An assessment of a social–cognitive model of academic performance in mathematics in Argentinean middle school students

Learning and Individual Differences 20 (2010) 659–663

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Learning and Individual Differences j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / l i n d i f

An assessment of a social–cognitive model of academic performance in mathematics in Argentinean middle school students☆ Marcos Cupani a,⁎, María Cristina Richaud de Minzi b, Edgardo Raúl Pérez a, Ricardo Marcos Pautassi a,c a b c

Laboratorio de Psicología de la Personalidad, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina Centro Interdisciplinario de Investigaciones en Psicología Matemática y Experimental (CIIPME-CONICET), Buenos Aires, Argentina Instituto de Investigaciones Medicas M. y M. Ferreyra (INIMEC–CONICET), Friuli 2434, Córdoba, Córdoba, 5016, Argentina

a r t i c l e

i n f o

Article history: Received 20 February 2009 Received in revised form 18 March 2010 Accepted 20 March 2010 Keywords: Self-efficacy Outcome expectations Performance goals Academic performance

a b s t r a c t This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13–15 years) were assessed using the following instruments: logical–mathematical self-efficacy scale, mathematics outcome expectations, mathematics performance goals, and mathematics ability test. All of these instruments had been adapted for use in Argentinean students. Academic achievement in mathematics (i.e., grades obtained on regular school exams) was the variable to be modeled through the path analysis technique. The analysis allowed identification of interrelations among the variables and identification of direct and indirect effects. Academic achievement in mathematics was partially explained by the model. Overall, the results support the theoretical postulates of Social Cognitive Career Theory. © 2010 Elsevier Inc. All rights reserved.

1. Introduction Recent years have seen a growing trend toward applying Bandura's social–cognitive theory (1986) to career behavior (Lent, Brown & Hackett, 2002). A parallel line of research uses social–cognitive theory as a framework for scrutinizing academic motivation and achievement. These two branches have focused on developmentally linked skill domains, produced complementary findings on the correlates and effects of cognitive-expectancy variables, and been guided by similar conceptualizations of educational–vocational functioning. Noting such commonalities, a theory has been proposed to unify the social–cognitive framework in order to conceptualize and study both career and academic behavior (Lent, Brown & Hackett, 1994). The Social Cognitive Career Theory (SCCT) explains the development of vocational interests, career choice, and academic performance using different but interrelated theoretical models. Based on Bandura's general social cognitive theory (1986), the SCCT focuses on the triadic interaction among person, environment, and behavior and how this interaction shapes career development. Selfefficacy beliefs (i.e., a person's judgment about his or her ability to properly execute a set of actions), outcome expectations (i.e., imagined consequences of performing particular behaviors), and

☆ This work was supported by Agencia Nacional de Promocion Cientifica y Tecnologica (Argentina), PICT 07-255, grant from Consejo Nacional de Investigaciones Científicas (MC) and grant PRH-UNC (FONCyT-SPU) (Argentina) to RMP. ⁎ Corresponding author. Tel./fax: +54 351 4334104. E-mail address: [email protected] (M. Cupani). 1041-6080/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.lindif.2010.03.006

goals (i.e., determination to engage in a particular activity or affect a particular outcome) are central among these variables. The SCCT is also focused on the causal paths by which additional personal and environmental inputs (e.g., race/ethnicity, ability, and educational experiences) influence career outcomes. The SCCT's performance model (Fig. 1) hypothesizes that cognitive ability influences student performance directly (through academicrelated skills) and indirectly (through self-efficacy beliefs and outcome expectations). College academic achievement, therefore, could relate to abilities and knowledge acquired during the educational and social trajectories of a given student. These trajectories involve a sequence of challenges and key events (such as performance accomplishments) occurring in high school and college, in which students are given the opportunity to develop skills (e.g., studying and taking tests), academic self-efficacy beliefs, and outcome expectations that contribute to academic success. Those who develop these expectations will be more likely to approach (and less likely to avoid) challenging academic tasks (Lent et al., 1994). The SCCT posits that self-efficacy and outcome expectations affect performance through the intervening influence of students' performance goals. Thus, students with stronger self-efficacy beliefs and outcome expectations will set and work toward more challenging academic goals than those with weaker self-efficacy beliefs or less positive outcome expectations (Lent et al., 1994). Studies have examined subsets of this model. Meta-analyses have yielded correlations of .38 and .50 between self-efficacy beliefs and college academic performance (Multon, Brown & Lent, 1991; Robbins et al., 2004; respectively). Robbins et al. (2004) reported a fully corrected correlation

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Fig. 1. Social Cognitive Career Theory Performance Model. Model of task performance, highlighting the role of ability, self-efficacy, outcomes expectations and performance goals. (adapted from Lent et al., 1994).

of .39 between cognitive ability and academic performance. This metaanalysis found support, via fully corrected bivariate correlations, for each hypothesized path (.28 between self-efficacy and cognitive ability; .49 between academic self-efficacy beliefs and academic goals; .18 between academic goals and performance; all pb .05). Recently, Brown et al. (2008) provided substantial support for SCCT's model of academic performance, but the correlation between goals and academic performance did not achieve statistical significance. To our knowledge, a large scale assessment of the complete performance model has yet to be published. Mathematics self-efficacy can be operationalized at different specificity levels (Betz & Hackett, 2006; Lent & Brown, 2006). The present work defined this concept as the student's belief in his or her ability to perform math-related tasks. Self-efficacy beliefs also act in concert with other common mechanisms of personal agency, such as self-concept beliefs (Pajares & Graham, 1999). Self-concept is usually measured at a broader level of specificity and includes the evaluation of a given competence and the feelings of self-worth associated with that skill. Self-concept differs from self-efficacy in that it is a context-specific assessment of the competence to perform a specific task (Pajares, 1996). Self-efficacy beliefs represent an important bridge between educational and vocational psychology (Betz & Hackett, 2006). The area of mathematics has been the focus of substantial research (Pajares & Schunk, 2001). Mathematics knowledge and scores are usually decisive for level placement and admission to college and have been usually considered a critical barrier for high school students aiming at scientific and technical careers (Sells, 1980). Most empirical research on the SCCT has focused on the field of science, technology, engineering, and mathematics (STEM). STEM-related self-efficacy explains a substantial amount of the variance in STEM goals, interests, choices, and performance (Ferry, Fouad & Smith, 2000; O'Brien, Martinez-Pons & Kopala, 1999). Social cognitive research has also mainly focused on high school (e.g., Lopez, Lent, Brown & Gore, 1997; O'Brien et al., 1999) or college students (e.g., Ferry et al., 2000; Lent et al., 2001). Only a few studies assessed the utility of SCCT to measure math and science goal intentions of an ethnically diverse group of middle school students (e.g., Fouad & Smith, 1996; Navarro, Flores & Worthington, 2007). Moreover, U.S. college students have been the subjects in the vast majority of SCCT studies. Still unknown, however, is how well the SCCT generalizes to the educational and career development of younger (or older) persons from diverse national contexts and across different domains of academic and career activity (e.g., Lent, Brown, Nota, & Soresi, 2003). Lent et al. (1994) focused their research on late adolescence and early adulthood, developmental periods likely to involve exploration and implementation of career choices. Previous research, however, found that it is during middle school when students begin to acquire academic abilities and take decisions that will have a strong impact on

later academic outcomes (e.g., Fouad & Smith, 1996; Turner & Lapan, 2005). It is thus important to understand how social cognitive mechanisms influence the development of performance in middle school students. The present study executed a global, comprehensive assessment of the SCCT model in the domain of mathematics in a sample of Argentinean middle school students. According to the Argentine Program for International Student Assessment, academic mathematics performance in this population has been very disappointing (Organization for Economic Cooperation and Development, 2001). Therefore, the present study also sought to provide information relevant to increase academic success in this population. Consistent with the SCCT's basic academic performance hypotheses (Lent et al., 1994), we predicted that (i) mathematics abilities will be significantly and positively related to academic performance in mathematics (hypothesis 1, H1), (ii) logical–mathematical self-efficacy beliefs will partially mediate the relationship between mathematics abilities and academic performance in mathematics (H2), (iii) mathematics outcome expectations will fully mediate the relationship between mathematics abilities and academic performance in mathematics (H3), (iv) self-efficacy beliefs will be significantly and positively related to academic performance in mathematics (H4), (v) performance goals in mathematics will partially mediate the relationship between logical and mathematical self-efficacy beliefs and academic performance in mathematics (H5), (vi) performance goals in mathematics will fully mediate the relationship between math outcome expectations and academic performance in mathematics (H6), and (vii) performance goals in mathematics will be significantly and positively related to academic performance in mathematics (H7). 2. Methods 2.1. Participants Two-hundred seventy-seven 8th (45.8%) and 9th (53.4%) graders participated in the study (175 boys and 102 girls; Mage = 13.74 ± .67 years). Students were enrolled in private educational institutions in Cordoba, Argentina, thus representing a socioeconomic microcosm of the larger society and belonging to families of skilled workers, large-production farmers, professionals, and local merchants. 2.2. Instruments 2.2.1. Mathematics outcome expectations The Mathematics Outcome Expectations Scale (MOES; Cupani, in press) is a modified version of the Mathematics/Science Outcome

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Expectations Scale (MSOES; Fouad, Smith, & Enochs, 1997). The scale consists of nine items assessing middle school students' beliefs about the potential consequences of mathematics-related courses, activities, and achievements. Participants rated each item (e.g., “If I learn math, I will have more options when choosing my major”) on a 5-point scale, ranging from 1 (agree totally) to 5 (disagree totally). Item scores were summed and divided by 9. MOES have adequate reliability and construct validity (Cupani, in press). The present study yielded a Cronbach's alpha of .83 for MOES scores. 2.2.2. Mathematics performance goals The Mathematics Performance Goals Scale (MPGS; Cupani, in press) is the modified version of the subscale for Mathematics/Science Intentions and Goals Scale (MSIGS; Fouad et al., 1997). It has 10 items assessing middle school students' intentions to pursue and persist in mathematics-related courses in high school. Participants rated each item (e.g., “This year I propose to get good grades in mathematics”) on a 5-point scale, ranging from 1 (agree totally) to 5 (disagree totally). Scores were summed and divided by 10. MPGS have adequate reliability and construct validity (Cupani, in press). The present study yielded a Cronbach's alpha of .87 for MPGS scores.

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grades (8th vs. 9th; t275 6.47, p N .05). Therefore, the groups were pooled for subsequent analyses. 2.3. Procedure All measurements, including consent forms, were gathered within a single class period during the first class term. Tests were taken collectively during the course of a regular school day at four educational institutions and in three different sessions. Detailed instructions on how to complete the survey were provided to the students by the researcher. The measures were taken following the theoretical and causal links proposed by the SCCT. The Numerical Reasoning subtest was administered during the first session (April), one college per week, followed 1 month later by the MOES and LMSS (second session). The MPGS was applied about 3 weeks later (third session). Mathematics grade scores for each student were collected directly from school records at the end of the second school term. 3. Results 3.1. Preliminary analyses

2.2.3. Logical–mathematical self-efficacy The Logical–Mathematical Self-efficacy Scale (LMSS) has six items, and participants rated each item (e.g., “Solve mathematics equation”) on a 10-point scale, ranging from 1 (Cannot do at all) to 10 (Certain can do). The scores were summed and divided by 6. The present study yielded a Cronbach's alpha of .83 for LMSS scores. Originally, this scale was included in the revised version of the Multiple Intelligences SelfEfficacy Inventory (MISEI-R), which has adequate reliability and construct validity (Pérez & Cupani, 2008). 2.2.4. Mathematics abilities The Numerical Reasoning subscale of the Differential Aptitude Test, Version 5, was used (Bennett, Seashore & Wesman, 2000). The Numerical Reasoning subscale measures the ability to use numbers in a logical and efficient way. In the present study, a Kuder Richardson (KR-20) coefficient of .81 was found for Numerical Reasoning scores. 2.2.5. Academic Performance in Mathematic Academic Performance in Mathematic (APM) was assessed by accessing the students' high school records for mathematics courses. In Argentina, students are assessed at mid-term (June) and at the end of the academic year (December). Grades are given on a 10-point scale, with 7 the cut-off for passing a course. The two assessments (which were highly correlated, r = .78, p b .001) were summed and divided by 2. No significant differences in APM were found between

Univariate atypical cases (i.e., z N 3.29; two-tailed test, p b.001) were identified by calculating standard scores for each variable. Atypical multivariate cases were identified through the Mahalanobis test (Tabachnick & Fidell, 2001; p b .001). As a result of these tests, four cases were removed from the dataset. Multivariate normality was evaluated by Mardia ratio (3.202, p N .05). Across variables, the values for asymmetry and kurtosis were optimal for the proposed parametric analysis (−.85 to −.08 and −.48 to .92, respectively; George & Mallery, 2001). Table 1 presents zero-order correlation coefficients for the measures. All variables were significantly correlated with math performance: mathematics performance goals (r = .40), mathematics abilities (r = .47), and logical–mathematical self-efficacy (r = .54). 3.2. Path analysis Model fit should be assessed using several indices to ensure more reliable and accurate decisions (Hu & Bentler, 1995). Therefore, the following indices were employed: the χ2 test of significance, the ratio of the χ2 statistic to degrees of freedom (χ2/df), the comparative fit index (CFI), the goodness-of-fit index (GFI), and the root–mean– square error of approximation (RMSEA). When this ratio is less than 3.0, a good model fit can be inferred (Kline, 2005). CFI and GFI values between ≥.90 and ≥.95 and RMSEA values between ≤.05 and ≤.08 indicate of good model fit (Hu & Bentler, 1995).

Table 1 Descriptive data and interrelation between variables pertinent to the model. Descriptive

Interrelation

Variables

M

SD

AS

KS

MA

LMS

MOE

MPG

MP

Mathematics Ability (MA) Logic-Math Self-efficacy (LMS) Math Outcome Expectations (MOE) Math Performance Goals (MPG) Math Performance (MP)

20.08 6.94 3.60 3.43 6.03

6.47 1.67 .73 .74 1.83

−.08 −.85 −.49 −.68 −.22

−.48 .55 .24 .92 −.35

1.00

.40** 1.00

.02 .25** 1.00

.05 .38** .39** 1.00

.47** .54** .24** .40** 1.00

*p b .05, **p b .01 Note. The Mathematics abilities (MA) is from the Numerical Reasoning subscale of the Differential Aptitude Test, Version 5 (Bennett et al., 2000); The Logical–Mathematical Selfefficacy Scale (LMSS) is from the revised version of the Multiple Intelligences Self-Efficacy Inventory (MISEI-R; Pérez & Cupani, 2008); the Mathematics Outcome Expectations is from the Mathematics Outcome Expectations Scale (MOES; Cupani, in press), modified version of the subscale for Mathematics/Science Intentions and Goals Scale (MSIGS; Fouad et al., 1997); the Mathematics Performance Goals is from the Mathematics Performance Goals Scale (MPGS; Cupani, in press) modified version of the subscale for Mathematics/ Science Intentions and Goals Scale (MSIGS; Fouad et al., 1997). Academic Performance in Mathematic (APM) was assessed by accessing the students' high school records for mathematics courses. Grades are given on a 10-point scale, with 7 the cut-off for passing a course. All values represent raw, nonstandardized scores. M, mean; SD, standard deviation; Ss, skewness; Ks, kurtosis; Interrelation, zero-order correlations.

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Table 2 Decomposition of total, direct, and indirect effects of variables from the path analysis. Effect

Indirect effect

Total effect

.40***

.00

.40***

Outcome expectations Mathematics Ability Logic-Mathematics Self-efficacy

−.10 .29***

.11 .00

.02 .29***

Performance goals Mathematics Ability Logic-Mathematics Self-efficacy Outcome Expectations

.00 .30*** .31***

.13** .08*** .00

.13** .38*** .31***

Mathematics performance Mathematics Ability Logic-Mathematics Self-efficacy Outcome Expectations Performance Goals

.34*** .30*** .00 .27***

.10*** .10*** .09*** .00

.44*** .40*** .09*** .27***

Logic-Mathematics Self-efficacy Mathematics Ability

Direct effect

**p b .01, ***p b .001

All indices revealed optimal model adjustment (CFI = .99, CFI = .99, RMSEA = .06, χ2 = 4.308, p = .116, CMIN/DF = 2.154). The residuals were also small (median = .000, range = −.37 to.07). Therefore, the fitness of the model appears strong enough to allow the report and interpretation of the standardized path estimates (Browne, MacCallum, Kim, Anderson, & Glaser, 2002). Fig. 2 depicts the path coefficients for the proposed relationships among the variables in the theoretical model. The SCCT postulates indirect relationships among key variables. To assess these specific hypotheses, we used Sobel's test to examine indirect effects in the recursive model under scrutiny (Kline, 2005). Table 2 presents of total, direct, and indirect effects of variables. The test strongly supported the theoretical proposal, yielding a significant and positive relationship between mathematics performance and mathematics abilities (H1: β = .34, p b .01), logical–mathematical selfefficacy (H4: β = .30, p b .01), and mathematics performance goals (H7: β = .27, p = .01). With regard to indirect effects, an effect of academic abilities on mathematics performance was observed that was mediated by logical– mathematical self-efficacy beliefs (H2:.34 × .30 = .10, z = 5.24, p b .000). The total effect of academic abilities was .44 (.34+ [.34 × .30]). H3, however, was not corroborated by our data. The relationship between abilities and expectations was negative and far from reaching significance (β = −.10, p = .13). The analysis also allowed an estimation of the predictive contribution of logical–mathematical self-efficacy beliefs (H5:.30 × .27= .08, z = 3.62, p b .000) and mathematics outcome expectations (H6: .31 × .27 = .09, z = 3.32, p b .000) on mathematics

performance goals. A positive and significant (β = .29, p b .01) association was also found between logical–mathematical self-efficacy beliefs and mathematics outcome expectations. The total effect of self-efficacy on mathematics performance goals was .39 (.30+ [.29 × .31], z = 3.44, p b .000). Therefore, the total contribution of self-efficacy beliefs to mathematics performance is .40, whereas the indirect contribution of outcome expectation to mathematics performance mediated by performance goals is .09. In summary, the model generally explained 44% of the variance of academic achievement in mathematics. Mathematics abilities explained 16% of the variance of logical–mathematical self-efficacy beliefs. With regard to H5 and H6, the results indicated that selfefficacy beliefs and outcome expectations explained 23% of the variance of performance goals. Self-efficacy beliefs about outcome expectations also provided a significant contribution. 4. Discussion The present study, conducted in a sample of Argentinean highschool students, strongly supported the theoretical model of academic performance in mathematics of the SCCT. The current findings suggest that success in academic performance among Argentinean students is associated with greater mathematics ability, strong beliefs about this ability, and more optimistic and demanding performance targets. These successful students also have higher self-efficacy beliefs. Moreover, students who set more demanding performance targets are those with higher self-efficacy beliefs and higher expectations of positive results. The study replicates and extends early work conducted in U.S. students (e.g., Brown et al., 2008). An obvious yet important difference between the present and previous studies is that students in this study belong to a LatinAmerican population. The cross-cultural validity of the SCCT has recently become an increasingly popular focus of career inquiry (Lent & Sheu, 2010). Most of this research, however, has been conducted with Americans of foreign descent (e.g., Mexican–Americans; Navarro et al., 2007). Lent et al. (2001) argued for the need to examine the validity of the SCCT in culturally diverse groups. Research conducted in Western contexts has identified intrapersonal and contextual factors relating to academic performance. Country characteristics, such as average income, social inequality, and cultural values might be associated with student achievement directly or indirectly via family or motivation (Chiu & Xihua, 2008). Our study represents important progress in this direction. One limitation of generalizing these findings relates to the representativeness of the sample. Only students attending private schools were included; thus, the results should not be generalized to students from low socioeconomic status or attending state-based

Fig. 2. Standardized path coefficients from the Social Cognitive Model of Academic Performance in Mathematics (Lent et al., 1994) found in a sample of Argentinean middle school students. Standardized path coefficients and significance level are depicted over each path (***p b .001).

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institutions. Future research should use a more heterogeneous sample and explicitly assess the socioeconomic status of the students. Another limitation is that the measurement for academic achievement in mathematics can be influenced by the idiosyncratic policies of each institution or the educational orientation of each instructor. Also, we acknowledge that our instrument measures math self-efficacy beliefs at a general rather than at a specific level. The evidence shows that the predictability of self-efficacy measures depends on their specificity and correspondence to actual math performance tasks (Bandura, 1997). That is, predictors and dependent variables must be compatible in regards with content, context, temporal orientation and specificity level (Ajzen, 1988). Future studies should aim at creating new math self-efficacy scales that measure this construct at a specific level. The main theoretical contribution of this study is the assessment of the SCCT performance model in a novel cultural and linguistic context, namely, middle school students in Argentina. Interestingly, the study assessed all SCCT predictors jointly. To our knowledge, the literature has yet to show a single large-scale test of the complete performance model, although numerous studies have examined subsets of the model (e.g., Brown et al., 2008). The developmental stage in which the model is tested also deserves attention. Early adolescence is a critical stage for learning (Zimmerman, Bonner, & Kovach, 1996), characterized by a sharp decline in academic performance possibly caused by the increasing challenges posed by middle school as well as the inherent psychological and biological changes that occur during this period. Beyond these theoretical implications, the results suggest that the SCCT could be used as a screening tool to identify students at-risk for having, for example, diminished self-efficacy in a given academic domain. Educational institutions could use this knowledge to design experiences specifically aimed at improving these variables. Notably, adolescents usually have limited knowledge about their capabilities and career options, a fact that results in stereotyped and unstable vocational goals (Lent et al., 2004). Therefore, the development of career goals can be halted early in life if the students are exposed to educational environments that provide limited opportunities for nurturing appropriate efficacy or self-efficacy skills and outcome expectations. The results outlined in the present study could be used to design interventions aimed at increasing the level of exposure to a variety of career-relevant tasks and activities. These interventions will help develop task-specific concepts of self-efficacy that, in turn, will result in more realistic, stable, and useful vocational goals. References Ajzen, I. (1988). Attitudes, personality, and behavior. Stony Stratford, UK: Open University Press. Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice Hall. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman. Betz, N. E., & Hackett, G. (2006). Career self-efficacy theory: Back to the future. Journal of Career Assessment, 14(1), 3−11. Bennett, G. K., Seashore, H. G., & Wesman, A. G. (2000). Differential Aptitude Test (DAT-5). Madrid: TEA Ediciones. Brown, S. D., Tramayne, S., Hoxha, D., Telander, K., Fan, X., & Lent, R. W. (2008). Social cognitive predictors of college students' academic performance and persistence: A meta-analytic path analysis. Journal of Vocational Behavior, 72, 298−308. Browne, M. W., MacCallum, R. C., Kim, C. T., Anderson, B. L., & Glaser, R. (2002). When fit indices and residuals are incompatible. Psychological Methods, 7, 403−421. Chiu, M. M., & Xihua, Z. (2008). Family and motivation effects on mathematics achievement: Analyses of students in 41 countries. Learning and Instruction, 18(4), 321−336. Cupani, M. (in press). Validity evidence for the new scales for mathematics outcome expectancies and performance goals. Interdiciplinaria, 27(1).

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