Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs

Abstract

Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in junior high schools can be designed to scaffold students’ initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in ‘open problem’ situations are a useful form of scaffold. We do this by identifying the ‘scaffolding functions’ of flow-chart proofs with open problems through the analysis of classroom-based data from a class of Grade 8 students (aged 13–14 years old) and quantitative data from three classes. We find that using flow-chart proofs with open problems support students’ development of a structural understanding of proofs by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students’ understanding of introductory mathematical proofs.

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ORCID for Keith Jones: orcid.org/0000-0003-3677-8802

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