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A Research on the Curriculum Development based on the Epistemological Research into the Concept of Geometry

基于几何概念认识论研究的课程开发研究

基本信息

批准号：
13680319
负责人：
KAWASAKI Michihiro
金额：
$ 2.05万
依托单位：
Oita University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

The purpose of this research has been to carry out epistemological research into the concept of geometry so as to construct a fundamental theory on the curriculum of geometry. The epistemological research into the concept of geometry is classified to three categories : mathematical, psychological, and mathematics educational epistemology.In psychological epistemology, the cognitive nature of the concept of geometry has been discussed. The previous cognitive researches on the concept of geometry have been investigated and some issues have been identified. We have to carry out following four types of researches : research into the teaching process, research on the meaning of representational modes, curriculum research, and extended research.In mathematical epistemology, mathematical meanings of the concept of geometry have been clarified from three points of view : ontological view, metaphysical view, and historical view. It has been found that the mathematical meaning of the concept of geometry is recognized realistically and empirically. Moreover the curriculum of geometry has been reflected from mathematical perspective.In mathematics educational epistemology, phenomenological research and pedagogical research has been carried out in order to analyze the teaching of geometry. Firstly the characteristics and the functions of geometrical sense have been clarified and the best teaching of geometrical sense has been considered. Secondly the process from recognition of ideality on the concept of geometry to recognition of objectivity has been identified. Finally the curriculum of geometry into which intuition and logic are assimilated to realize the teaching of geometry for the sake of raising certain recognition of geometry has been designed.

本研究的目的是对几何概念进行认识论研究，以建构几何课程的基本理论。对几何概念的认识论研究可分为数学认识论、心理认识论和数学教育认识论三大类，其中心理认识论主要讨论几何概念的认知本质。对以往几何概念的认知研究进行了回顾，指出了一些问题。在数学认识论方面，从本体论、形而上学和历史观三个角度阐明了几何概念的数学意义。研究发现，几何概念的数学意义是现实的、经验的。从数学教育认识论的角度对几何课程进行了反思，对几何教学进行了现象学研究和教育学研究。本文首先阐明了几何感的特点和作用，并对几何感的最佳教学进行了思考。其次，对几何概念从理想性认识到客观性认识的过程进行了论证。最后，设计了一个将直觉与逻辑融为一体的几何课程，以实现几何教学，提高对几何的一定认识。