数学学習における「例づくり」に関する研究 : 「例づくり」による数学的知識の構成

抄録

The aim of this paper is to consider a constructive activity through "make up an example of" tasks. I named them "REIZUKURI", and presented a lesson plan to construct mathematical knowledge in the classroom (15-years-old students). According to previous research, asking students to provide examples stimulates class participation and produces an active atmosphere. Most of them were descriptions of developing and deepening mathematical knowledge in teaching. "REIZUKURI" addresses different mathematical objects and requires different mathematical knowledge, and it has three features: providing opportunities to deal with abstract mathematical notions, reversing the usual role of what is "given" and what is "to be found" and being open-ended. The lesson plan which I presented aims at constructing the concept of the factorization in prime numbers and the knowledge of how to examine the number of factors. This lesson starts by the task "make up an example of some integers that have only two factors". After students confirm the definition of the word "factor", they are told the definition of the word "prime number" by teacher through many examples concerning this task. And then, teacher asks students to make up an example of some integers that have only five factors, only six factors, only seven factors and eight factors. They will make up many examples by trial and error. I guess that presenting the task "make up an example of some integers that have only twelve factors" for the last time prompts their inductive reasoning and is achieved the aim of this lesson. In addition, the last task acts a important function as Being Mediative in the "Constructive Approach" (Nakahara, 1995).