高校生の数学的思考をはぐくむ授業の創造 : 導入の工夫と生徒の話し合いの活動を通して

抄録

Nowadays, the improvement of teaching toward students oriented activity in the high school mathematics class is strongly required to enhance the mathematical thinking of students. The author has a belief that the essences of teaching matters should be found out by students themselves in the class, and the teacher should prepare appropriate situations to realize such findings. In particular, it appears often at the introduction of teaching contents. In this paper, we study a practical plan to realize the aspect stated above in high school mathematics classes, through teaching materials and actual practices. We put the theoretical base of our assertion on the constructive approach proposed by Ito (1993) and other authors. The main findings are as follows: (1) We show that it is effective to provide opportunities that students consult or discuss with neighboring students each other about the focused problem they are facing in the class, and that such effective communication by students is possible if the teacher prepares proper situation and set appropriate time allocation. (2) We analyze what are the important factors on teaching materials to be used at the introduction, and we show several concrete samples of teaching materials that satisfy such factors. The samples have been examined in actual classes and proved to inspire students' mathematics thinking at introduction. (3) We report one practice of a class by the author, which incorporates the factors in (1) and (2), and analyze the assessment of it through the questionnaire to the students. As a result, high percentage of students give positive answers to the planned class activities by expressing their satisfaction for good understanding.