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

为了我们的未来，我们迫切需要改善教育。特别是对数学教育而言，新课程要求数学教育要以培养学生的逻辑思维和灵活直觉为目标，我国的数学教育也沿着这一方向发展。但几何教学的基础研究相对于计算和方程的教学来说还是一个新的领域，还没有得到充分的发展，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。特别是在小学到高中阶段，我们着重于几何概念的建立与证明。首先，我们审视了当前学校数学的现状，明确了需要考虑的问题。也就是说，我们澄清了学生判断真假的能力非常差，并且在每种情况下都能准确表达。第二，明确了“新学力观”下的学校数学问题的特点和实践视角。在这个观点下，学生的学习动机和自主性是最重要的，因此我们以这个观点来组织学校数学的改革。并以我国几何教育的传承、接受和确立过程为重点，对这一观点进行了历史性的思考。通过这种思考，我们可以认为，有必要将日本古典数学“和三”中的传统和力量--直觉和归纳法与西方数学中的形式和逻辑结合起来。在理论研究方面，提出了“几何学习的实践研究”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。

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.