Learning trajectory of geometry proof construction: Studying the emerging understanding of the structure of Euclidean proof
Lathiful Anwar 1 2 * , Martin J. Goedhart 2 , Angeliki Mali 3
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1 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Malang, Malang, INDONESIA2 Institute for Science Education and Communication, University of Groningen, Groningen, NETHERLANDS3 Department of Mathematics and Applied Mathematics, University of Crete, Crete, GREECE* Corresponding Author


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.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 19, Issue 5, May 2023, Article No: em2266


Publication date: 01 May 2023

Online publication date: 06 Apr 2023

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