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

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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.