The proving process within a dynamic geometry environment

Abstract : Proof and proving have been objects of investigation from the point of view of mathematics and mathematics education for the past few years. Historical and epistemological studies show that proof is a crucial activity within mathematical practice. Didactical studies show that students encounter many difficulties when approaching proving in the classroom. Research at a cognitive level has developed frameworks interpreting students' difficulties. Studies concerned with the use of new technologies have been investigating the use of tools to support students with proving. In particular, a strand of research has studied specifically the impact of dynamic geometry software with respect to the teaching and learning of proving in geometry. The main difficulty with respect to proof and proving that emerges from current research is the gap between empirical and theoretical elements involved with these activities. This study addressed the problem of how a dynamic geometry software (Cabri) may support students in managing the relationship between the spatio-graphical (empirical) field and the theoretical field. Through a detailed analysis of students' processes when working with open geometry problems involving conjecturing and proving in Cabri, an analytical and explanatory framework has been developed. This framework also takes into account interactions between the students and the tools used and between the students themselves. The research findings suggest that proving within a dynamic geometry environment develops as a focusing process, in which the shifts between ascending and descending processes between the spatio-graphical and the theoretical field appear to be key elements for the construction of conjectures and proofs. The analysis also shows that Cabri works as a shared workspace, i.e. as a space which supports the interaction between students' internal contexts and the construction of shared knowledge.
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Federica Olivero. The proving process within a dynamic geometry environment. 2003. ⟨hal-00190412⟩

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