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

本研究的目的是为了阐明使用计算机软件CABRI-GEOMETRY作为帮助几何证明问题解决困难的学生的手段的效果。本研究也被定为日法合作研究，因此我们可以从国际比较研究的角度来考虑实验结果。为此，我们利用加布里几何进行了教学实验。研究对象为初中生。实验问题所用的问题一般可以用泰利斯定理解决。主要结论如下：(1)利用卡布里几何的“图形变换功能”，学生获得了“动态的图形观点”，发展了他们的猜想活动。(2)利用卡布里几何的“图形变换功能”，使学生获得问题的“专业化”和“图形观点的转换”。(3)利用“几何作图”功能，使学生了解问题的条件和推理链。(4)使用卡布里几何，日本学生获得了更多令人印象深刻的“动态图形观点”，法国学生获得了良好的几何图形“可视化”。(5)从“教学情境”的分析来看，卡布里几何被学生用作几何证明问题解决中的“生成猜想的手段”、“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”帮助学生解决几何证明问题的方法。

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".