The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments

In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose.This revised version was published online in September 2005 with corrections to the Cover Date.