Approaching proof in geometry by folding problems with pre-service teachers

Abstract

This study focuses on the geometric thinking of first-year pre-service middle school mathematics teachers and the potential contribution of folding prob lems to improving their geometric thinking regarding proofs. A significant propor tion of these students do not work with the level of geometric thinking that might be expected: When asked to prove a geometric property, they base their argumen tation partly on observations or measurements on the geometric diagram, whereas an answer based solely on deductive reasoning is required. To foster the entry of these students into deductive geometry, while at the same time offering to every student a first discovery of concepts related to the teaching and learning of plane geometry, we designed and experimented a teaching sequence based on folding problems.