図形指導における図形概念の理念性と客観性の認識について

抄録

The concept of geometry is being investigated very actively on the basis of cognitive theory. But there are very few reports about the methods to develop the curriculum of the teaching of geometry as well as to describe the process through which the concept of geometry is recognized. So to reflect upon the teaching of geometry, I intended to investigate the recognition of the concept of geometry by use of phenomenology. The main purpose of this study is to clarify the meaning of ideality and objectivity on the concept of geometry. First I reviewed the results of a series of previously reported studies on the concept of geometry. Then I listed up the problems worthwhile to investigate. What is ideality and objectivity on the concept of geometry? What characteristics dose ideality and objectivity has? How is ideality and objectivity recognized? How is ideality and objectivity taught? The characteristics of ideality on the concept of geometry are as follows: nonentity, identity, repeatability, meaningfulness, consideration, recognition along stages and dependence upon perception. Ideality on the concept of geometry is recognized along the following three stages: sensitivity, imagination and ideality. There are two types of recognition from sensitivity to ideality, that is to say, from sensitive entity to idealistic entity. One type of recognition is so-called "abstraction" from object to shape, and the other is so-called "generalization" from diagram to figure. In this study I used the term "objectivity" on the concept of geometry from the idealistic point of view. The characteristics of objectivity on the concept of geometry can be expressed as follows: intersubjectivity, identity, evidence, dependence upon anyone, anytime and anywhere, repeatability and linguistics. Objectivity on the concept of geometry is recognized along the following three stages: dialogue, linguistics and objectivity. Special attention should be paid to the recognition from "ideality" of individual concept of geometry to "objectivity" in the teaching of geometry. Then "imagination" of treating sensitive entity, "dialogue" among classroom members and "linguistics" which is objective in mathematical world should be emphasized.