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Basic Study for improving the teaching of gepmetry on new views on scholastic ability

学力新观改进几何学教学的基础研究

基本信息

批准号：
07458025
负责人：
SHIMIZU Shizumi
金额：
$ 3.14万
依托单位：
University of TSUKUBA
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1997
项目状态：
已结题

项目摘要

Improvement of education is strongly required for our future. Especially, for mathematics education, the new course of study requires the instruction that aims to help student's developments of logical thinking and flexible intuition.Our mathematics education goes on the line of this direction. But the basic research for geometry teaching is still new field than teaching about calculation and equation, and is not enough developed.In this paper, we discuss fundamental views to improve guiding student's learning in geometry. Especially we focus on conceptual formulation and proof in geometry from elementary school to high school.The main part of research findings is as follows. The first, we examined the condition of the present school mathematics and to clarify the problems to be considered. That is, we clarified that students have very poor ability to judge the truth or the false and to express precisely in each situation. The second, we made clear the characteristic of the issues and the practical perspectives for school mathematics based on 'New views on scholastic ability'. On this perspective, the student's motivation and autonomy are the most important and so we organized the perspectives with this idea for reforming the school mathematics. Furthermore, we historically considered the perspectives by focusing on the process that geometry education in our country was transferred, accepted and established. By the consideration, we could suggest that it is necessary to integrate the intuition and induction which are tradition and power in Japanese classic mathematics, "wasan", with the formality and logic in western mathematics. On the theoretical research, we advanced "Practical research about learning geometry", and "Comparative study of learning geometry". Through the researches, we suggested many findings to improve learning geometry and also implied the future tasks.

我们的未来迫切需要改善教育。特别是对数学教育来说，新课程的学习要求以培养学生的逻辑思维和灵活的直觉为指导。我们的数学教育就是沿着这个方向发展的。但与计算、方程教学相比，几何教学的基础研究仍是一个新的领域，尚未得到充分的发展。本文就如何更好地指导学生几何学习的基本观点进行了探讨。我们特别关注从小学到高中的几何概念公式和证明。研究结果的主要部分如下。首先，我们考察了目前学校数学的状况，并阐明了需要考虑的问题。也就是说，我们澄清了学生判断真假和在每种情况下准确表达的能力非常差。第二，在“新学力观”的基础上，明确了学校数学问题的特点和实践前景。在这一观点下，学生的积极性和自主性是最重要的，因此我们以这一观点组织了学校数学改革的观点。此外，我们通过关注我国几何教育的转移，接受和建立的过程，历史地考虑了这些观点。通过思考，我们可以认为，有必要将日本经典数学“wasan”的传统和力量——直觉和归纳法与西方数学的形式和逻辑相结合。在理论研究方面，提出了“几何学习的实践性研究”和“几何学习的比较研究”。通过研究，我们提出了许多改进几何学习的发现，并暗示了未来的任务。