幅広い学力差を許容する数学科教材・教授法の開発

抄録

A mathematical proposition is usually constructed in the following order: (1) Idea construttion. (2) Expectation of the proposition based on the idea. (3) Proving of the expectation. Therefore, we may say the mathematical proposition and its proof are completed simultaneously in most cases. In an ordinary math class, however, a proposition and its proof are not constructed in this way. Obviously, it is very important for the students to create an idea in order to construct a proposition and its proof in the above-mentioned process. In this paper, we show a new teaching-learning process on the proposition P, which is made up of the following steps. (Step 1) By solving the simple given problems (Q_n), the students unconsciously make preparations for the concepts (C_n) and thinking fields (Fn) necessary for idea-constrution of P. (Step 2) By combining (C_n) with (F_n) in various ways, the students construct an idea I, which develops into P. (Step 3) The students construct an expectation of P on the basis of I. (Step 4) The students construct an idea I^*, which develops into the proof of P. (Step 5) The students construct P and its proof on the basis of I and I^* respectively. The main purpose of this paper is to show the new teaching-learning process which will be able to allow wide differences in students' achievements.