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

日法跨文化研究学生解决几何问题的误解

• 批准号: 11680278
• 负责人: HARADA Kouhei
• 金额: $ 1.28万
• 依托单位: KAWAMURA-GAKUEN WOMEN'S UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11680278/
• 关键词: PROBLEM SOLVING; GEOMETRY; PROOF; CABRI-GEOMETRY; カブリ・ジオメトリー; 問題解決; 作図

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.

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)我们可以明确克服他们在解决问题时的误解的方法：“给出证明程序”、“确认证明中命题的有效性”、“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。(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。

项目成果

原田耕平: "幾何の証明問題の解決における困難の原因"日本数学教育学会第32回数学教育論文発表会論文集. 32. 227-232 (1999)

Kohei Harada：“解决几何证明问题的困难原因”日本数学教育学会第 32 届数学教育论文发表论文集 32. 227-232 (1999)。