The role of conjectures on teaching geometry with computer

猜想在计算机几何教学中的作用

• 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-

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) ;

小组除了在节目中安排的时间外，还在三个两小时的时间段内举行会议。小组的共同目标是发现导致学生猜测活动的条件，研究猜测类型与数学内容和环境(有或没有计算机)之间的关系，最后分析可能产生的证明。这项工作的主要目标之一是对法国和日本学生的猜想和问题解决策略的产生进行点分析。这项研究的文化益处在于，它可能表明两国在数学方法上的根本差异。事实上，与验证问题有关的现象是两国将科学活动和数学作为一门学科的方式的重要指标，无论是作为教学对象还是作为文化对象。尤其是。矛盾的概念先验地不具有与日语主体相同的地位，特别是在社会互动中。起点是已经在日本和法国进行的三项实验研究活动。这些研究活动在这里作了简要介绍：(I)对法国学生和日本学生的证明和反驳过程进行了分析，其主要特点是重复了在格勒诺布尔已经进行的研究(巴拉切夫关于多角形的工作)。我们建议分析和比较小学生对待反例的方式；(Ii)分析电脑化环境对法国和日本小学生解决问题策略的影响。这种纸和铅笔环境的效果与计算机环境的效果的比较是在泰勒斯定理起关键作用的情况下进行的(加卢的工作)；

项目成果

NOHDA N.: "Study of problem-solving with CABRI-geometre in secondary shool" Tsukuba:Institute of Education.1-13 (1991)

NOHDA N.：“中学中使用 CABRI 几何解决问题的研究”筑波：教育学院.1-13 (1991)

Balacheff N.: "Une etude des processus de preuve en mathematiques chez des eleves de College. These de doctorat d'etat." Grenoble Univ.1-18 (1992)

Balacheff N.：“Une etude des processus de preuve en mathematiques chez des eleves de College。这些是博士学位。”