Beyond direct proof in the approach to the culture of theorems: a case study on 10-th grade students’ difficulties and potential Fiorenza Turiano, Paolo Boero To cite this version: Fiorenza Turiano, Paolo Boero. Beyond direct proof in the approach to the culture of theorems: a case study on 10-th grade students’ difficulties and potential. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. hal-02398527 HAL Id: hal-02398527 https://hal.archives-ouvertes.fr/hal-02398527 Submitted on 7 Dec 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Beyond direct proof in the approach to the culture of theorems: a case study on 10-th grade students’ difficulties and potential Fiorenza Turiano1 and Paolo Boero2 1I. I. S. Arimondi – Eula, Savigliano, Italy;
[email protected] 2University of Genoa, Italy;
[email protected] 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.