Using Cabri-Geometry of Helping Students in Geometrical Proof-Problem Solving

利用Cabri-Geometry帮助学生解决几何证明问题

• 批准号: 06680269
• 负责人: HARADA Kouhei
• 金额: $ 0.96万
• 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 General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06680269/
• 关键词: Problem-Solving; Geometry; Proof-Problem; Computer

The purpose of this research is to clarify the effects of using Computer Sofware : Cabri-Geometry as the means of helping students who had difficulties in the geometrical proof-probelm solving. Also this resesrch is planed as Japan-France Collaboreative Research, so we can consider the results of experiments from viewpoints of the international comparative research.For this purpose, we made "didactical experiments" using Gabri-Geometry. Subjects were junior high school students. The problems of experiments employed problems which genearally can be solved using Thales'Theorem. The main conclusions are as follows : (1) By using "function of transforming figures" of Cabri-Geometry, students gained "dynamic viewpoints of figures" and their conjectual activities were developed. (2) By using "function of transforming figures" of Cabri-Geometry, students gained "specialization" of problems and "changing viewpoints of figures". (3) By using "function of drawing figures" of Cabri-Geometry, students could understand the conditions of problems and the chain of inferences. (4) By using Cabri-Geometry, Japanese students were given more impressively "dynamic viewpoints of figures" and French students gained good " visualization" of geometrical figures. (5) From viewpoints of the analysis of "didactical situations", Cabri-Geometry was used by students as "the means of generating conjectures", "the means of coping with refutation", and "the means of establishing validity of conjectures" in geometrical proof-problem solving. Setteing up the "didactical situation" by using Cabri-Geometry is a method of helping sutudents in geometrical proof-problem solving based on the "social interactions".

本研究的目的是为了阐明使用Cabri-Geometry计算机软件作为帮助在几何证明问题解决方面有困难的学生的手段的效果。此外，本研究计划为日法合作研究，因此我们可以从国际比较研究的角度考虑实验结果。为此，我们使用加布里几何进行了“教学实验”。研究对象为初中生。实验问题所采用的问题通常可以用泰勒斯定理来解决。主要结论如下：(1)利用卡布里几何的“变换图形的功能”，学生获得了“动态的图形视点”，发展了他们的猜想活动。(2)利用卡布里几何的“变换图形的功能”，学生获得了问题的“专业化”和“变换图形的视点”。(3)通过卡布里几何中的“绘图函数”，学生能够理解问题的条件和推论链。(4)通过Cabri-Geometry，日本学生获得了更深刻的“图形动态视点”，法国学生获得了较好的几何图形“可视化”。(5)从“教学情境”分析的角度看，卡布里几何在几何证明解题中被学生用作“产生猜想的手段”、“应对反驳的手段”和“确立猜想有效性的手段”。利用卡布里几何创设“教学情境”是一种基于“社会互动”的几何证明解题方法。

项目成果

原田耕平・能田伸彦・エリザベート・ガル-・ダミール: "幾何の証明問題の解決を支援するCabri-Geometryの利用" 日本数学教育学会第27回数学教育論文発表会論文集. 329-334 (1994)

Kohei Harada、Nobuhiko Noda、Elisabeth Gal-Damir：“使用 Cabri-Geometry 支持解决几何证明问题”日本数学教育学会第 27 届数学教育论文发表论文集 329-334 (1994)。

原田耕平,能田伸彦,エリザベート・ガル-・ダミール: "幾何の証明問題の解決を支援するCabri-Geometryの利用" 日本数学教育学会第28回数学教育論文発表会論文集. 275-280 (1995)

Kohei Harada、Nobuhiko Noda、Elisabeth Gal-Damille：“使用 Cabri-Geometry 支持解决几何证明问题”日本数学教育学会第 28 届数学教育论文发表论文集 275-280 (1995)。

HARADA,Kouhei NOHDA,Nobuhiko: "Student's knowledge Generated by Using Cabri-Creometry" Tsukuba Journal of Educational Study in Mathematics. 13. 103-111 (1995)

HARADA、Kouhei NOHDA、Nobuhiko：“使用 Cabri-Creometry 生成学生的知识”筑波数学教育研究杂志。

HARADA,Kouhei & NOHDA,Nobuhiko: "Students' Knowledge Generated by Using Cabri-Geometry" Tsukuba Journal of Educational Study in Mathematics. Vol.14. 103-111 (1995)

原田耕平

原田耕平: "幾何の証明問題の解決を支援するカブリ・ジオメトリーの利用" 日本科学教育学会20周年記念論文集. 285-292 (1996)

Kohei Harada：“利用卡夫里几何支持解决几何证明问题”日本科学教育学会 20 周年纪念论文集 285-292 (1996)。