Students approaching proof through conjectures: snapshots in a classroom

Abstract

The paper presents a classroom experiment in which students were asked to solve an open problem. It is the authors' premise that this kind of task fosters a ‘smooth’ approach to proofs that are constructed around the production and validation of conjectures. This experiment is aimed at constructing a shared classroom culture. Classroom discussion and collaborative group work help to achieve this aim. The analysis of the experiment shows that the discussion makes explicit aspects of students' thinking which would be hidden in a normal activity. It is demonstrated that a deeper analysis of students' reasoning and behaviours can be better performed if lessons are video-recorded. There is a twofold pedagogic gain in using videotapes as a tool for analysing students' behaviour: first, it offers the teacher a tool that encourages students to reflect on their reasoning; secondly, and conversely, it offers researchers a further tool for analysing students' performances.