How do self-efficacy and self-concept impact mathematical achievement? The case of mathematical modelling

According to the self-enhancement perspective, self-efficacy and self-concept are shaped by prior achievement and have a crucial impact on future development. Their role in improving performance on challenging tasks, such as mathematical modelling (i.e., solving realistic problems mathematically), has barely been studied.

We investigated patterns of self-efficacy and self-concept and their predictive effects on mathematical modelling while taking into account school grades as measure of prior achievement and reasoning to reveal cognitive and motivational effects on achievement.

N = 279 secondary students in Grade 8 or 9 from 16 classes and 6 schools participated in the study.

The multi-informant design consisted of teachers' reports of school grades, students' reports of self-efficacy and self-concept (questionnaire-based), and assessment of students' reasoning and mathematical modelling.

Using random-intercept models, we found that the predictive effect of self-efficacy on mathematical modelling withstood taking the school-classroom-related nested structure into account, whereas self-concept lost its predictive value. Further, self-efficacy fully mediated the effect of school grades on mathematical modelling.

In line with the self-enhancement perspective on self-efficacy, our findings highlight the strength of motivational effects on mathematical modelling. When we take the nested structure into account, our results indicate an impact of school grades via self-efficacy on mathematical modelling independent of students' cognitive level or classroom. Given the diverse challenges such complex tasks present, important pedagogical and didactical recommendations, such as targeting the enhancement of students' self-efficacy by teachers and educational decision makers, can be drawn.