The relationship between domain- and task-specific self-efficacy and mathematical problem posing: a large-scale study of eighth-grade students in China

Abstract

This study explored 1634 Chinese eighth-grade students’ domain- and task-specific self-efficacy and its relationship to their problem-posing performance. In particular, the linear regression model, generalized additive model (GAM), and piecewise regression model (PRM) were used to detail the linear and non-linear relationships between these variables. The findings indicate that most (92.5%) of the students could pose mathematical problems in all tasks, but the effect of their domain-specific self-efficacy on their problem-posing performance was lower than the effect of their task-specific self-efficacy. Students’ problem-posing performance and their task-specific self-efficacy were not always matched when the requirements of the problem they posed varied in difficulty. As the level of difficulty increased, the correlation coefficient between task-specific self-efficacy and problem posing declined from 0.22 to 0.06. Furthermore, PRM confirmed that there were significant changes of the slope around the cut-point of the relationship between task-specific self-efficacy and students’ problem-posing performance. Moreover, the relationship between task-specific self-efficacy and posing performance was different for easy and difficult problems, as the cut-point and slopes before and after the point varied. The findings of this study contribute both to understanding self-efficacy as well as advancing understanding about the characteristics of problem posing from a non-cognitive perspective.