Abstract
The purpose of this study is to establish levels from an inductive proof to an algebraic demonstration in lower secondary school mathematics. I propose that we can establish six levels of proof in lower secondary school mathematics as steps from an inductive proof to an algebraic demonstration on the basis of three axes (contents of proof, representation of proof, and students' thinking). To reach this conclusion, I firstly examine the meaning of ‘demonstration in lower secondary school mathematics’ and ‘proof in lower secondary school mathematics’, and show the relationships between them. Secondly, I set out four basic levels of proof, as seen from two aspects (contents and representation of proof). Thirdly, I subdivide them into six levels from the third aspect of students' thinking. Finally, I illustrate my discussion with a 7th grader's activities.
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Miyazaki, M. Levels of Proof in Lower Secondary School Mathematics. Educational Studies in Mathematics 41, 47–68 (2000). https://doi.org/10.1023/A:1003956532587
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DOI: https://doi.org/10.1023/A:1003956532587