Openness in mathematical modelling: do experiences of competence and autonomy mediate the effects of an intervention on modelling problems on task values and cost?

Abstract Motivation is crucial for learning and achievement. An effective way to increase students’ motivational outcomes, such as task values and cost, can be to incorporate modelling problems in mathematics lessons. Due to their openness, working on modelling problems can lead to experiences of competence and autonomy. In this study, we aimed to analyze (1) whether an intervention on modelling problems with open initial state affects students’ task values and cost, (2) whether this intervention affects students’ experiences of competence and autonomy, (3) whether experiences of competence and autonomy affect task values and cost, and (4) whether this intervention has an indirect effect on students’ task values and cost via their experiences of competence and autonomy. To achieve this aim, we conducted an experimental study with 295 ninth graders using a pre-posttest design. We found positive effects of the intervention on students’ motivational outcomes. Furthermore, experiences of competence and autonomy mediated these effects. By demonstrating effects of the intervention on modelling problems with open initial state on task values and cost, our study contributes to the theory of modelling. Furthermore, the results of our study contribute to motivational theories by uncovering the crucial role of the experiences of competence and autonomy as an intervening variable that explains how the intervention on modelling problems with open initial state affects intrinsic and attainment values.