How do teachers’ approaches to geometric work relate to geometry students’ learning difficulties

摘要

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric work conducted, in sometimes unintended ways, by their students. This is done by analysing teachers’ reactions to specific answers students offered to the Charlotte and Marie problem, an “ambiguous” problem with various solutions depending on the paradigm adopted. As a result of the study, we found that, beyond similarities due to a shared mathematical background, the way secondary schoolteachers handle students’ answers varies with their conceptions of geometric work. Implications are drawn regarding the teaching of geometry and the training of teachers.