Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof

This paper presents a learning trajectory of geometry proof (LTGP) for Indonesian prospective mathematics teachers (PMTs) during their first year of studies at an Indonesian university. The trajectory aims at PMTs’ progression of their understanding of the structure of proof and their proof construction abilities. We designed and implemented teaching materials with geometry problems based on the use of the flow-chart proof format and the model of understanding of proof structure from Miyazaki et al. (2017). We present an analysis of data from pre- and post-tests of proof construction problems, written answers to proof problems during intervention with 60 PMTs, and individual interviews with eight PMTs. We found that the intervention supports PMTs’ understanding of the structure of proof and their proof construction abilities. Our findings contribute to knowledge about teaching strategies to support students in their understanding and construction of a proof. From our findings, we suggest the use of the flow-chart proof format together with other more formal proof formats in creating, reading, and rewriting proof of geometric propositions and the use of open problems to encourage students to think forward and backwards interactively to help students plan for proof construction.