Beyond direct proof in the approach to the culture of theorems: a case study on 10-th grade students’ difficulties and potential
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6 février 2019
- handle: 10670/1.h0pytq
- hal: hal-02398527
info:eu-repo/semantics/OpenAccess
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Culture of theorems euclidean geometry indirect proofs figural concepts meta-knowledge of proofSujets proches
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Fiorenza Turiano et al., « Beyond direct proof in the approach to the culture of theorems: a case study on 10-th grade students’ difficulties and potential », HAL-SHS : sciences de l'éducation, ID : 10670/1.h0pytq
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In this paper, we aim to contribute to the discussion on the students’ cognitive processes inherent in proof by contradiction in geometry, particularly as concerns the role played by images. We will present an episode from a one-year experimental pathway in Euclidean geometry designed to develop the culture of theorems in 10th grade: in crucial moments of proof by contradiction, we observed some students’ gestures and reasoning aimed to restore the harmony between visual and conceptual aspects, which had been broken by conflicts due to specific features of that proof in geometry. The students’ need of keeping such harmony poses didactical questions, which, if conveniently taken in charge by the teacher, might contribute to design smoother pathways to the indirect proofs.