The role of conjectures on teaching geometry with computer

猜想在计算机几何教学中的作用

基本信息

批准号：
03045015
负责人：
NOHDA Nobuhiko
金额：
$ 2.43万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for international Scientific Research
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03045015/
关键词：
Computer Cabri-Geomitry conjecture Inference proof Mathematics Education カブリ・ジオメトリ-

项目摘要

The group met during three two hours time-slots in addition to the time-slots scheduled in the program.The common aim of the group is to discover the conditions which lead to conjectural activity for pupils, to study the relationship between the types of conjectures and mathematical contents and environments(with or without a computer), and finally to analyze the possible production of proofs. One of the main targets of the work is a point analysis of the production of conjectures and of problem solving strategies of both French and Japanese pupils.The cultural benefit of this research lies in the fact that it is likely to demonstrate fundamental differences in the way mathematics is approached in both countries. Indeed, phenomena related to problems of validations are significant indicators of the ways scientific activity and mathematics as a discipline are considered in both countries whether as didactical objects or as cultural objects. In particular. the notion of contradiction does not have a priori the same status for a French subject as for a Japanese subject, In particular as it appears in social interaction.The starting point consists of three experimental research activities already carried out in Japan and in France. These research activities are briefly described here :(i) an analysis of the processes of proofs and refutations on the part of French pupils and Japanese pupils, repeating in its main features the study already done in Grenoble (Balacheff's work on polygones). We propose to analyze and to compare, in particular, the ways pupils treat counter-examples ;(ii) an analysis of the effect of a computerized environment on the problem-solving strategies of French and Japanese pupils. This comparison of the effects of a paper and pencil environment with the effects of a computer environment is performed in the case of situations in Which Thales theorem plays a crucial role (Gallou's work) ;

该小组在计划中安排的时间插槽外，在两个两个小时的时间插槽中开会。该小组的共同目的是发现导致学生猜想活动的条件，以研究猜想的类型之间的关系以及数学内容和环境（有或没有计算机），最后分析可能的证据产生。这项工作的主要目标之一是对法国和日本学生的猜想产生以及解决问题的策略的观点分析。这项研究的文化利益在于，它很可能在路上证明了基本差异在两个国家都接触了数学。实际上，与验证问题有关的现象是两国在教学对象或文化对象中考虑科学活动和数学作为学科的重要指标。尤其。矛盾的概念对法国主题没有与日本主题相同的状态，尤其是在社交互动中出现的，起点包括在日本和法国已经进行的三项实验研究活动。这些研究活动在这里简要介绍：（i）对法国学生和日本学生的证明和反驳过程的分析，在其主要特征中重复了这项研究已经在格勒诺布尔（Grenoble）所做的（Balacheff在多边形上的工作）。我们建议分析和比较学生对反审查的方式；（ii）分析计算机环境对法国和日本学生解决问题的策略的影响。在Thales定理起着至关重要的作用的情况下，对纸张和铅笔环境的影响与计算机环境的影响进行了比较（Gallou的工作）；