The role of conjectures on teaching geometry with computer

小组在三个两小时的时间段内开会，除了计划中安排的时间段外，小组的共同目标是发现导致学生数学活动的条件，研究数学内容和环境（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小学生的数学成绩和解题策略进行点分析。这项研究的文化益处在于，它很可能展示出两国在数学学习方式上的根本差异。事实上，与验证问题有关的现象是科学活动和数学作为一门学科在这两个国家被视为教学对象或文化对象的方式的重要指标。尤其是。矛盾的概念在法国学科中的地位与在日本学科中的地位不同，特别是在社会交往中。2本文的出发点是在日本和法国进行的三项实验研究。这些研究活动在这里简要介绍：（一）分析的过程中的证据和反驳的一部分，法国小学生和日本小学生，重复其主要特点的研究已经在格勒诺布尔（Balacheff的工作polygones）。我们建议分析和比较，特别是，学生对待反例的方式;（ii）分析的计算机化环境的法国和日本的小学生解决问题的策略的影响。这种比较的影响，一个纸和铅笔的环境与计算机环境的影响进行的情况下，泰勒斯定理发挥了至关重要的作用（加洛的工作）;

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) ;