学習者の作問エラー診断のための実験的検討

抄録

Problem posing by which learners create problems by themselves has been identified as an important activity in mathematics education. However, problem posing is a heavy task for both learners and teachers because it is a divergent task that has various possible answers. To develop problem posing skill of learners, it is indispensable to evaluate posed problems, particularly when they include errors in mathematical structures. To provide a basis in designing computational support for addressing errors to improve problem posing skill, this study empirically investigated errors of mathematical word problems posed by novices. Undergraduates were engaged in a problem-posing task where they were asked to pose many, diverse and unique problems from a problem initially given. Posed problems that included errors were analyzed, with the result indicating that the undergraduates failed to pose problems due to failures in setting constraints or inconsistencies between texts and solutions. A computational system can detect constraint errors because they are represented in formal structures of solutions. On the other hand, it cannot detect inconsistent errors because semantic analysis of problem texts is required. We then discussed how to approach errors in problem posing by computational systems.