Mathematical modelling and self-efficacy: immediate and long-lasting effects of teaching mathematical modelling with a solution plan

Abstract Mathematical modelling requires both mathematical competencies and skills and is influenced by motivational beliefs, such as self-efficacy. However, limited research has explored how teaching modelling using a solution plan impacts modelling competence and self-efficacy in both the short and long term, or whether self-efficacy contributes to improvements in mathematical modelling. In this study, we examined (a) the immediate and long-term effects of teaching modelling on modelling competence, (b) the effects of teaching modelling on self-efficacy, and (c) the role of self-efficacy as a predictor of modelling competence among students receiving an intervention. A total of 157 Swiss secondary school students, representative of socioeconomic status and gender, from nine classes participated in the study. The intervention group solved modelling problems using a solution plan over four mathematics lessons, while the control group continued with their regular curriculum. Mathematical modelling competence and self-efficacy were assessed through pre-, post-, and follow-up tests. The analyses revealed a positive effect of teaching modelling using a solution plan on modelling competence, which persisted at follow-up. Although the intervention did not directly affect self-efficacy, self-efficacy was found to predict improvement in mathematical modelling from pretest to posttest in the intervention group. This exploratory study highlights the immediate and long-term positive impact of teaching mathematical modelling with a solution plan on students’ modelling competence. A key contribution of this study is the demonstration of the crucial role of self-efficacy in the development of modelling competence, as proposed by social cognitive theory.