Untangling the Relations Among High School Students' Motivation, Achievement and Advanced Course-Taking in Mathematics: Using Structural Equation Modeling with Complex Samples

This study adapted the expectancy-value model of achievement motivation theory (Eccles & Wigfield, 1995; Wigfield & Eccles, 2000) to investigate the relationships among students’ motivation, achievement and advanced course-taking in mathematics. Students’ motivation was represented with educational expectation, self-efficacy, intrinsic and utility task value. A hypothesized conceptual model was constructed and tested using structural equation modeling (SEM). A total sample of 8,976 students, who participated in the Educational Longitudinal Study: 2002 survey at 10th grade then 12th grade, were utilized for the present study. Indicated from the SEM analysis for the all participants, statistically and practically significant positive associations were found between (a) self-efficacy and achievement, (b) self-efficacy and advanced course-taking, (c) intrinsic value and advanced course-taking. Furthermore, the positive mediating qualities of educational expectation for the linkage between math self-efficacy, utility value and outcome variables were also demonstrated. However, it is inarguable that students are from a heterogeneous group, which justifies making separate estimates for subpopulation. Prior studies have indicated gender, ethnicity, and SES subgroup differences in students’ math achievement and math advanced course-taking (Byrnes, 2003; Byrnes & Takahira, 1993). Therefore, a secondary purpose of the present study was to investigate model differences across gender and four main ethnic groups (Asian, African-American, Hispanic and Caucasian). Primarily, the interrelationship patterns indicated by path coefficients among all the identified factors showed no significant differences in terms of SEM analyses for female and male students. This is in spite of the fact that females reported higher utility value in learning and higher educational expectation than males. The female students also expressed lower math self-efficacy, intrinsic value, and were outperformed in standardized math assessment by male counterparts. Theoretically, the aforementioned results suggested the hypothesized models were equally viable for both male and female students. Conversely, many results emerged indicating the expectancy-value model of achievement motivation theory fits differently across ethnic groups. For example, African-American students reported higher math intrinsic value than Caucasian peers. Furthermore, African-American students differed from Caucasian students in that math intrinsic value was not significantly associated with advanced math course-taking for African-American students. In light of the results from the present study, the repertoire of empirical findings was extended to better understand the expectancy-value model of achievement motivation. Accordingly, potential educational implications including increasing students’ math self-efficacy, establishing alignment between intrinsic value and course choice, associating utility value with math subject were discussed to help promote math learning for students across gender and ethnic groups.