As 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.

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In mathematics education, pre-formulated modelling problems are used to teach mathematical modelling. However, in out-of-school scenarios problems have to be identified and posed often first before they can be solved. Despite the ongoing emphasis on the activities involved in solving given modelling problems, little is known about the activities involved in developing and solving own modelling problems and the connection between these activities. To help fill this gap, we explored the modelling process from a problem posing perspective by asking the questions: (1) What activities are involved in developing modelling problems? and (2) What activities are involved in solving self-generated modelling problems? To answer these research questions, we conducted a qualitative study with seven pre-service teachers. The pre-service teachers were asked to pose problems that were based on given real-world situations and to solve their self-generated problems while thinking aloud. We analyzed pre-service teachers’ developing and subsequent solving phases with respect to the problem posing and modelling activities they were engaged in. Based on theories of problem posing and modelling, we developed an integrated process-model of posing and solving own modelling problems and validated it in the present study. The results indicate that posing own modelling problems might foster important modelling activities. The integrated process-model of developing and solving own modelling problems provides the basis for future research on modelling problems from a problem posing perspective.