AbstractAs problem posing has been shown to foster students’ problem-solving abilities, problem posing might serve as an innovative teaching approach for improving students’ modelling performance. However, there is little research on problem posing regarding real-world situations. The present paper addresses this research gap by using a modelling perspective to examine (1) what types of problems students pose (e.g., modelling vs. word problems) and (2) how students solve different types of self-generated problems. To answer these questions, we recruited 82 ninth- and tenth-graders from German high schools and middle schools to participate in this study. We presented students with different real-world situations. Then we asked them to pose problems that referred to these situations and to solve the problems they posed. We analyzed students’ self-generated problems and their solutions using criteria from research on modelling. Our analysis revealed that students posed problems that were related to reality and required the application of mathematical methods. Therefore, problem posing with respect to given real-world situations can be a beneficial approach for fostering modelling abilities. However, students showed a strong tendency to generate word problems for which important modelling activities (e.g., making assumptions) are not needed. Of the students who generated modelling problems, a few either neglected to make assumptions or made assumptions but were not able to integrate them adequately into their mathematical models, and therefore failed to solve those problems. We conclude that students should be taught to pose problems, in order to benefit more from this powerful teaching approach in the area of modelling.
Interactive Environment for Learning by Problem-Posing for Reverse-Thinking Problems in Arithmetical Word Problems and Its Practical Use