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误区，并阐明克服误区的方法。为此，我们对初中生进行了四个教学实验。实验一：用纸和笔分别解决问题；实验二：用纸和笔成对解决问题；实验三：用卡布里几何分别解决问题；实验四：用卡布里几何成对解决问题。主要结论如下：(1)我们可以识别出学生在几何证明问题解决过程中产生的错误概念，它们分别是：图形理解的错误概念、图形共性的错误概念、证明的普遍有效性错误概念、(2)我们可以从“给出证明程序”、“确认证明命题的正确性”、“用卡布里几何给出动态的图形观点”、“给出社会互动情境”等方面来阐明克服他们在问题解决中的误区的方法。(3)我们可以发现，每个国家在解决问题时对数字的认识和对证明的描述形式都体现了各自的文化特征。

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.