Abstract
Recent curriculum reforms underline mathematical activity related to proof validation , but few studies have explicitly addressed proof validation at the secondary school level. This chapter reports on our study of this issue. We suggest a specific kind of task for introducing proof validation in secondary school geometry and define the meanings of proof validation and proof modification in terms of Lakatos’s notion of the local counterexample . We briefly report on a classroom-based intervention implemented using such tasks in a lower secondary school in Japan. We then analyze the results of a task-based questionnaire conducted after the intervention to investigate how well the students did in proof validation and modification. The analysis shows that student failure in proof validation arose mainly from their difficulty with producing diagrams that satisfied the condition of the proof problem.
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Acknowledgements
This study is supported by the Japan Society for the Promotion of Science (Nos. 15H05402, 16H02068, and 26282039).
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Komatsu, K., Ishikawa, T., Narazaki, A. (2018). Proof Validation and Modification by Example Generation: A Classroom-Based Intervention in Secondary School Geometry. In: Stylianides, A., Harel, G. (eds) Advances in Mathematics Education Research on Proof and Proving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70996-3_9
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