Bridging the gap between mathematical conjecture and proof through computer-supported cognitive conflicts

摘要

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. 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 up with students’ conviction based only on empirical experience and to create a need for deductive explanations, we developed a problem-solving activity with technology support intended to cause cognitive conflict. In this article, we describe the process conducted for this activity that led students to contradictions between conjectures and findings. The teacher could create familiar problem-solving situations and use students’ na?ve inductive approaches to make students think mathematically and establish the necessity for proof via computer support.