JAPAN-FRANCE CROSS-CULTURAL RESEARCH ON STUDENTS' MISCONCEPTIONS IN GEOMETRICAL PROBLEM SOLVING

本研究的目的是从日法跨文化研究的角度，找出学生在几何问题解决中的错误概念，并阐明克服错误概念的方法。本研究以初中生为被试，进行了四个教学实验：实验一：纸与纸的单独解题实验二：纸与纸的成对解题实验三：卡布里几何的单独解题实验四：卡布里几何的成对解题实验。（1）学生在几何证明问题解决中产生的错误概念主要有：“图形理解错误概念”、“图形一般性错误概念”、“证明的普遍有效性错误概念”等。(2)我们可以从“给出证明步骤”、“在证明中确认命题的有效性”、“利用卡布里几何给出图形的动态观点”、“给出社会互动的情境”等方面阐明克服解题中错误观念的方法。(3)从数字的表述方式和解题中的证明形式可以看出，各国的文化特点都有体现。

The purpose of this research is to identify students' misconceptions in geometrical problem solving and clarify the means to overcome their misconceptions from viewpoint of Japan-France cross-cultural research. For the purpose, we made four didactical experiments with junior high school students.Experiment 1 : Problem solving by using Paper and Pencil in dividuallyExperiment 2 : Problem solving by using Paper and Pencil in pairsExperiment 3 : Problem solving by using Cabri-Geometry in individuallyExperiment 4 : Problem solving by using Cabri-Geometry in pairsThe main conclusions are as follows :(1) We could identify students' misconceptions which were produced in the geometrical proof-problem solving as follows : "misconceptions of apprehension of figures", "misconceptions of generality of figures", "misconceptions of universal validity of proof", and so on.(2) We could clarify the means to overcome their misconceptions in the problem solving as follows : "giving procedures for proof", "confirming validity of propositions in proof", "giving dynamic viewpoints of figures by using Cabri-Geometry", "giving situation for social interactions", and so on.(3) We could find the fact the cultural characteristics in each country are reflected in their recognitions of figures and their forms of discription of proof in the problem solving.