1877-0428 © 2010 Published by Elsevier Ltd.doi:10.1016/j.sbspro.2010.07.186

Procedia Social and Behavioral Sciences 5 (2010) 791–797

Available online at www.sciencedirect.com

WCPCG-2010

The relation of epistemological beliefs and mathematics achievement: the mediating role of achievement goals, mathematics

self-efficacy, and cognitive engagement

Ahmad Rastegara, Reza Ghorban Jahromib *, Abdorahman Salim Haghighic, Ahmad Reza Akbaria

aPayame Noor University, Kharameh 767676, Fars, IranbUniversity of Tehran, Tehran 14155-6456, Tehran, Iran cAzad University of Sepidan, Sepidan 73617 , Fars, Iran

Received January 4, 2010; revised January 20, 2010; accepted March 17, 2010

Abstract

The aim of this study was investigating the relationship between epistemological beliefs and mathematics achievement, as for the mediating role of achievement goals, mathematics self-efficacy, and cognitive engagement. To do this, 473 (283 female and 190 male) students from basic sciences fields of Fars Payame Noor University were chosen through multistage cluster sampling. They then, answered to a questionnaire composed of 4 subscales. The math course score was also considered as the math achievement index. The results showed that achievement goals, mathematics self-efficacy, and cognitive engagement have a mediating role between dimensions of epistemological beliefs and math achievement. © 2010 Elsevier Ltd. All rights reserved.

Keywords: Epistemological beliefs, achievement goals, mathematics self-efficacy, cognitive engagement, mathematics achievement.

1. Introduction

Today, higher education systems around the world are trying to help develop mental abilities and logical reasoning power in their learners by including mathematics in their curriculum and also aid them to be synchronized with scientific advances, technology developments and future life. Certainly, the attainment of such goals requires that the problems over the way students learn math courses are identified.

In the past few years a lot of researches have been done on metacognition and individuals’ beliefs about the nature of knowledge and learning, or epistemological beliefs, have recently been investigated with the assumption that they comprise a part of the underlying mechanism of metacognition (Schommer, 1990). Educational psychologists have viewed epistemological beliefs typically as systems of implicit assumptions and beliefs about the nature of knowledge and its acquisition held by students (Bruning, Schraw, & Ronning, 1999). This

* Reza Ghorban Jahromi. Tel.: +98-917-190-4652; fax: +98-21-8824-4328. E-mail address: rjahromi@ut.ac.ir.

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multidimensional system comprises beliefs about the structure of knowledge, the stability of knowledge, the speed of knowledge acquisition and the control of knowledge acquisition (Paulsen & Feldman, 2005). These dimensions lay on a continuum with the naïve beliefs on one end and the sophisticated beliefs on the other. Those with naïve beliefs believe that knowledge is simple and attained from an authority, moreover the person has no control on his learning and only intelligent people are able to learn. On the other hand, those with sophisticated beliefs think that knowledge has a complex structure and its information is less stable, the individual himself constructs the meaning and concept, and has control on has learning.

“Achievement goals” stands for a comprehensive semantic system of situations or contexts which have cognitive, emotional, and behavioral outcomes and learners use them to interpret their performances (Dweck & Legget, 1988; Kaplan & Maehr, 1999). The concept of achievement goals generally denotes the students’ reasons for doing tasks (Braten & Stromso, 2004). Recently, Elliot et al. (Elliot & Church, 1997; Elliot & Harachkiewicz, 1996) has proposed a three dimensional framework of achievement goals. According to this view, the students with performance-approach goals assume the activity they do to achieve a goal and demonstrate themselves to others a competition. Moreover, these students tend to emphasize demonstrating their skills in comparison with others. Further, those who adopt performance-avoidance goals concentrate on avoiding lack of skills in comparison with peers and classmates and their attention is on avoiding failure. Finally, the outcome of such a goal setting is feeling inefficient. At last, those who adopt mastery goals insist on elaborating their skills, learning, and mastery.

Recently, some research has studied the relationship between epistemological beliefs and achievement goals. For example, some research has considered epistemological beliefs as a personal agent and a very important antecedent for achievement goals (Braten & Stromso, 2004, 2005; Ghorban-Jahromi, 2007).

Also, some researchers have studied the relationship between achievement goals and academic achievement. For example, some studies have shown that mastery goals are positively (Church, Elliot, & Gable, 2001; Wolters, Yu, & Pintrich, 1996), performance-approach goals are positively (Elliot & McGregor, 2001; Harackiewicz et al. 2000), and performance-avoidance goals are negatively (Elliot & McGregor, 1999; Rastegar, 2006) related to academic achievement. In contrast, some research in this regard has achieved findings which are inconsistent with the abovementioned ones (Harackiewicz et al. 2000; Elliot & McGregor, 2001; Pintrich, 2000). Considering this, it seems that achievement goals, through other variables like self-efficacy and cognitive engagement, can influence mathematics achievement (Ekizo lu & Tezer, 2007). Mathematics self-efficacy refers to individual beliefs about his personal ability for successful performance on the math tasks.

Cognitive engagement refers to all kinds of processing processes used by students for learning (Ravindran, Greene, & DeBacker, 2000) and includes cognitive and metacognitive strategies.

In this area and according to achievement goals theory, mastery goals are related to adaptive patterns of learning such as self-efficacy (Schunk, 1996; Skaalvik, 1997) and persistence in doing academic tasks (Elliot, McGregor, & Gable, 1999). In addition, the relation of performance-approach goals and learning efficiencies is different with regard to the nature of efficiencies, characteristics of individuals, and environmental conditions. For example, in Midgley, Anderman, & Hicks (1995), and Midgley & Urdan's (1995) research, there was a positive relationship, but in Anderman & Young's (1994) studies there was a negative relationship between performance-approach goals and self-efficacy. Meanwhile, the results of some research have also shown that people's perceptions of their own abilities are related to high levels of utilization of learning strategies and metacognition (Elliot, McGregor, & Gable, 1999; Wolters, 2004; Mohsenpour, 2005). Researchers have also reported that the adoption of mastery goals is positively related to deep processing strategies such as metacognitive strategies (Ravindran, et al. 2000; Dupeyrat & Marine, 2005; Simons, Dewitte, Lens, 2004; Rastegar, 2006). Adoption of performance-approach goals (Ravindran, et al. 2000; Dupeyrat & Marine, 2005; Rastegar, 2006) and also performance-avoidance goals (Elliot, McGregor & Gable, 1999; Simons, et al. 2004) has been positively related to using low-level and cognitive strategies. On the other hand, some studies have investigated the relations between cognitive and metacognitive strategies with academic achievement. Research has shown that the use of deep and metacognitive strategies has positive (Simons, et al. 2004; Rastegar, 2006) and low-level cognitive strategies has negative relation with academic achievement (Ravindran, et al. 2000; Simons, et al. 2004; Rastegar, 2006). With regard to what was mentioned, the basic problem in the present study is investigating the meditational roles of achievement goals, mathematics self-efficacy, and different dimensions of cognitive engagement among epistemological beliefs and math performance of Fars Payame Noor University students in mathematics related courses. Thus, for this purpose, based on the existing theoretical basis and previous research results that were referred to, a conceptual model is introduced (Figure 1).

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Figure 1. A theoretical model depicting the relations between epistemological beliefs, achievement goals, mathematics self-efficacy, cognitive engagement, and mathematics achievement.

2. Methodology

The present study was done with a correlation design and qualitative (non experimental) method.

2.1. Participants

All students in basic science (except for mathematics discipline) that had chosen the general mathematics course (No.2) constitutes the population of this study (N=5783). In this study, multi-stage cluster sampling was used. For this purpose, each of the north, south, east, west, and centre areas of Fars province was considered as a cluster and with regard to the approximately equal number of students and university centres in the abovementioned areas, a university centre was selected randomly from each area. In next step, from each centre, two classes which had chosen the course were randomly selected as our sample. This way, totally 10 classes were selected including 490 students (290 girls and 200 boys). Of course, leaving the undermined collected questionnaires, the sample size was ultimately lessened to 473 (283 girls and 190 boys).

2.2. Instruments

Based on the self-report questionnaires of achievement goals and mathematics self-efficacy by Middleton & Midgley (1997), the revised form of the Schommer epistemological beliefs questionnaire (SEQ) by Braten & Stromso (2004), and the subscale of cognitive engagement (MSLQ) by Pintrich et al. (1991), a questionnaire containing 61 items was formed to collect data. The reliability of the subscales was calculated through Cronbach's method and confirmatory factor analysis was run to find its construct validity. Moreover, the students' score in general mathematics course was considered as their mathematics achievement.

3. Findings

Path analysis was applied to test the conceptual model. Table 1 includes information about correlation matrix of the sample along with correlation coefficients and their significance level.

Fixed Ability

Simple Knowledge

Performance-Approach

Goals

Mastery Goals

Performance-Avoidance

Goals

Math Performance

Certain Knowledge

Quick Learning

Cognitive Strategies

Math Self-efficacy

Metacognitive Strategies

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Table 1. The correlations among variables involved in the model

* P< .05 ** P< .01

As the table shows, belief in certain knowledge (-.08) among exogenous variables and metacognitive strategies (.55) among endogenous variables had the most total effect on mathematics achievement. Besides, all the three direct, indirect and total effects of performance-avoidance goals on mathematics achievement are negative. Also the explained variance for mathematics achievement is 42%.

None of the exogenous variables have direct effect on metacognitive strategies. The most indirect effect on metacognitive strategies__ among exogenous variables __ was associated with belief in certain knowledge (.36) whereas, belief in quick learning had no effect on metacognitive strategies. Among endogenous variables, mastery goals influence metacognitive strategies directly (.25) and indirectly (.05), both significant. Totally, mastery goals had larger total effect on metacognitive strategies. In addition, the explained variance for mathematics achievement through achievement goals and mathematics self-efficacy is 9%. All endogenous variables have only indirect effect on cognitive strategies among them belief in certain knowledge has the most total effect (.04). Among endogenous variables, only performance-approach goals influence cognitive strategies directly (.21) and indirectly (.01), which only the direct effect is significant. The explained variance for cognitive strategies is 8%.

None of the exogenous variables have direct effect on mathematics self-efficacy; among them, belief in fixed ability and certain knowledge have the most indirect effect on mathematics self-efficacy. None of the endogenous variables have indirect effect on mathematics self-efficacy; among them, mastery goals have the most direct and total effect on mathematics self-efficacy (.42). The explained variance for mathematics self-efficacy is 20%.

None of the exogenous variables have indirect effect on achievement goals. Among them, belief in certain knowledge and certain knowledge has the most direct effect on mastery goals (-.20) whereas, the direct effect of belief in simple knowledge and quick learning on mastery goals is not significant.

In addition, belief in quick learning _among exogenous variables_ has the most direct effect on performance-approach goals. Also, belief in simple knowledge and certain knowledge have no direct effect on performance-approach goals.

Among exogenous variables, belief in certain knowledge has the most direct effect on performance-avoidance goals. Finally, the direct effect of belief in simple knowledge on performance-avoidance goals is not significant. The explained variance for mastery goals, performance-approach goals, and performance-avoidance goals is 7%, 4% and 7% respectively.

11 10 9 8 7 6 5 4 3 2 1 Variables .1 Belief in fixed

ability

.73 1 -.02 Belief in simple

knowledge

.75 1 .21** -.06 Belief in quick learning

.1 .03 .04 -.02 Belief in certain

knowledge

.1 .20** .07 .19** .11* Performance-

avoidance goals

.1 -.02 -.20** -.001 -.03 -.16** Mastery goals

.1 .009 .14** -.02 .15** .10* -.13** Performance-

approach goals

.1 .15** .43** .05 -.02 -.003 .07 -.04 Math self-efficacy

.1 -.05 .22** -.11* .21** .11* .02 .03 -.01 Cognitive strategies

.1 -.12** .21** -.02 .29** -.21** -.09 -.004 -.06 -.08 Metacognitive strategies

1 .62** -.20** .29** .09 .26** -.25** -.07 -.07 -.04 -.13** Mathematics achievement

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Figure. 2. The fitted model of mathematics achievement prediction, depicting the relations between epistemological beliefs, achievement goals, mathematics self-efficacy, cognitive engagement, and mathematics achievement.

4. Discussion

The results of path analysis revealed that the proposed model is relatively well-fitted with the present study’s data and can explain 42% of mathematics achievement variance.

The direct negative effect of the belief in fixed ability on mastery goals is in line with Paulsen & Feldman (2005), and Ghorban-Jahromi’s (2007) research findings. However, regarding the negative relation between the belief in fixed ability and performance-approach goals, our results are contrary to Ghorban-Jahromi (2007) and consistent with Paulsen & Feldman’s (2005) findings. Regarding this difference in findings, Midgley, Kaplan, & Middleton (2001) believe that performance-approach goals are influenced by the nature of learning efficiencies, characteristics of individuals, and environmental conditions.

The results rejected the direct and negative effect of the belief in simple knowledge on mastery goals but showed that this belief influence performance-avoidance goals directly and positively. In this regard, our findings are in line with Paulsen & Feldman (2005) and Ghorban-Jahromi’s (2007) findings.

The results also revealed that the belief in quick learning has a direct positive effect on performance-approach goals, whereas the direct and negative effect of this belief on mastery goals on one hand and the direct and positive effect of that on performance-avoidance goals were not confirmed on the other. Regarding the direct effect of the belief in quick learning, our findings are consistent with that of Braten & Stromso (2004). In addition, our findings regarding mastery goals are in line with Ghorban-Jahromi’s (2007) research findings but regarding performance-avoidance goals, the results are not consistent with Braten & Stromso (2005), Paulsen & Feldman (2005), and Ghorban-Jahromi’s (2007) findings. Regarding this inconsistency we think that it is because of the different education system of Payame Noor University with other ones.

Moreover, the direct positive effect of the belief in certain knowledge on performance-avoidance goals is consistent with Braten & Stromso (2004), and Ghorban-Jahromi’s (2007) findings.

Regarding the relationships between dimensions of epistemological beliefs and achievement goals, the results generally indicate that those students who believe that the knowledge is certain and absolute, don't consider learning as a valuable goal and don't intend to increase their understandings and gain new insights. These students focus on avoiding lack of skills compared with peers and avoiding failure. Finally, the outcome of such a goal setting is feeling inefficiency.

Mastery Goals

Performance-Avoidance

Goals

Math Performance

Cognitive Strategies

Metacognitive Strategies

- .12**

- .16**

.15**

- .20**

.19**

Quick Learning

Certain Knowledge

Simple Knowledge

Fixed Ability

.19**

- .13** .21**

.14**

.42**

.18**

Performance-Approach

GoalsMath

Self-efficacy

.55**

.18**

.25**

.11**

- .10**

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The direct positive effect of performance-avoidance goals on cognitive strategies is in line with Elliot & McGregor (2001), Rastegar (2006), and Hejazi et al.’s (2008) research findings. Also, the direct negative effect of performance-avoidance goals on mathematics achievement is consistent with those of Elliot et al. (1999), Church, Elliot, & Gable (2001), Wolters (2004), Rastegar (2006), and Hejazi, et al.’s (2008) research findings.

Findings also revealed that performance-approach goals have direct positive effect on cognitive strategies. This is in line with Elliot & McGregor (2001), Simons et al. (2004), Dupeyrat & Marine (2005), Rastegar (2006), and Hejazi, et al.’s (2008) findings. The direct positive effect of performance-approach goals on mathematics self-efficacy is consistent with Midgley, Anderman, & Hicks (1995), and Midgley & Urdan’s (1995) findings, but is not consistent with that of Anderman & Young (1994). Regarding these contradictions, Midgley, Kaplan, & Middleton (2001) believe that performance-approach goals are influenced by the nature of learning efficiencies, characteristics of individuals, and environmental conditions. Moreover, the positive direct effect of mastery goals on metacognitive strategies is in line with Elliot & McGregor (2001), Dupeyrat & Marine (2005), Rastegar (2006), and Hejazi, et al.’s (2008) research findings. And, regarding the direct positive effect of mastery goals on mathematics self-efficacy, results are consistent with Elliot, McGregor & Gable (1999), and Middleton & Midgley (1997).

The direct positive effect of mathematics self-efficacy on mathematics achievement is consistent with Greene et al. (2004), and findings. The positive direct effect of mathematics self-efficacy on metacognitive strategies being significant and the direct effect of it on cognitive strategies being no significant, it should be said that in accordance with Wolters (2004), and Elliot, McGregor & Gable's (1999) research, self-efficacy is related to high levels of benefiting from learning strategies.

The significant direct negative effect of cognitive strategies on mathematics achievement is in line with Ravindran et al. (2000), Rastegar (2006), and Hejazi, et al.’s (2008) research findings.

The significant direct effect of metacognitive strategies on mathematics achievement is in line with Ravindran et al. (2000), Rastegar (2006), and Hejazi, et al.’s (2008) findings.

It should be mentioned that the indirect effect of epistemological beliefs on mathematics performance which is done through achievement goals, mathematics self-efficacy and cognitive engagement, is not far from expectation; as Braten & Stromso (2004) have considered students’ beliefs about knowledge and knowing, or personal epistemologies, as an especially important antecedent of achievement goals.

The indirect negative effect of Performance-avoidance goals on mathematics achievement through cognitive strategies indirectly is in line with Rastegar (2006), and Hejazi, et al.’s (2008) findings.

The indirect positive effect of mastery goals on mathematics achievement through metacognitive strategies and mathematics self-efficacy is in line with Elliot, McGregor & Gable (1999), Middleton & Midgley (1997), Rastegar (2006), and Mohsenpour, et al.’s (2006) findings.

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