Mathematical argumentation, a precursor concept to mathematical proof
DOI:
https://doi.org/10.23925/1983-3156.2024v26i4p389-412Keywords:
Mathematical argumentation, Early learning of proof, EpistemologyAbstract
This lecture offers a reflection on the challenge posed by the current trend of curricula and standards to recommend starting the learning of proof from the very beginning of the compulsory school. This trend pushes on the fore the notion of argumentation, it is here discussed as well as its relations to proof as a convincing and an explaining legitimate means to support the truth of a statement in the mathematics classroom. Eventually, a didactical concept of mathematical argumentation is discussed, and elements of its characterization are proposed.
Metrics
References
Arsac, G. (2013). Cauchy, Abel, Seidel, Stokes et la convergence uniforme: De la difficulté historique du raisonnement sur les limites. Hermann.
Austin, J. L. (1950). In: Longworth, G. (ed.), Truth (The virtual issue n°1−2013). The Aristotelian Society.
Balacheff, N. (1990). Beyond a psychological approach of the psychology of mathematics education. For the Learning of Mathematics, 10(3), 2‒8.
Balacheff, N. (2013). CK¢, a model to reason on learners’ conceptions. In: Martinez, M. V. and Castro, A. (eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group PME (PME-NA). pp. 2‒15.
Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1‒2), 23‒40.
Boero, P. (ed.). (2007). Theorems in School: From History, Epistemology and Cognition to Classroom Practice. Sense Publishers.
Bradley, R. E. and Sandifer, C. E. (2010). Cauchy’s Cours d’analyse: An Annotated Translation. Springer Science & Business Media.
Cassin, B. (ed.) (2004). Vocabulaire européen des philosophies. Seuil — Le Robert.
Cobb, P. and Yackel E. (1996). Constructivist, emergent, and sociocultural perspectives in
the context of developmental research. Educational Psychologist, 31(3/4), 175‒190.
Davidson, D. (1996). The folly of trying to define truth. The Journal of Philosophy, 93(6), 263-278.
Delarivière, S., Frans, J. and Van Kerkhove B. (2017). Mathematical explanation: a contextual approach. Journal of Indian Council of Philosophical Research, 34(2), 309‒329.
Durand-Guerrier, V. (2008). Truth versus validity in mathematical proof. ZDM - Mathematics Education, 40(3), 373−384.
Duval, R. (1992). Argumenter, prouver, expliquer : Continuité ou rupture cognitive ? Petit x, 31, 37‒61.
Freudenthal, H. (1973). Mathematics as an Educational Task. Springer Netherlands.
Hanna, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics, 15(3), 42‒49.
Hanna, G. (2017, September 22). Connecting two different views of mathematical explanation. enabling mathematical cultures. Enabling Mathematical Cultures, Mathematical Institute, University of Oxford.
Hanna, G. and Villiers M. de (eds.). (2012). Proof and Proving in Mathematics Education: The 19th ICMI Study (corrected edition 2021). Springer.
Harel, G.and Sowder L. (1998). Students’ proof schemes: Results from exploratory studies. In: A. Schoenfeld, J. Kaput, E. Dubinsky, and T. Dick (eds.), CBMS Issues in Mathematics Education (Vol. 7, pp. 234‒283). American Mathematical Society.
Herbst, P. and Balacheff, N. (2009). Proving and Knowing in Public: The Nature of Proof in a Classroom. In: D. A. Stylianou, M. L. Blanton, and E. J. Knuth (eds.), Teaching and Learning Proof Across the Grades: A K-16 Perspective (pp. 40‒63). Routledge.
Legrand M. (1990). Rationalité et démonstration mathématiques, le rapport de la classe à une communauté scientifique. Recherches en Didactique des Mathématiques, 9(3), 365‒406.
Mariotti M. A. (2001). Justifying and proving in the Cabri environment. International Journal of Computer for Mathematical Learning, 6(3), 257‒281.
Mariotti, M. A. Bussi, M. G. B., Boero, P., Ferri, F. and Garuti R. (1997). Approaching
geometry theorems in contexts: From history and epistemology to cognition. In: E. Pehkonen (ed.), Proceedings of the 21st PME Conference (Vol. 1, pp. 180‒195). University of Helsinki.
Miyakawa T. (2005). Une étude du rapport entre connaissance et preuve : Le cas de la notion de symétrie orthogonale [Université Joseph Fourier]. http://www.juen.ac.jp/math/miyakawa/article/these_main.pdf
Miyakawa, T. (2016). Comparative analysis on the nature of proof to be taught in geometry: The cases of French and Japanese lower secondary schools. Educational Studies in Mathematics, 92(2), 37‒54.
Pedemonte, B. (2005). Quelques outils pour l’analyse cognitive du rapport entre argumentation et démonstration. Recherches en Didactique des Mathématiques, 25(3), 313‒347.
Plantin, C. (1990). Essai sur l’argumentation. Éditions Kimé.
Putnam, H. (1975). What is mathematical truth. Historia Mathematica, 2, 529‒533.
Reid, D. A. (2011). Understanding proof and transforming teaching. PME-NA 211 Proceedings, 15‒18.
Stylianides, A. J. (2007). Proof and Proving in School Mathematics. Journal for Research in Mathematics, 38(3), 289‒321.
Tarski, A. (1944). The Semantic Conception of Truth: And the Foundations of Semantics. Philosophy and Phenomenological Research, 4(3), 341.
Villani, C. and Torossian C. (2018). 21 mesures pour l’enseignement des mathématiques. La documentation française. Ministère de l’éducation nationale.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Autores que publicam nesta revista concordam com os seguintes termos:- Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, com o trabalho simultaneamente licenciado sob a Licença Creative Commons Attribution que permite o compartilhamento do trabalho com reconhecimento da autoria e publicação inicial nesta revista.
- Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
- Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex.: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado (Veja O Efeito do Acesso Livre).