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.

由于问题解决已被证明可以培养学生解决问题的能力，因此问题解决可以作为一种创新的教学方法来提高学生的建模表现。但是，关于现实情况中的问题构成的研究很少。本论文通过使用建模视角来研究（1）学生提出什么类型的问题（例如，建模与单词问题）以及（2）学生如何解决不同类型的自发问题，从而解决了这一研究空白。为了回答这些问题，我们从德国的中学和中学招募了82名9年级和10年级的学生参加这项研究。我们向学生展示了不同的现实情况。然后，我们要求他们提出与这些情况有关的问题，并解决他们提出的问题。我们使用建模研究中的标准来分析学生的自我产生的问题及其解决方案。我们的分析表明，学生提出了与现实有关的问题，需要运用数学方法。因此，针对给定的实际情况提出的问题可能是培养建模能力的有益方法。但是，学生表现出产生单词问题的强烈趋势，而这些单词问题不需要进行重要的建模活动（例如进行假设）。在产生建模问题的学生中，有少数人忽略了假设或做出了假设，但无法将它们充分地整合到数学模型中，因此未能解决这些问题。我们得出结论，应该教导学生提出问题，