• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.