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HOW STUDENTS WRITE AND TALK PROOF IN GEOMETRY PROBLEM -ANALYSIS OF STUDENTS ACTIVITIES BY USING SOFTWARE-

学生如何在几何问题中写和说证明 -使用软件分析学生活动-

基本信息

批准号：
07808018
负责人：
KAKIHANA Kyoko
金额：
$ 1.02万
依托单位：
TOKYO KASEI GAKUIN TSUKUBA 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：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07808018/
关键词：
GEOMETRY COMPUTER MIDDLE SCHOOL PROOF EXPERIMENT & OBSERVATION MEASUREMENT 幾何(Geometry)実験数学

项目摘要

Usually in a secondary school geometry, conditions and a conclusion are given and students are asked to draw logically the conclusion based on these conditions. In these situation, students have seemed to have no motivation to make proof and to have difficulties to write proof. When middle school students solve proof problems in the geometric computer environment, the use of measurements helps them to confirm the geometric properties they discover, and measurements provide stron evidence to convince them of these properties. At that time, students are involved in the problems very actively (Kakihana & Shimizu, 1993). The purpose of this research is to investigate how students' strategies talk and write the reason of the properties which they found themselves in the geometric computer environment. And an effect of property finding activities by software on write in proof was examined.Junior high school level geometry problems were given to five pairs of women's junior college students and their activities were videotaped and analyzed. Students' worksheets were also collected and analyzed. From the results, it was identified that (1) the use of measurements for conjecturing in pair conversations helped to explain logically the reasoning or to construct statements for formal proof and (2) the use of measurement helps to convince students of the logical reasoning in a statement of proof.

在中学几何中，通常会给出条件和结论，并要求学生根据这些条件逻辑地得出结论。在这种情况下，学生似乎没有动力去做证明，写证明也有困难。中学生在几何计算机环境下解决证明问题时，测量的使用有助于他们确认所发现的几何性质，而测量又为他们提供了强有力的证据使他们相信这些性质。在那个时候，学生们非常积极地参与到问题中来（Kakihana和Shimizu，1993年）。本研究旨在探讨学生在电脑几何环境中，如何运用说和写的策略，来解释他们所发现的几何性质。本研究以五对女性大专生为研究对象，以初中几何问题为题，对她们的活动进行录像和分析。学生的问卷也被收集和分析。结果表明：（1）在配对对话中使用测量手段有助于逻辑地解释推理或构建正式证明的陈述;（2）使用测量手段有助于说服学生相信证明陈述中的逻辑推理。