Empirical study on the teaching via problem solving in junior and high school mathematics focusing on the mental construction of problem

本研究以“几何证明”和“正弦定理”导论的教与学过程为中心，考察了日本学术能力的观点和现状，探讨了教师在通过问题解决进行教学的问题理解阶段的作用。因此，强调解决问题的必要性的效果是有限的，承认问题是自己的问题。相反，有人建议通过具体活动发现问题（提议）并认识到问题的局限性。此外，这种活动可能有助于改变学生对数学学习方式的看法。

In this study, I examined the views and the actual state of academic ability in Japan, and investigated the role of the teacher in the stage of problem-understanding in teaching via problem solving, focusing on the teaching-learning process of the introduction to "geometrical proof" and "sine theorem". As a result, it is suggested that the effect of emphasizing on the necessity to solve the problem is limited for recognizing the problem as one's own problem. Instead, the effectiveness of finding a problem (proposition) through concrete activity and recognizing a limit of it was suggested. Besides, such an activity might contribute to the change of the students' view of the way of learning of mathematics.