the relationship among self-concept, self-efficacy, and performance in mathematics during secondary...

The Relationship Among Self-Concept, Self-Efficacy, and Performance inMathematics During Secondary School

James Pietsch, Richard Walker, and Elaine ChapmanUniversity of Sydney

The relationship among self-concept, self-efficacy, and performance in mathematics was examinedamong 416 high school students. Participants completed a questionnaire assessing mathematics self-concept and mathematics self-efficacy. Performance was assessed using end-of-term exam results inmathematics. Confirmatory factor analyses supported the existence of two self-concept components—acompetency component and an affective component. Self-efficacy items and the competency items ofself-concept also loaded on a single factor. Social comparison information was equally influential in theformation of each construct. Self-efficacy beliefs, however, were identified as most highly related withperformance in mathematics and percentages.

Research into self-perceptions has identified self-efficacy as asignificant self-perception across a wide range of academic con-texts. Self-efficacy refers to beliefs in one’s capabilities to organizeand execute courses of action required to achieve certain perfor-mance outcomes (Bandura, 1997). The influence of efficacy be-liefs within academic contexts is pervasive as a significant predic-tor of academic performance (Bandura, 1997; Chemers, Hu, &Garcia, 2001; Zimmerman, Bandura, & Martinez-Pons, 1992) andas a mediating variable influencing students’ levels of effort,persistence and perseverance (Brown & Inouye, 1978; Schunk,1984, 1989; Zeldin & Pajares, 2000), emotional states (Bandura,1993; Meece, Wigfield, & Eccles, 1990), and self-regulation(Schunk & Swartz, 1993). Research in a wide range of academiccontexts attests to the importance of enhancing efficacy beliefs toachieve substantive outcomes, such as increased levels of aca-demic performance in writing (Schunk & Rice, 1987; Schunk &Swartz, 1993), mathematics (Schunk, 1983, 1984; Schunk & Cox,1986), and general academic performance (Bandura, 1997; Lent,Brown, & Gore, 1997; Multon, Brown, & Lent, 1991; Zimmermanet al., 1992).

Recently, more explicit attention has been focused on constructcomparisons and differentiating between self-efficacy and otherself-perceptions such as self-concept. Self-concept refers to self-perceptions formed through experience with the environment and,in particular, through environmental reinforcements and the re-flected appraisals of others (Marsh & Craven, 1997) and is typi-

cally measured at a higher level of generality than self-efficacy(Pajares & Miller, 1994). This approach has been taken to maxi-mize predictive utility by ensuring correspondence between theself-efficacy items and the target performance (Pajares, 1997;Pajares & Schunk, 2002).

This has led some researchers to distinguish between these twoconstructs on the basis of the level of generality at which eachconstruct is formed. Bandura (1997), however, has argued forefficacy beliefs existing at different levels of generality and hasassessed self-efficacy using general items such as “How well canyou learn science?” when investigating students’ general perfor-mance in academic subjects (Bandura, 2001; Zimmerman et al.,1992). According to Bandura (1997), efficacy beliefs demonstratethe greatest predictive utility when measured at the same level ofgenerality as the performance under investigation. Accordingly,more recent research within the area has assessed self-efficacy atdifferent levels of generality (Bong, 1999).

Beyond the issue of generality, three key distinctions betweenthese constructs have been made, each of which form the basis forthe hypotheses of the present study. First, whereas both constructsincorporate cognitive appraisals of the self, definitions of self-concept incorporate affective responses to the self (Bong & Clark,1999; Pajares & Miller, 1994; Pajares & Schunk, 2002). Second,theorists have also argued that self-concept beliefs are moreheavily influenced by processes of social comparison than efficacybeliefs (Bong & Clark, 1999). Third, attempts to compare thepredictive utility of each of these constructs have demonstratedthat efficacy beliefs have a stronger association with academicperformance than self-concept (Marsh, Roche, Pajares, & Miller,1997; Pajares & Miller, 1994; Skaalvik & Rankin, 1998).

Affective Component of Self-Concept

One distinction relates to the relative complexity of each con-struct (Bong & Clark, 1999). Self-efficacy beliefs represent pri-marily cognitive assessments of competence (Bandura, 1977,1997; Bong & Clark, 1999), whereas self-concept beliefs, asmeasured by the Self-Description Questionnaire—II (SDQ–II;Marsh, 1992), include affective self-perceptions relevant within

James Pietsch, Richard Walker, and Elaine Chapman, School of Devel-opment and Learning, University of Sydney, Sydney, New South Wales,Australia.

This article is based on a dissertation completed at the University ofSydney. An earlier version of this article was presented at the 14th AnnualAustralasian Human Development Association Conference in Brisbane,Queensland, Australia, July 2001. We thank Ray Debus for his invaluablesuggestions.

Correspondence concerning this article should be addressed to JamesPietsch, School of Development and Learning, Faculty of Education,University of Sydney, Sydney, New South Wales 2006, Australia. E-mail:[email protected]

Journal of Educational Psychology Copyright 2003 by the American Psychological Association, Inc.2003, Vol. 95, No. 3, 589–603 0022-0663/03/$12.00 DOI: 10.1037/0022-0663.95.3.589

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different contexts as well as cognitive descriptions of competence.Although there exist multiple theoretical definitions of self-concept, some of which do separate the cognitive and the affectivecomponents into two distinct constructs, researchers using a widerange of self-concept instruments have incorporated affectiveitems in their measures of self-concept (Chapman & Tunmer,1995; Lent et al., 1997; Markus & Nurius, 1986; Marsh, Craven,& Debus, 1999; Pajares & Miller, 1994).

Efficacy beliefs linked to different domains of functioning, incontrast to domain-specific self-concept, deal primarily with cog-nitive perceptions of capability (Bong & Clark, 1999) and areformed through reflecting on enactive mastery experiences, vicar-ious experiences, persuasory messages, and physiological infor-mation (Bandura, 1977, 1997; Schunk, 1994). The existence of anaffective component within subject-specific self-concepts (Chap-man & Tunmer, 1995; Marsh et al., 1999) may differentiatesubject-specific self-concept beliefs from efficacy beliefs mea-sured at the same level of generality.

Pajares and Schunk (2002) offered a useful conceptual frame-work for comparing the two constructs. They suggested that thedevelopment of efficacy beliefs and self-concept beliefs occurthrough asking different questions. Efficacy beliefs are formed byasking “can” questions (“Can I do this mathematical problem?”),whereas self-concept beliefs are formed by asking questions of“being” and “feeling” (“Am I good at mathematics?” “How do Ifeel about myself as a mathematics learner?”). Similarly, Bong andSkaalvik (2003) argued that self-concept has a cognitive and anaffective component, whereas self-efficacy relates to cognitiveappraisals of competence.

This framework, drawn from Bong and Clark (1999), makes aclear distinction between self-concept and self-efficacy by present-ing the former as a more complex construct incorporating bothcognitive and affective self-perceptions. Notions of being that leadto the development of subject-specific self-concept beliefs, how-ever, are likely to be closely linked with perceptions of compe-tence. Thus, can questions (efficacy beliefs) and being questions(self-concept beliefs) may contain significant conceptual overlapwithin academic contexts such as mathematics. When affectiveitems are removed from self-concept measures, therefore, theremaining self-concept items and items measuring self-efficacybeliefs are likely to load on a single factor. Several studies havedemonstrated that self-concept, as measured by the SDQ–II, con-sists of two distinct components (Marsh et al., 1999; Skaalvik &Rankin, 1996; Tanzer, 1996). Marsh et al. (1999) obtained empir-ical evidence for the existence of a competency and an affectivecomponent within each subject-specific self-concept.

The Role of Social Comparison Information

A second theoretical distinction between self-concept and effi-cacy beliefs relates to the role that social comparison plays in theformation of these beliefs (Bong & Clark, 1999; Bong & Skaalvik,2003). The self-concept is partially formed through the reflectedappraisals of others. Self-efficacy, by way of contrast, is primarilybased on perceptions of mastery rather than normative criteria(Zimmerman, 1995). Although Bandura (1986, 1997) identifiedvicarious experience as a source of efficacy information, priormastery experience is by far the most significant source of efficacyinformation.

Despite this point, efficacy theory does acknowledge the rolethat social comparisons in the form of vicarious experiences canplay in the formation of efficacy beliefs. Studies have demon-strated that social comparison information does influence efficacybeliefs (Schunk, 1983; Zeldin & Pajares, 2000). Self-efficacytheorists do, however, argue that efficacy beliefs develop fromsocial information of a somewhat different nature. Instead ofnormative criteria, efficacy beliefs develop from vicarious experi-ence, by interpreting the performances of others to develop one’sown perceptions of competence. Cognitive assessments of one’srelative similarity to the person performing the task and the rela-tive difficulty of the task performed contribute to the formation ofefficacy beliefs (Schunk, 1981, 1987; Schunk & Hanson, 1985).

The relative importance of social comparison in the formation ofthe two constructs may, however, depend on the level of generalityat which the constructs are assessed. General perceptions of com-petence may rely more heavily on social comparisons rather thanon prior experience in circumstances where prior experience is notreadily available (Skaalvik & Rankin, 1997, 1998). For example,in mathematics, students do not have prior experience in theparticular mathematics course they are currently attempting. Todetermine perceived competence for successfully completing theirmathematics course, therefore, students cannot rely on past mas-tery experiences in these particular courses. Instead, students mayuse normative information regarding their relative standing in theirgrade or year at school to determine their own perceptions ofcompetence at higher levels of generality. General efficacy formathematics and mathematics self-concept, therefore, may beequally dependent on students’ perceptions of their relative stand-ing with their peers.

The Predictive Utility of Self-Efficacy and Self-Concept

Evidence for the predictive utility of self-efficacy and self-concept suggests that the causal relationship between self-efficacyand academic performance is more consistent (Bandura, 1997;Schunk, 1989; Zimmerman, 1995) than that for self-concept(Marsh, 1990; Marsh & Craven, 1997), according to Bong andClark (1999). The results of previous research do not, however,provide clear evidence for the superior predictive utility of self-efficacy. Self-efficacy and self-concept need to be measured atcomparable levels of generality that correspond with the level ofgenerality of the performance indicator. Studies incorporatingmeasures of self-concept and self-efficacy, however, have revealedconflicting results. Much research into self-efficacy and self-concept, in attempting to compare the predictive utility ofself-efficacy and self-concept, has measured self-efficacy and self-concept using different scales developed independently for eachconstruct measuring both constructs at different levels of general-ity (Lent et al., 1997; Norwich, 1987; Pajares & Miller, 1994;Skaalvik & Rankin, 1998). Typically, the construct measured atthe same level of generality as the performance outcome demon-strates greater predictive utility (Marsh et al., 1997; Norwich,1987; Pajares & Miller, 1994). Furthermore, such studies haveincorporated in their measures of self-concept an evaluative oraffective component that may be less related to academic perfor-mance than the competence component.

As outlined previously, however, a conceptual distinction be-tween efficacy beliefs and competence-related self-concept beliefs

590 PIETSCH, WALKER, AND CHAPMAN

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has been offered by Pajares and Schunk (2002) who suggested thatefficacy beliefs are formed by asking can questions, whereasself-concept beliefs are formed by asking questions about being.Although significant conceptual overlap appears to exist betweenthese constructs, it remains to be seen whether the framing ofcompetence in terms of tasks that can be achieved or in terms ofpersonal ability is most clearly associated with performance onthese tasks. Self-efficacy beliefs should be more highly related toacademic achievement than self-concept because efficacy scalesrequire responses relating to personal confidence of achievingcertain outcomes, rather than the assessment of personal charac-teristics regarding general ability.

Hypotheses

Three hypotheses were examined within the present study re-lating to self-efficacy and self-concept for mathematics drawing onthe theoretical framework offered by Bong and Clark (1999). Itwas hypothesized that when the affective component of self-concept was removed from measures of mathematics self-concept,the remaining competence component of mathematics self-conceptand efficacy beliefs for mathematics would load on a single factor.Before examining this hypothesis, we examined the complexity ofself-concept beliefs through a replication of Marsh et al.’s (1999)study identifying two components to subject-specific self-con-cepts—a competency-based component and an affective compo-nent. The second hypothesis was directly related to Bong andClark’s second distinction between self-efficacy and self-con-cept—the greater role of social comparison information in theformation of self-concept beliefs compared with efficacy beliefs.In the present study, it was hypothesized that measures of socialcomparison would have an equal impact on self-concept beliefsand domain-specific self-efficacy beliefs when these constructs aremeasured at higher levels of generality because students are morelikely to rely on normative information when prior experience inparticular mathematics courses is not readily available for theformation of efficacy beliefs. Finally, it was hypothesized thatself-efficacy measures demonstrate more predictive utility thancompetency-related self-concept measures because of the perfor-mance focus of self-efficacy items in comparison with the personalcharacteristic focus of self-concept items.

Method

Participants

Four-hundred and sixteen high school students ranging in age from 13years to 16 years (M � 15.0 years, SD � 0.5 years) from a coeducationalcomprehensive high school in southwest Sydney, New South Wales, Aus-tralia, participated in this study. The particular school that participated inthe study was chosen because of its comprehensive character and diversecultural groups whose students perform just below the state average inEnglish exams. All students from Grades 9 and 10 participated in the study(207 from Grade 9 and 209 from Grade 10) including students of very highability and students of very low ability in mathematics (136 from theadvanced stream, 137 from the middle stream, and 143 from the lowerstream). Participants in this study were from a low socioeconomic back-ground, and 80% of participants were from non-English-speaking back-grounds reflecting the multicultural environment of many schools in south-western Sydney. A wide range of over 20 cultural groups participated in the

present study, the largest group being Vietnamese students (104 students),and 174 students in total were from southeast Asian cultural groups.

MeasureData were collected primarily through a questionnaire with items de-

signed to measure self-concept and self-efficacy at two levels (mathematicsand percentages). Measures of social comparison were also included in thequestionnaire. Abbreviations used for different items are included in Ap-pendix A. Questionnaire items were randomly interspersed to preventpotential “set effects” in which students identify contiguous items as itemsmeasuring similar attributes (Bong, 1997).

Self-concept items. Self-concept items were drawn from the SDQ–II(Marsh, 1992) designed for high school students. The SDQ–II consists of102 items measuring general self-concept, three areas of academic self-concept (reading, mathematics, and general school self-concept), and fourareas of nonacademic self-concept (physical ability, physical appearance,peer relations, and parent relations). The 10 items within the SDQ–IImeasuring self-concept for mathematics were used in the present study(� � .86). The response format for the questionnaire was modified fromthe original format of the SDQ–II so that the same format could be used forself-concept items and domain-specific efficacy items. Instead of six pos-sible discrete responses, individuals were provided with a continuousbipolar scale, which ranged from 0 (definitely not true) to 6 (definitelytrue).

Nine items measuring self-concept for percentages were formed parallelto the SDQ–II self-concept for mathematics items principally by changingthe word mathematics to percentages and making small revisions to thestructure of the original items (� � .89). For example, the mathematicsself-concept item from the SDQ–II “I never want to take another mathe-matics course” was rewritten as “I never want to study percentages again.”No percentages item parallel to “Mathematics is one of my best subjects”was used because it was deemed inappropriate to consider comparingpercentages with other subjects, or even comparing percentages with othertopics. The response format for each of these nine items was the samecontinuous bipolar scale as that used for self-concept for mathematicsitems.

Self-efficacy items. Five items were used to measure subject-specificself-efficacy for mathematics (� � .79). The five items were designed tomeasure efficacy beliefs at different levels by asking students whether theywere capable of achieving certain outcomes in mathematics. These in-cluded their capacity to achieve general results (“I am able to achieve highgrades in mathematics”) and specific results (“I am able to achieve at least90% in my mathematics course this year”). The same response scale wasused for subject-specific self-efficacy, topic-specific self-efficacy, andself-concept items (see Appendix B). These items are similar to items usedby Zimmerman et al. (1992) who investigated academic self-efficacy usingitems measuring subject-specific self-efficacy such as “How well can youlearn science?” Bandura (2001) also provided examples of efficacy mea-sures of performance in mathematics that measure mathematics perfor-mance at different levels by asking respondents to rate how confident theyare of achieving results of 10%, 20%, 30%, and so forth in different subjectareas. Items measuring efficacy for percentages were parallel to itemsmeasuring efficacy for mathematics (� � .86) such as “I am able to achieveat least 90% on a percentages topic test.” Problem-specific efficacy scalesrelating to percentages questions were also constructed using a traditionalself-efficacy response format (� � .91) in which respondents were requiredto indicate their confidence for correctly answering five specific questionsabout percentages by circling a number from 1 (not sure at all) to 10 (verysure). These questions differed numerically from the questions used tomeasure percentages performance to overcome the problem of correlateduniquenesses between the efficacy measures and the performance measure(Marsh et al., 1997).

Measures of social comparison. The construct of social comparisonwas estimated from three observed measures of social comparison for

591MATHEMATICS SELF-EFFICACY AND SELF-CONCEPT

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mathematics (� � .76) using parallel wording to items from Marsh’sAcademic Self-Description Questionnaire for high school students(ASDQ–II; Marsh & Yeung, 1997). For each social comparison item,students were required to select one of six possible responses—false,mostly false, more false than true, more true than false, mostly true, andtrue (see Appendix B). The first measure was presented without a specificreference group (“Compared to others my age I am good at mathematics”),whereas the other two measures specified the reference groups with whichstudents were to compare themselves, these being either their own class(“Compared to others in my class I am good at mathematics”) or theirwhole year group (“Compared to others in my year I am good at mathe-matics”). Parallel worded items were also used as measures of socialcomparison within the domain of percentages by replacing the wordmathematics with percentages.

Performance in mathematics. Students’ performance in their end-of-term examination 2 weeks after completing the questionnaire in mathe-matics was used as a measure of their performance in general mathematicsperformance. Students in Grades 9 and 10 are divided into three separatecourses in New South Wales, each of which has its own separate end-of-term examination varying in difficulty. Students are only graded withineach course. To assist in the analysis of examination results obtained fromend-of-term examinations, we scaled students’ marks to enable compari-sons across both academic years as well as across different mathematicscourses. Because all Grade 8 students attempt the same mathematicscourse, we used end-of-year Grade 8 marks for the Grade 9 and Grade 10students to determine new means and standard deviations for each math-ematics course in each grade. Exam results of students from Grade 10attempting the Advanced Mathematics course, for example, were scaled sothat these students’ scores had the same mean and standard deviation thatthis group of students achieved on their end-of-year exam in Grade 8. Thus,all students received a scaled mark for the purposes of analysis that wascomparable with other students in other courses and other grades. Students’performance on a 30-question percentages multiple-choice test completedimmediately after completing the questionnaire was used as a measure oftheir performance in the topic of percentages.

Analysis and ResultsConfirmatory factor analysis (CFA) and structural equation

modeling (SEM) techniques were used to compare the varioustheoretical models examined in this study. All CFAs and SEMswere performed using LISREL 8.3 (Joreskog & Sorbom, 1999). Asis customary, several goodness-of-fit indexes (GFIs) were used indetermining model fit for CFAs: the GFI, the comparative fit index(CFI), and the nonnormed fit index (NNFI). The criterion foracceptable model fit with the GFI, NNFI, and CFI is normally .9,with values greater than .9 indicating adequate model fit (Hoyle &Panter, 1995). Chi-square values and the ratio of chi-square valuesto the degrees of freedom are also provided. The ratio of thechi-square value to its degrees of freedom was preferred over thechi-square value alone as an indicator of model fit because thechi-square statistic is known to be biased against a large samplesize. Acceptable ratios of the chi-square statistic to the degrees offreedom are often cited as less than two or three (Byrne, 1989).However, CFAs incorporating measures of self-efficacy (Bong,1997) and self-concept (Bong, 1998; Marsh, 1990; Marsh &Yeung, 1997) have adopted models that demonstrate adequate fitaccording to other indices such as the NNFI even when the ratio ofthe chi-square statistic to the degrees of freedom has exceeded thistraditional cutoff. Consistent with other research in this area,model fit was assessed using the NNFI, GFI, and CFI.

Models were compared using the change in chi-square value.Because the change-in-chi-square-value criterion can lead to an

overestimation of the underlying factors (Velicer & Jackson,1990), the relative parsimony of different models was also takeninto consideration when comparing different models. Preliminaryscreening analyses indicated adequate conformity to multivariatelinear regression assumptions. Distributions for most of the vari-ables demonstrated no substantial departures from normality, withskewness and kurtosis coefficients falling between –1 and 1 for89% of the variables (mean skewness coefficient � –.406, meankurtosis coefficient � –.247). Mahalanobis distances were gener-ated for each case to identify potential multivariate outliers. Usinga conservative alpha level of .0001, 14 cases were identified asmultivariate outliers and were removed from subsequent analyses.Five cases with missing values were also removed. Table 1 reportsintercorrelations among the 19 variables used in mathematicsdomain analyses. Table 2 reports intercorrelations among the 23variables used in percentages domain analyses.

Component Structure of Self-Concept

Means and standard deviations for each of the self-conceptitems are presented in Table 3. CFAs were initially performed todetermine whether the results of this study replicated the findingsof Marsh et al. (1999). These results are presented in Table 4.Models 1A–1D were developed to compare different componentstructures of mathematics self-concept.

Initially neither the single-factor model for mathematics self-concept (Model 1A) nor the two-factor model (Model 1B) fit thedata well. After the path from Comp1 (“Mathematics is one of mybest subjects”) to the affective factor was freed, however, thetwo-factor model fit the data adequately. In fact, the path coeffi-cient from Comp1 was larger for the affective factor (.51) than forthe competency factor (.31), and as a result, Comp1 was treated asan affective scale item in all subsequent analyses. Where both thecompetency component and the affective component were ana-lyzed, Comp1 was allowed to load on both factors.

Modification indices also suggested that the path from Aff2 (“Inever want to take another mathematics course”) to the compe-tency component of mathematics self-concept be freed. When Aff2was allowed to load on both factors, the path coefficient to both thecompetency and the affective factor were both low (.19 and .41),suggesting that Aff2 was not a good measure for either factor. Theitem Aff2 was therefore removed from the present analysis andsubsequent analyses.

Finally, the Lagrange Multiplier Test also suggested freeing thecovariance between the error terms for Comp1 (“I have alwaysdone well in mathematics”) and Aff1 (“I enjoy studying for math-ematics”). As these were the second and third items in the ques-tionnaire, it seemed reasonable to expect the error terms for themto covary because of order effects. As a result, this modificationwas also incorporated into Models 1C and 1D. The final modifiedmodel is shown in Figure 1.

Model descriptions of parallel analyses performed on percent-ages self-concept and the fit indices are also presented in Table 4(Models 2A to 2D). Neither the single-factor model (Model 2A)nor the two-factor model (Model 2B) fit the data adequately. Therelative similarity of two of the items measuring competenceperceptions of percentages (“I have always done well in tests onpercentages” and “I get good marks in tests on percentages”)suggested that one of these items was obsolete and could be


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removed. When the second of these items was removed and theitem Aff2 was allowed to load on both factors, the two-factormodel fit the data adequately on each of the criteria used in theanalysis. As indicated, results within this domain were consistentwith those obtained in mathematics.

Relationship Between Self-Efficacy and Self-Concept

Means and standard deviations for each of the self-efficacyitems are presented in Table 3. At the subject-specific level ofmathematics, two hypothesized models were compared: (a) a one-factor model in which self-efficacy items and competence-basedself-concept for mathematics items loaded on a single factor and(b) a two-factor model separating self-efficacy items andcompetence-based self-concept items. Models 3A and 3B werecompared to test this hypothesis and are presented in Table 4.

Both Models 3A and 3B fit the data reasonably well prior tomaking any modifications. Although the chi-square difference testwas significant, ��2(1) � 19.34, p � .01, several considerationsled to the adoption of the one-factor model, which is presented inFigure 2. First, the correlation between the two factors was highenough (.93) to suggest the presence of a single factor. Second,apart from the chi-square statistic, each of the fit indices wasadequate for the one-factor model and did not differ significantlybetween the one-factor model and the two-factor model. Third, theresults summarized previously were obtained prior to adding anyerror covariances. Modification indices suggested freeing two er-ror covariances between the efficacy items Semok and Sem50 andbetween Sem50 and Sem70. The fit of each model improvedaccordingly. Model 3C is presented in Figure 2. Once such mod-ifications had been incorporated, the chi-square difference betweenthe one-factor and the two-factor model was not significant,��2(1) � 6.14, p � .01, and the correlation between these twofactors remained very high in the two-factor model (.96). Cautionis required when interpreting these results, however, consideringthe modifications made. Thus, the results should be cross-validatedin future studies with independent samples.

Results in the domain of percentages were also consistent withthose obtained in the domain of mathematics, although a relativelylarge number of post hoc modifications (seven) were made to theoriginal model. The one-factor model and the two-factor modelboth fit the data well according to each of the fit indices, suggest-ing that the more parsimonious one-factor model should be ac-cepted. However, the ratio of the chi-square statistic to the degreesof freedom for the one-factor model was very high (7.17). Theparallel wording of the self-efficacy items again suggested freeingall of the error covariances between the efficacy items, however,this resulted in a nonpositive definite theta-delta matrix in thetwo-factor model. When seven error covariances were freed, how-ever, the chi-square statistic was almost equal for both the one-factor and the two-factor model, suggesting that the one-factormodel should be accepted. Given the relatively large number ofmodifications, the validity of these findings would again need to becross-validated on an independent sample. Results obtained in thisstudy, however, suggest that the competency component of self-concept and self-efficacy are different measures of the same un-derlying construct.Ta

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.401

.317

.375

.475

.276

.503

—16

.Soc

oclm

.463

.343

.419

.286

.395

.526

.317

.188

.361

.296

.360

.441

.357

.441

.517

—17

.Soc

oym

.437

.363

.483

.292

.374

.489

.253

.184

.214

.222

.385

.475

.358

.414

.450

.589

—18

.Soc

cm.4

43.3

33.5

23.3

63.3

33.5

56.2

78.2

45.2

11.2

49.3

95.5

38.4

09.4

09.4

59.4

40.6

09—

19.S

core

.318

.180

.388

.328

.162

.332

.050

.230

.220

.162

.290

.342

.320

.369

.226

.115

.433

.408

—

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Tabl

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Spec

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34

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78

910

1112

1314

1516

1718

1920

2122

23

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omp1

—2.

Com

p2.4

81—

3.C

omp3

.533

.620

—4.

Com

p4.6

51.6

47.6

43—

5.C

omp5

.431

.624

.611

.579

—6.

Aff

1.2

20.4

72.4

21.4

60.4

53—

7.A

ff2

.318

.593

.452

.473

.459

.504

—8.

Aff

3.3

83.4

84.4

05.5

90.3

64.5

75.5

76—

9.A

ff4

.345

.393

.353

.508

.359

.510

.503

.761

—10

.Sep

ok.4

92.5

41.4

86.6

22.5

12.3

54.3

84.3

84.3

14—

11.S

eph

.563

.613

.612

.761

.521

.388

.458

.492

.396

.585

—12

.Sep

50.4

53.4

75.4

78.5

84.4

58.3

28.3

52.3

69.2

78.6

67.6

39—

13.S

ep70

.516

.529

.503

.684

.485

.279

.395

.397

.324

.599

.710

.652

—14

.Sep

90.4

38.4

28.4

15.5

49.3

73.2

64.3

47.3

96.4

03.3

70.6

22.4

40.5

81—

15.S

e1.5

66.4

99.5

32.5

79.5

01.3

58.3

23.3

99.3

32.5

27.5

63.4

85.5

09.2

83—

16.S

e2.5

86.4

59.5

59.5

73.5

00.2

57.3

55.3

85.3

26.5

52.5

51.4

86.5

76.3

34.7

43—

17.S

e3.5

58.5

02.5

06.5

63.5

43.3

23.3

70.3

97.3

37.4

99.5

66.5

08.5

44.3

64.7

72.7

72—

18.S

e4.5

78.4

64.5

29.5

00.4

73.2

89.3

67.3

93.3

36.5

21.5

61.5

25.5

48.3

59.7

28.7

02.7

67—

19.S

e5.5

83.3

97.4

92.5

08.4

65.1

96.3

24.3

38.3

22.4

68.5

30.4

53.5

37.4

20.6

84.7

37.7

02.8

07—

20.S

ococ

lp.4

14.3

70.3

37.4

92.2

99.2

14.2

35.3

68.3

11.3

77.5

24.3

89.4

46.3

99.4

73.4

39.4

96.4

26.3

97—

21.S

ocoy

p.5

55.4

26.4

97.5

47.3

52.2

16.3

07.3

48.3

09.4

03.5

65.4

75.5

38.4

31.5

52.5

47.5

71.5

65.6

02.7

43—

22.S

occp

.555

.549

.584

.627

.521

.357

.393

.424

.413

.516

.626

.514

.555

.453

.583

.575

.561

.587

.571

.544

.618

—23

.Sco

re.4

85.4

10.5

11.5

05.4

41.2

86.2

86.2

61.2

69.5

15.4

76.4

21.4

82.2

85.6

94.7

34.6

25.5

87.6

03.3

57.4

75.4

66—

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The Role of Social Comparison in the Formation ofSelf-Concept and Self-Efficacy

Fit indices and model descriptions for parallel analyses con-ducted within the domains of mathematics and percentages arepresented in Table 4. The means and standard deviations foreach of the items contributing to the measure of social com-parison are included in Table 3. Paths were freed from themeasure of social comparison to each of the beliefs relating tomathematics. Error covariances between each of the socialcomparison items were also freed. The fit of Model 5, presentedin Figure 3, was adequate according to each of the fit indices,and all paths were significant at an alpha level of significanceof .05, except for the error covariance between Soccm andSococlm. Paths from the measure of social comparison toself-efficacy for mathematics and competency component ofmathematics self-concept were both very high (.97 and .97,respectively), whereas the path to affective mathematics self-concept was lower (.59). Thus, no significant difference in therelationship between social comparison processes and the com-petency self-perceptions was evident in the domain of mathe-matics. Parallel analyses conducted without the item “Com-pared to others I am good at mathematics” produced almostidentical path coefficients and model fit. Parallel results wereobtained in the domain of percentages (see Model 6 for adescription and fit indices) with the path coefficients from thesocial comparison measure to topic-specific self-efficacy andthe competency component of self-concept both very high andapproximately equal (.93 and .97).

The Predictive Utility of Self-Concept and Self-Efficacy

Two structural models were developed to examine the pre-dictive utility of these self-perceptions in the domain of math-ematics. The fit indices for these models are presented inTable 4. In the first model (7A), it was hypothesized thatmathematics self-efficacy and mathematics self-concept(both the competency and the affective components) were re-lated to performance in mathematics (M � 54.10, SD � 19.44on the end-of-term mathematics exams). The fit of this first

model was adequate according to the NNFI, GFI, and CFI,however, none of the paths from the self-perception variablesto the performance indicator were significant, suggesting thatnot all three constructs were related to performance inmathematics.

In Model 7B, it was hypothesized that only mathematics self-efficacy and the competency component of mathematics self-concept were causally prior to mathematics performance. Thismodel demonstrated adequate fit according to all of the fit indicesand is presented in Figure 4. Only self-efficacy for mathematicshad a significant impact on performance in mathematics. The pathfrom the competency component of self-concept to performance inmathematics was not significant. Sensitivity analyses indicated,however, that the conclusions were relatively robust using differ-ent estimates for the error variance of the single measure forperformance in the domain of mathematics. The path from self-efficacy for mathematics to performance in mathematics variedfrom .53, when the error was set at .10, to .59, when the error wasset at .36.

However, LISREL automatically frees the paths among exoge-nous variables, allowing them to correlate, and consequently thecommon variance was attributed wholly to the variable accountingfor most of the variance—in this case, self-efficacy. A secondanalysis in which the correlation between self-efficacy for math-ematics and self-concept for mathematics was set to zero did notdemonstrate adequate fit to the data (because self-efficacy formathematics and self-concept for mathematics are highly correlat-ed). This model did, however, distribute the variance betweenself-efficacy and self-concept. The path coefficient for self-efficacy in this second model was .33, whereas the path coefficientfor self-concept was .23.

Model 8 included topic-specific self-efficacy, percentages self-concept (both the competency and the affective components) andproblem-specific efficacy items. Only the problem-specific self-efficacy items had a significant positive impact on performance onthe percentages test (path coefficient � .79, � � .05; M � 18.81,SD � 8.07 for the percentages topic test). This model showedadequate fit according to each of the fit indices.

Table 3Means and Standard Deviations of Self-Concept, Self-Efficacy, and Social Comparison Items

Self-concept formathematics

Self-concept forpercentages

Self-efficacy forpercentages

Self-efficacy formathematics

Social comparisonitems

Item M SD Item M SD Item M SD Item M SD Item M SD

Comp1 2.48 1.69 Comp1 3.14 1.31 Se1 7.96 2.47 Semok 4.39 1.30 Sococlp 3.90 1.16Comp2 3.64 1.22 Comp2 4.00 1.18 Se2 8.32 2.55 Semh 3.24 1.55 Socoyp 3.64 1.25Comp3 2.69 1.48 Comp3 3.94 1.27 Se3 7.70 2.61 Sem50 4.25 1.49 Soccp 3.85 1.18Comp4 4.02 1.25 Comp4 3.40 1.46 Se4 7.07 2.79 Sem70 3.63 1.48 Sococlm 3.67 1.22Comp5 3.10 1.29 Comp5 3.84 1.24 Se5 6.80 2.81 Sem90 2.18 1.47 Socoym 3.59 1.24Comp6 3.19 1.43 Aff1 3.63 1.27 Sepok 4.05 1.38 Soccm 3.78 1.14Aff1 2.47 1.12 Aff2 3.97 1.38 Seph 3.56 1.47Aff2 3.67 1.43 Aff3 3.01 1.46 Sep50 4.16 1.49Aff3 2.20 1.45 Aff4 2.56 1.47 Sep70 3.67 1.52Aff4 3.34 1.71 Sep90 2.95 1.57

Note. See Appendix A for definitions of the items.


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Discussion

The purpose of the present study was to examine the relation-ship between self-concept and self-efficacy by empirically testingseveral theoretical points of differentiation suggested by Bong andClark (1999) between the two constructs. The results indicated thatin the area of mathematics, the competency component of self-concept is distinct from the affective component but overlaps withself-efficacy when measured at the same level of generality.Clearly, these implications are restricted by the study sample toearly adolescents (13–15-year-olds), and further research is neededto determine whether the results will generalize to otherpopulations.

The Relationship Between Self-Concept and Self-Efficacy

The initial replication of Marsh et al.’s results (1999) supportedthe existence of two components—a competency component andan affective component at both levels of generality. The present

findings also provided support for the hypothesis that the affectivecomponent of self-concept differentiates self-concept from self-efficacy. Specifically, the present data support the idea that self-efficacy and competence-related self-concept, when measured atthe same level of generality, assess the same underlying construct.

Unlike previous comparisons of self-efficacy and self-conceptthat have adopted problem-specific measures for self-efficacy andsubject-specific measures for self-concept (Marsh, Walker, & De-bus, 1991; Pajares & Miller, 1995; Skaalvik & Rankin, 1998), thepresent study examined self-efficacy and competence-related self-concept beliefs at the same level of generality. At the subject-specific level of mathematics and at the topic-specific level ofpercentages, a single-factor model provided an adequate fit of thedata and was preferred over the two-factor model on grounds ofparsimony.

At first glance, the concept of a single mathematics self-perception factor, as proposed by Skaalvik and Rankin (1997,1998), may seem to be a more suitable construct than either

Table 4Descriptions of Confirmatory Factor Analysis Models and Structural Equation Models Tested and Their Fit Indices for theComponent Structure of Self-Concept

Model Description �2 df �2/df GFI NNFI CFI SRMR

1A One-factor model of self-concept for mathematics 510.27 35 14.58 .80 .75 .80 .0901B Two-factor model of self-concept for mathematics 321.88 34 9.47 .86 .81 .85 .0751C One-factor model of self-concept with error covariance of Comp1 and

Aff1 freed and Aff2 removed313.57 26 12.06 .85 .79 .85 .090

1D Two-factor model of self-concept for mathematics with Comp1 loadingon both factors, error covariance between Comp1 and Aff1 freed, andAff2 removed

70.58 24 2.94 .96 .96 .97 .043

2A One-factor model of percentages self-concept 477.13 27 17.68 .79 .74 .81 .0842B Two-factor model of percentages self-concept 200.52 26 7.71 .90 .89 .81 .0842C One-factor model of percentages with the item Comp4 removed 392.75 20 19.64 .80 .72 .80 .0852D Two-factor model of percentages self-concept with Aff2 loading on both

factors and Comp4 removed88.14 18 4.90 .95 .93 .96 .047

3A Single factor representing competency beliefs for mathematics 160.80 35 4.59 .92 .91 .93 .0503B Two-factor model with a self-concept competence factor and an efficacy

factor for mathematics141.46 34 4.16 .93 .92 .94 .047

3C Single factor representing competency beliefs for mathematics plus twoerror covariances freed between efficacy items

105.26 33 3.19 .95 .94 .96 .041

3D Two-factor model with a self-concept competence factor and an efficacyfactor for mathematics plus two error covariances freed betweenefficacy items

99.12 32 3.10 .95 .94 .96 .040

4A Single factor representing competency beliefs for percentages 250.97 35 7.17 .89 .90 .92 .0504B Two-factor model with a self-concept competence factor and an efficacy

factor for percentages175.62 34 5.17 .92 .93 .95 .042

4C Single factor representing competency beliefs for percentages plus sevenerror covariances freed between efficacy items

93.90 28 3.35 .95 .96 .98 .031

4D Two-factor model with a self-concept competence factor and an efficacyfactor for percentages plus seven error covariances freed betweenefficacy items

93.55 27 3.46 .95 .96 .98 .030

5 Social comparison processes causally prior to each self-perception formathematics

391.79 113 3.47 .90 .90 .92 .055

6 Social comparison processes causally prior to each self-perception forpercentages

673.85 181 3.72 .86 .91 .93 .051

7A Each self-perception causally prior to performance in mathematics 328.35 84 3.91 .90 .89 .91 .0577B Comparison of predictive utility of competence component and subject-

specific self-efficacy for mathematics217.72 52 4.19 .92 .90 .92 .050

8 Each self-perception causally prior to performance in percentages 629.85 142 4.43 .86 .90 .92 .055

Note. N � 397. See Appendix A for definitions of the items. GFI � goodness-of-fit index; NNFI � Bentler–Bonnett nonnormed fit index; CFI �comparative fit index; SRMR � standardized root mean residual.


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self-concept or self-efficacy. However, as indicated previously,there remain significant theoretical differences between self-efficacy and self-concept in terms of how they characterize per-ceptions of competence. These differences become evident whenexamining the predictive utility of these constructs. The nature ofself-efficacy items reflects the contextual nature of efficacy beliefsas task focused (in this study, the task consisted of an end-of-termexam in mathematics) in contrast with self-concept items thatfocus on personal characteristics rather than specific tasks. Self-efficacy beliefs are more closely related to specific tasks and aretherefore more likely to be related to future performance on thosetasks.

In the present study, confirmatory factor models developed tocompare competence-related self-concept beliefs and self-efficacy beliefs were modified incorporating error covariancesbetween self-efficacy items. Such modifications may, however,be capitalizing on chance and conceptual relationships uniqueto the population of students participating in the presentstudy. Thus, there remains a need to cross-validate these resultswith independent samples to determine whether such modifica-tions lead to replicable results with a range of differentparticipants.

The additional usefulness of self-concept over and above effi-cacy beliefs may, however, reside in the inclusion of the affectivefactor. Examining the affective component of the self-concept mayreveal additional information relevant to academic contexts. Futureresearch may focus on the individual contribution of the compe-tence and affective components of self-concept toward predictinga wide range of variables including academic performance, anxi-ety, and social competency.

The Role of Social Comparison Information

At the subject-specific level of mathematics and the topic-specific level of percentages, the path coefficients obtained forpaths from the social comparison measure to competence-relatedself-concept and subject-specific efficacy beliefs were almost thesame. This result is surprising considering that the measures ofsocial comparison are, in some sense, frame-specific self-conceptitems adapted from the ASDQ–II and should, therefore, be moreclosely related to self-concept rather than self-efficacy. The simi-larity observed in the present study, however, suggests that the roleof social comparison is similar for both constructs when they aremeasured at the same degree of generality.

Although students in different classes attempt courses varying indifficulty, comparisons with classmates and with students in thesame year were similar for most students. Given that students inNew South Wales are only streamed into three different bands inGrades 9 and 10, this similarity in the normative comparisonsstudents performed suggests that students have developed a notionof their own normative performance in mathematics over manyyears of experience, in which classroom comparisons and yearcomparisons lead to the same conclusions. The period of 6 or 18months in streamed classes does not appear to result in any majorchange in students’ normative self-perceptions using their class asthe frame of reference.

Efficacy theorists have acknowledged the role of social com-parison information (Bandura, 1977, 1995, 1997; Schunk, 1983;Zeldin & Pajares, 2000). In particular, when a task is unfamiliar ornovel, it is likely that individuals will resort to comparing them-selves with other students whom they perceive to be similar interms of capabilities. Skaalvik and Rankin (1997) claimed that

Figure 1. Component structure of mathematics self-concept (Model 1D). All paths are significant at p � .05.SC � self-concept. See Appendix A for definitions of the items.


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general competency beliefs are more likely to be informed bysocial comparison processes because prior mastery experiences arenot available to inform such beliefs. Further support for a singleunderlying construct incorporating both types of competency be-liefs, as measured by self-concept scales and self-efficacy beliefs,is therefore provided by the social comparison structural models.These results, however, were obtained in the absence of priorachievement information, which may have an impact on the rela-tionship between social comparison processes and self-efficacyand self-concept.

Predictive Utility of Self-Efficacy and Self-Concept

The results of the present study suggest that self-efficacymeasures are more suitable measures for predicting future per-formance in mathematics. At the subject-specific level of math-ematics, mathematics self-efficacy was more highly related toperformance in mathematics when compared with the compe-tency component of mathematics self-concept, although bothconstructs were related to performance to varying degrees. Atthe topic-specific level of percentages, problem-specific self-efficacy was a more predictive measure of performance inpercentages. Neither the competency component of percentagesself-concept nor the topic-specific self-efficacy items werefound to be significantly related to performance on the percent-

ages test. Clearly, there was a greater degree of correspondencebetween the problem-specific items and the topic-specific itemsthat would account for this difference in predictive utility. AsBandura (1997), Pajares and Miller (1994, 1995), and Pajaresand Schunk (2002) argued, correspondence between the effi-cacy items and the performance measure enhances the predic-tive power of the efficacy measures. However, it is surprisingthat the topic-specific measure for percentages performance didnot demonstrate any predictive utility. One possible explanationfor this result may be the ill-formed nature of self-perceptionsrelated to the topic of percentages. Compared with performancein mathematics in general, for which students receive continualfeedback through exams, class tests, and the relative perfor-mances of other students, students’ experiences of more spe-cific areas of mathematics may be too infrequent for them todevelop perceptions of competence at this intermediate level ofgenerality.

The problem-specific measure of percentages self-efficacy,however, proved to be highly related to performance, suggestingthat in this domain it was a more appropriate measure of self-efficacy. When given specific problems on which to assess theircompetence, students appear more likely to consider each problemand their perceived competence to solve it individually. Hence, inthe domain of percentages, for which students may not have

Figure 2. Single mathematics competency factor (Model 2C). All paths are significant at p � .05. SeeAppendix A for definitions of the items.


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sufficient prior mastery experience on percentages tests, theproblem-specific measures provided the most appropriate mea-sures of self-efficacy.

Although efficacy beliefs can be measured at more generallevels, such as for mathematics using general items of the kindused in the present study and by Bandura (2001), where possible,problem-specific items should be developed to maximize corre-spondence. Within less general domains such as percentages, inwhich encapsulating the tasks that constitute the domain within asmall number of items is possible, problem-specific items repre-sent the most effective items for predicting future perfor-mance. Within more general domains such as mathematics,however, in which the tasks that constitute the domain cannotbe easily captured by a small number of items, more generalmeasures of efficacy beliefs represent efficient predictors of futureperformance. Researchers and teachers need to work toward de-veloping self-efficacy items that are closely related to the type oftasks most salient for developing perceptions of competence inthese domains.

Although the superior predictive utility of efficacy beliefs isevident in both the domains of mathematics and percentages, it isimportant to recognize the limitations of the present research. First,it is possible that some students had difficulty reading the ques-tionnaire items coming from a non-English-speaking background.Second, no measure of prior mastery experience in the domains ofinterest was included. Because prior mastery experience is themost potent source of influence on perceptions of efficacy (Ban-dura, 1997) and on self-concept perceptions (Marsh, 1990), it ispossible that once the impact of prior mastery experience had beentaken into account, the relative predictive utility of each self-perception may differ. Third, these results were only obtained

within the single subject area of mathematics. The development ofperceptions of competence in the domain of mathematics mayinvolve different reasoning processes to the development of per-ceptions of competence in less well-structured domains. Resultsfrom mathematics exams provide students with clear informationpertaining to their own competence, detailing areas of strength andweakness. Feedback pertaining to performances in other domainsmay provide students with more ambiguous information pertainingto their own competence. Thus, efficacy beliefs in other domainsmay not display the same level of predictive utility.

Fourth, the fact that performance in the domain of mathematicswas not inferred from multiple indicators undermined many of theadvantages of the SEM approach. Sensitivity analyses indicated,however, that the conclusions were relatively robust. Fifth, stu-dents participating in this study were completing different coursesin mathematics that may have had an impact on their perceptionsof competence. Although some efficacy items for mathematicswere expressed in terms of performance in mathematics courses(such as “I am able to achieve at least 50% in my mathematicscourse this year”), students appeared to consider their efficacy forachieving certain results on mathematics tests attempted by thewhole grade rather than by students in specific courses. Prelimi-nary analyses demonstrated that perceptions of efficacy and self-concept beliefs were not related to performances on their (un-scaled) end-of-term course exams. Responses to efficacy itemswere, however, related to the scaled result that allowed for com-parisons across different courses and reflected their performancelevel relative to the whole grade rather than just students in theirown course. It appears that 13- to 15-year-old students are able todevelop efficacy beliefs from enactive mastery experiences that

Figure 3. The relative impact of social comparison information on mathematics self-perceptions (Model 5). Allpaths are significant at p � .05. SC � self-concept. See Appendix A for definitions of the items.


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take into account the relative difficulty of the tasks as well as theirperformance in developing perceptions of efficacy within the do-main of mathematics.

References

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Figure 4. Relative predictive utility of mathematics self-perceptions (Model 7B). All paths are significant atp � .05, except for the path from the competence factor of self-concept to mathematics performance. SE �self-efficacy; SC � self-concept. See Appendix A for definitions of the items.


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(Appendixes follow)


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Appendix A

List of Items and Abbreviations Used

Item abbreviation Item

Mathematics self-conceptitemsa

Comp1 “Mathematics is one of my best subjects.”Comp2 “I do badly in tests of mathematics.”Comp3 “I have always done well in mathematics.”Comp4 “I have trouble understanding anything with mathematics in it.”Comp5 “I often need help with mathematics.”Comp6 “I get good marks in mathematics.”Aff1 “I enjoy studying for mathematics.”Aff2 “I never want to take another mathematics course.”Aff3 “I look forward to mathematics classes.”Aff4 “I hate mathematics.”

Percentages self-conceptitems

Comp1 “I have always done well in tests on percentages.”Comp2 “I do badly in tests on percentages.”Comp3 “I often need help with percentages questions.”Comp4 “I get good marks in tests on percentages.”Comp5 “I have trouble understanding questions with percentages in them.”Aff1 “I hate doing questions on percentages.”Aff2 “I never want to study percentages again.”Aff3 “I enjoy learning about percentages.”Aff4 “I look forward to mathematics lessons involving percentages.”

Mathematics self-efficacyitems

Semok “I am able to achieve at least OK grades in mathematics.”Semc “I am able to achieve high grades in mathematics.”Sem50 “I am able to achieve at least 50% in my mathematics course this

year.”Sem70 “I am able to achieve at least 70% in my mathematics course this

year.”Sem90 “I am able to achieve at least 90% in my mathematics course this

year.”Topic-specific percentages

efficacy itemsSepok “I am able to achieve at least OK grades on percentages topic tests.”Seph “I am able to achieve high marks on percentages tests.”Sep50 “I am able to achieve at least 50% on a percentages topic test.”Sep70 “I am able to achieve at least 70% on a percentages topic test.”Sep90 “I am able to achieve at least 90% on a percentages topic test.”

Problem-specific percentagesefficacy items

“Please state how sure you are that can answer the following questionscorrectly.”

Se1 “How much is 15% of 300?”Se2 “Write 47% as a fraction.”Se3 “In a class of 25 students, 48% play softball. How many students play

softball?”Se4 “18 is what percentage of 72?”Se5 “If 18 is 3% of a particular amount, what is the original amount?”

Social comparison items formathematics

Soccm “Compared to others I am good at mathematics.”Sococlm “Compared to others in my class I am good at mathematics.”Socoym “Compared to others in my year I am good at mathematics.”

Social comparison items forpercentages

Soccp “Compared to others I am good at percentages.”Sococlp “Compared to others in my class I am good at percentages.”Socoyp “Compared to others in my year I am good at percentages.”

a From Self-Description Questionnaire—II. Manual (p. 5), by H. W. Marsh, 1992, New South Wales, Australia:University of Western Sydney, Macarthur, Faculty of Education, Publication Unit. Copyright 1992 by theUniversity of Western Sydney, Macarthur. Reprinted with permission.


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Appendix B

Sample Response Scales for Each of the Self-Report Scales

Measures of self-concept, topic-specific self-efficacy, and subject-specific self-efficacy

I am able to achieve at least 90% in my mathematics course this year.

definitely not true definitely true} }

Measures of social comparison

Compared to others my age I am good at percentages.

false mostly false more false than true more true than false mostly true true

Measures of problem-specific self-efficacy

How much is 15% of 300?Not sure at all Very sure1 2 3 4 5 6 7 8 9 10

Received April 2, 2002Revision received March 12, 2003

Accepted March 14, 2003 �


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the relationship among self-concept, self-efficacy, and performance in mathematics during secondary...

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