The role of conjectures on teaching geometry with computer

除了节目安排的时间段外，小组还在三个两小时的时间段会面。该小组的共同目标是发现导致学生进行猜想活动的条件，研究猜想类型与数学内容和环境（有或没有计算机）之间的关系，最后分析可能的证明结果。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。这项研究的文化效益在于，它很可能展示出两国在数学研究方式上的根本差异。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。在特定的。矛盾的概念在法国主体和日本主体中并不具有先天的相同地位，尤其是在社会互动中。起点包括已经在日本和法国开展的三项实验研究活动。这些研究活动简述如下：(i)分析法国学生和日本学生的证明和反驳过程，在其主要特点上重复格勒诺布尔已经完成的研究（Balacheff关于多边形的工作）。我们建议分析和比较，特别是学生对待反例的方式；（ii）分析电脑化环境对法语和日语学生解决问题策略的影响。将纸笔环境的效果与计算机环境的效果进行比较，是在泰勒斯定理发挥关键作用的情况下进行的（加卢的工作）；

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) ;