Cognitive Conflicts as a Teaching Strategy to Enhance the Need of Mathematical Proofs with Technology Support

Abstract

In solving mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiments and experiences. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope with students’ conviction based on empirical experience only and to create a need for deductive explanations, we developed a teaching activity with technology support intended to cause cognitive conflicts. In this paper, we describe the conducting process throughout this activity that led students to contradictions between original conjectures and new findings. The teacher could create familiar problem situations and use students’ naïve inductive approaches to make students think mathematically and establish the necessity for proofs via technology support.