Detecting and sharing praxeologies in solving interconnecting problems: some observations from teacher education viewpoint<br>Détecter et partager les praxéologies dans la résolution de problèmes d'interconnexion: quelques observations du point de vue de la formation des enseignants

Autores

DOI:

https://doi.org/10.23925/1983-3156.2020v22i4p472-486

Palavras-chave:

teacher education, praxeological development, mathematical problems with multiple solutions

Resumo

Abstract

This paper discusses praxeologies available at different levels of schooling in view of a problem, which permits multiple solutions ranging from elementary to more advanced mathematical approaches. Solutions of the problem produced by mixed groups of K-12 teachers included numerical, pictorial and algebraic methods, and allowed observing possible paths within a finalized activity of study and research.  They also gave some insights regarding teachers’ readiness to support the continuity of students’ praxeological development, and more generally, the potential within teachers’ educational backgrounds to pursue the new paradigm of questioning the world.

Keywords: Teacher education, Praxeological development, Mathematical problems with multiple solutions.

Résumé

Ce texte discute les praxéologies disponibles à différents niveaux de la scolarité pour résoudre un problème qui permet des résolutions multiples, depuis des approches élémentaires aux plus avancées. Les résolutions proposées par un groupe mixte d’enseignants de l’école élémentaire jusqu’au lycée ont employé des méthodes numériques, graphiques et algébriques, et permettent d’observer les parcours possibles d’une activité finalisée d’étude et de recherche. Elles nous laissent aussi percevoir la capacité des enseignants pour soutenir la continuité du développement praxéologique des élèves, et plus généralement le potentiel résultant de la formation des enseignants à poursuivre le nouveau paradigme du questionnement du monde.

Mots-clés: formation des enseignants, développement praxéologique, problèmes mathématiques aux solutions multiples.

Metrics

Carregando Métricas ...

Biografia do Autor

Margo Kondratieva, Memorial University, Canada

Associate professor

Faculty of Education and Dept. of Mathematics and Statistics

Memorial University

Referências

Biza, I., Nardi, E, Zahariades, T. (2009). Do images disprove but do not prove? Teachers' believes about visualization. In Lin, F.-L., Hsieh, F.-J., Hanna, G., DeVilliers, M. (Eds.), Proc. of the ICMI Study 19: Proof and Proving in Mathematics Education (Vol. 1, pp. 59-64). National Taiwan Normal University, Taipei, Taiwan.

Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19/2, 221-226.

Chevallard, Y. (2011). La notion d’ingénierie didactique, un concept à refonder. Questionnement et éléments de réponse à partir de la TAD. In C. Margolinas, M. Abboud-Blanchard, L. Bueno-Ravel, N. Douek, A. Fluckiger, P. Gibel, F. Vandebrouck, & F. Wozniak (Eds.), En amont et en aval des ingénieries didactiques (pp. 81–108). Grenoble: La Pensée Sauvage.

Chevallard, Y. (2012) Teaching mathematics in tomorrow’s society: a case for an oncoming counterparadigm. 12th Int. congress of math education. Seoul, Korea.

Dreyfus, T. (2000). Some views on proofs by teachers and

mathematicians. In Gagatsis, A. (Ed.), Proceedings of the 2nd

Mediterranean Conference on Mathematics Education (Vol. 1, pp. 11- 25). Nicosia: The University of Cyprus.

Hanna, G., DeVilliers, M. (2012). Aspects of proof in mathematics education. In Hanna, G., DeVilliers, M. (Eds.), Proof and Proving in Mathematics Education. The 19th ICMI study (pp. 1-12). Springer.

Kondratieva, M. (2011). The promise of interconnecting problems for enriching students’ experiences in mathematics. Montana Mathematics Enthusiast, 8 (1-2), 355-382.

Kondratieva, M. (2013). Changing teachers’ beliefs in the process of collective production of proofs. In Lindmeier, A. M., Heinze, A. (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, p. 91). Kiel, Germany: PME.

Leikin, R., Levav-Waynberg, A. (2008). Solution spaces of multiple solution connecting tasks as a mirror of the development of mathematics teachers’ knowledge. Canadian Journal of Science, Mathematics and Technology Education, 8(3), 233-251.

Lin, F.-L., Yang, K.-L., Lo, J.-J., Tsamir, P., Tirosh, D., Stylianides, G. (2012). Teachers' professional learning of teaching proof and proving. In Hanna, G., DeVilliers, M. (Eds.), Proof and proving in

mathematics education. The 19th ICMI study (pp. 327-346). Springer.

Mason, J., Burton, L., & Stacey, K. (1982). Thinking Mathematically. London: Addison Wesley.

Simon, M.A., Blume G.W. (1996). Justification in mathematics

classroom: A study of prospective elementary teachers. The Journal of Mathematical Behaviour, 15, 3-31.

Sun, X., Chan, K., (2009). Regenerate the proving experiences: an attempt for improvement original theorem proof construction of student teachers by using spiral variation curriculum. In Lin, F.-L., Hsieh, F.-J., Hanna, G., DeVilliers, M. (Eds.), Proceedings of the ICMI Study 19: Proof and Proving in Mathematics Education (Vol. 2, pp. 172-177). National Taiwan Normal University, Taipei, Taiwan.

Tall, D. O., Yevdokimov, O., Koichu, B., Whiteley, W., Kondratieva, M., Cheng, Y.-H. (2012). Cognitive development of proof. In Hanna, G., DeVilliers, M. (Eds.), Proof and proving in mathematics education. The 19th ICMI study (pp. 13-50). Springer.

Downloads

Publicado

2020-09-15

Como Citar

KONDRATIEVA, M. Detecting and sharing praxeologies in solving interconnecting problems: some observations from teacher education viewpoint&lt;br&gt;Détecter et partager les praxéologies dans la résolution de problèmes d’interconnexion: quelques observations du point de vue de la formation des enseignants. Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática, São Paulo, v. 22, n. 4, p. 472–486, 2020. DOI: 10.23925/1983-3156.2020v22i4p472-486. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/49176. Acesso em: 21 nov. 2024.

Edição

Seção

Finalizada - Volume 22 - 4 - Advances of the anthropological theory of the didactic