test. This is in line with previous results (see Hembree (1990) for areview, and for general test anxiety, see Cassady & Johnson (2002)) showing thateven though girls are significantly more anxious, they do not perform more poorlythan boys. Applying the control-value theory, we expected that these gender differ-ences in mathematics anxiety would be mediated by different outcome expectancies(H2). Our results confirmed this hypothesis, supporting the results of Frenzel et al.(2007). Compared with the boys, the girls had lower outcome expectancies but equalachievement value (the importance of succeeding). Thus, the gap between judgementsof confidence of one’s own mathematics skills and the value of success or failure, onaverage, was larger among the girls than among the boys, which is likely to producethe gender differences in mathematics anxiety.

Third, we tested the hypothesis that prior low achievement in mathematicspredicts later mathematics anxiety and that the effect of previous mathematicsachievement on later mathematics anxiety is mediated by outcome expectancies (H3).The results are in line with those of Ma and Xu (2004), indicating that prior lowachievement in mathematics seems to predict later anxiety in mathematics. However,prior mathematics achievement has only an indirect effect on later mathematics anxi-ety. The effect of prior mathematics performance on anxiety is mediated by outcomeexpectancies. Those students who perform more poorly at the beginning of the eighthgrade have lower self-related outcome expectancies and higher anxiety levels at thebeginning of the ninth grade, which is the final year of compulsory school in Finland.However, mathematics anxiety in the ninth grade reflects far more than performanceexperiences in the eighth grade. If we accept the assumption suggested by the control-value theory that anxiety is a result of an imbalance between outcome expectanciesand outcome values, the reason for this state of anxiety is either inaccurately lowoutcome expectancies or inaccurately high outcome values, not just previous perfor-mance experiences.

Fourth, we tested the hypothesis that the effect of previous mathematics achieve-ment on later mathematics performance is both direct and mediated by outcomeexpectancies but not by mathematics anxiety. The results support our hypothesis (H4)only to a certain extent. First of all, they suggest that among Finnish adolescents, inpredicting later mathematics performance, the effect of prior achievement is not medi-ated by cognitive appraisals. Second, the results show that prior performance is themost powerful predictor of later mathematics performance, which is not surprisingconsidering that mathematical skills at these two time points were measured withparallel versions of the Test for Basic Mathematical Skills. However, in addition, bothoutcome expectancies and outcome values predict later mathematics achievement.Albeit being in line with previous studies showing that self-related outcome expectan-cies and outcome values are important predictors of later success, these results do not

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support the mediation hypothesis. In fact, these results suggest that among Finnishadolescents, mathematics self-related outcome expectations mediate the influence ofsomething other than actual skills.

As expected, based on the results of Ma and Xu (2004), mathematics anxiety didnot predict later mathematics performance. There are at least two potential reasons forthis, which may be either exclusive or supplementary. First of all, according to theattentional control theory (Eysenck et al., 2007), anxiety impairs the performanceoutcome (response accuracy) only when the task demands are high. It is possible thatthese basic calculation tasks used in this study were too easy. Albeit possible, thisexplanation is still unlikely because of the large variation in the test performance andthe lack of a ceiling effect. Second, it is possible that affective mathematics anxiety issimply a less powerful predictor of later mathematical skills than outcome expectan-cies. The outcome expectancies correlated with anxiety, but all the adolescents withlow self-related outcome expectancies were not anxious, most likely because anxietyis a function of an appraisal conflict in which one simultaneously thinks of oneself asa potential failure and values good performance in mathematics. Thus, the students’judgements of confidence in the mathematical domain predicted later performance inmathematics better than mathematics anxiety determined by the instability betweenoutcome expectancies and outcome value.

Fifth, we tested the hypothesis that the effect of prior mathematics performance onfuture career orientation is mediated by outcome expectancies and anxiety (H5). Ourresults do support the hypothesis to some extent. The effect of prior performance onlater career orientation was mediated by outcome expectancies but not anxiety. Foranxiety, this is somewhat against our expectations. Because academic emotions areconsidered to predict well future career choices (Wigfield et al., 2002), we thoughtthat the amount of experienced anxiety would predict career orientation. However,this was not the case. Both outcome expectancies and outcome values were morepowerful predictors of the later career orientation of Finnish students.

Finally, we tested the hypothesis that the functional relations between affectiveanxiety, appraisals and achievement are universal across genders. Our results supportthis gender universality hypothesis, suggesting that the causal pattern between priormathematics performance, cognitive appraisals, anxiety, later mathematics perfor-mance and future career orientation is similar among Finnish boys and girls. Thus,despite the gender differences at the mean level, the functional relations are similar.Our results support the results of Frenzel et al. (2007), suggesting that the antecedentsof mathematics anxiety are universal across genders. Thus, if boys and girls haveequal outcome expectations, they would experience similar anxiety.

When discussing our results, it is important to recognise the limitations of thisstudy. Despite the longitudinal nature of the design, it should be noted that the dataare partly correlational. The relationships between cognitive appraisals, mathematicsanxiety and career orientation are correlational. Thus, the paths between them arepurely based on theoretical premises. Even though this strong theoretical basis can beconsidered a strength, it can also be considered a potential limitation of the designbecause it dismisses possible reversed paths between the variables. It is also importantto note that in addition to the variables studied in this study, other factors also affectmathematics anxiety and later mathematics performance. For example, outcomeexpectancies are not just a sum of prior performance. Other factors, such as parents’beliefs of the academic efficacy of their children (Bandura, Barbaranelli, Caprara, &Pastorelli, 1996) may shape expectancies as well. Further, as the study consists of only

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three measurement time points, opportunities to make judgements about the reciprocalrelationships between the development of mathematical skills and affective mathe-matics anxiety are limited.

Finally, even though our results suggest that affective mathematics anxiety doesnot predict later mathematics performance, it is possible that this result is derived fromour use of linear analysis methods. It has been argued that the relationship betweenmathematics anxiety and performance might in fact be curvilinear (Keeley, Zayac, &Correia, 2008). Keeley et al. (2008) use the term ‘an optimal level of statistics anxi-ety’, that is, a level that can benefit performance. Thus, the anxiety might benefit theperformance to a certain point and depress the performance only after a critical point.Therefore, the use of linear analysis methods may undermine the effect of anxiety.

Conclusions

Our results suggest that anxiety as a negative affective emotion is not a mediator butrather an educational outcome. It is a problem not only for those who perform poorlybut probably also for certain pupils across all achievement levels. Although affectivemathematics anxiety does not seem to predict later mathematics performance or futurecareer orientation, it is likely to affect students’ well-being by creating a negative,constantly high, mathematics-specific state of fear and worry. In fact, Beasley et al.(2001) have suggested that affective mathematics anxiety is more like a pervasive traitthan a state varying occasionally. A trait anxiety is the sum of state anxieties. Thus, ifa person’s state anxiety is consistently high, he or she has a trait anxiety (see Newbegin& Owens, 1996). Compared with the performance level and with the boys, the girlsexhibited inaccurately low outcome expectancies in mathematics, and these lowoutcome expectancies connected to the perceived value of success or the negativevalue of failure are a potential cause for their higher anxiety level.

Educational implications

Our results suggest that when trying to decrease the level of mathematics anxiety, itmight be useful to direct the interventions to the imbalance between outcome expec-tations and outcome values. It should be noted that mathematics anxiety is a domain-specific emotion and perceiving it as a domain-general attribute of an individualdeceptively transfers responsibility from the school and the teacher to an anxious indi-vidual. Recent research shows that the whole learning environment, that is, theemotional atmosphere of the classroom, including the quality and structuredness ofinstruction, emotional experiences in the case of failure and the value beliefs deliveredby the teacher both directly and indirectly, is related to the experience of academicemotions (Frenzel et al., 2007). Thus, in addition to individual interventions, class-level interventions might also be useful.

Even though the functional relations between mathematics performance, outcomeexpectancies and outcome values are similar across genders, the negative self- andmathematics-related profile of girls is an educational problem. In Finland, forinstance, quite extensive comparisons of mathematics skills among comprehensiveschool pupils have suggested that gender differences in the performance level aresmall (Kupari, Reinikainen, Nevanpää, & Törnroos, 2001; OECD, 2004), but despitethis, males are overrepresented in fields related to mathematics and engineering.Based on international studies, this domination is probably not solely due to superior

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abilities (cf. Benbow, Lubinski, Shea, & Eftekhari-Sanjani, 2000; Quaiser-Pohl &Lehmann, 2002). Even girls with superior mathematical ability at the age of 13 appearto prefer careers other than those in the field of engineering and mathematics (Benbowet al., 2000). This problem cannot be solved just by perceiving the lower outcomeexpectancy and higher anxiety of the girls as a gender-specific attribute but rather aneducational outcome that can be affected.

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Appendix 1

Mathematics anxiety (i.e. the emotional worry component of mathematics anxiety [negativeaffective reactions: fear, discomfort and nervousness; see Wigfield & Meece, 1988])

1. When the teacher says that he or she is going to ask you some questions to find outhow much you know about math, how much do you worry that you will do poorly?(not at all, very much)

2. When the teacher is showing the class how to do a problem, how much do you worrythat other students might understand the problem better than you? (not at all, verymuch)

3. When I am in math class, I usually feel (not at all at ease and relaxed, very much atease and relaxed)

4. When I am taking math tests, I usually feel (not at all nervous and uneasy, very nervousand uneasy)

5. Taking math tests scares me. (I never feel this way, I very often feel this way)6. I dread having to do math. (I never feel this way, I very often feel this way)7. It scares me to think that I will have to do demanding math tasks. (not at all, very

much)

Cognitive appraisals

Outcome expectancies (Marsh, 1990):

1. I have always done well in mathematics. (I totally disagree, I totally agree)2. I get good marks in mathematics. (I totally disagree, I totally agree)3. I cannot cope with mathematics. (I totally disagree, I totally agree)

Outcome values (Wigfield & Meece, 1988):

1. If you are absent from school and you miss a math assignment, how much do you carethat you will be behind the other students when you come back to school? (not at all,very much)

2. In general, how much do you care about how well you are doing in math? (not at all,very much)

3. Compared to other subjects, how much do you care about how well you are doing inmath? (much less than other subjects, much more than other subjects)

Future career orientation

1. I am interested in occupations where mathematical skills are needed. (I totallydisagree, I totally agree)

2. I will avoid mathematics in the future if I only can. (I totally disagree, I totally agree)3. I am going to need mathematical skills in the future. (I totally disagree, I totally agree)

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prior mathematics achievement, cognitive appraisals and anxiety as predictors of finnish students’...

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