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

为了我们的未来，改善教育是非常必要的。特别是对于数学教育来说，新课程要求以发展学生的逻辑思维和灵活直觉为目标的教学，我们的数学教育就是朝着这个方向发展的。但相对于计算和方程教学而言，几何教学的基础研究还是一个新的领域，还不够发达。本文就如何更好地指导学生学习几何，提出了一些基本观点。特别关注从小学到高中的几何概念的表述和证明。主要研究成果如下。首先，我们考察了当前学校数学的现状，明确了要考虑的问题。也就是说，我们澄清了学生在每种情况下判断真假和准确表达的能力很差。其次，在新学力观的基础上，明确了问题的特点和学校数学的实践视角。在这个视角下，学生的主动性和自主性是最重要的，所以我们用这个理念组织了几个视角来改革学校数学。此外，我们还着眼于几何教育在我国的传承、接受和确立的过程，进行了历史的思考。由此可以看出，日本古典数学《和三》中的传统和力量--直觉和归纳--与西方数学中的形式化和逻辑性相结合是必要的。在理论研究上，提出了“学习几何的实践研究”和“学习几何的比较研究”。通过研究，我们提出了许多改进几何学习的发现，并对未来的任务进行了展望。

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.