Traces of school mathematical modeling for the teaching of polynomies
DOI:
https://doi.org/10.5007/1981-1322.2021.e78314Abstract
The objective of this article is to create certain conditions from the use of concrete materials inspired by objects of school geometry, which makes possible, in some way, the teaching of polynomials in the eighth grade of elementary school. This problem is inserted in the context of the didactic transposition of knowledge and, more broadly, of notions of the Anthropological Theory of Didactics delimited by one of the teaching problems of theoretical reference as well as the cognitive line. For this, we assume the resources of the Anthropological Theory of Didactics as an instrument of analysis from empirical experiments observed in a course with students of the eighth grade of elementary school in a public school. The results found reveal potentialities of the initial conditions created in the classroom, but only in the act, other conditions gradually emerged in the study process that made possible the algebraic mathematical modeling from the geometric structuring with concrete materials giving sense and meaning to the polynomial practices.
References
Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Recherches en didactique des mathématiques, v. 19, n.1, p.77-124. Recuperado de: http://yves.chevallard.free.fr/spip/spip/IMG/pdf/Sensibilite_aux_ostensifs.pdf
Bosch, M., Chevallard, Y., & Gascón, J. (2006). Science or magic? The use of models and theories in didactics of mathematics. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education.
Brasil. (2017). Base Nacional Comum Curricular. Brasília: MEC.
Brasil. (1998). Parâmetros Curriculares Nacionais: terceiro e quarto ciclos do Ensino Fundamental. Brasília: MEC - Secretaria de Educação Fundamental.
Burat, Émile. (1876). Traité d'algèbre élémentaire, à l'usage des lycées, des collèges et des candidats à l'école militaire de Saint-Cyr. Paris: Librairie Classique d’Eugène Belin.
Chevallard, Y. (1989). Arithmétique, algèbre, modélisation, étapes d‘une recherche. Publication de l‘IREM d‘Aix-Marseille.
Chevallard, Y. (2019a). INTRODUCING THE ANTHROPOLOGICAL THEORY OF THE DIDACTIC: AN ATTEMPT AT A PRINCIPLED APPROACH. Hiroshima journal of mathematics education - 12: p.71-114.
Chevallard, Y. (1999). L‘analise des pratiques enseignantes em theórie anthopologique du didactique, recherches em didactiques des mathematiques. Grenoble. La Pensée Sauvage Éditions, v. 19.2, p.221-265.
Chevallard, Y. (2009). La notion d´ingénierie didactique, un concept à refonder. Questionnement et élémentos de réponses à partir de la TAD. In: MARGOLINAS, C. et al. (org.): En amont et en aval des ingénieries didactiques, XVª École d´Été de Didactique des Mathématiques – Clermont-Ferrand (Puy-de-Dôme). Recherches em Didactique des Mathématiques. Grenoble: La Pensée Sauvage, v. 1, p. 81- 108.
Chevallard, Y. (2005). La Transposición Didáctica: del saber sabio al saber enseñado. 2. ed. 3. reimp. Buenos Aires: Aique Grupo Editor.
Chevallard, Y. (2019). On using the ATD: Some clarifications and comments. Educ. Matem. Pesq., São Paulo, v. 21, n.4, pp. 001-017.
Chevallard, Y. (2020). Some sensitive issues in the use and development of the anthropological theory of the didactic. Educ. Matem. Pesq., São Paulo, v.22, n. 4, pp. 013-053.
Chevallard, Y., Bosch, M. & Gascón, J. (2001). Estudar matemáticas: o elo perdido entre o ensino e aprendizagem. Porto Alegre: Artmed.
Garcia, F., Gascón, J., Higueras, l., & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM Mathematics Education, v. 38, n. 3, p. 226-246.
Gascón, J. (1999). La naturaleza prealgebraica de la matemática escolar. Educación Matemática, Barcelona, v. 11, n. 1, p. 77-88.
Gascón, J.; Bosch, M.; & Bolea, P. (2001). Cómo se construyen los problemas en didáctica de las matemáticas? Educación Matemática, Barcelona, v. 3, n. 3, diciembre, p. 22-63. Recuperado de: http://www.revista-educacion-matematica.org.mx/descargas/Vol13/03Gascon.pdf.
Matos, F. C. de. (2017). Praxeologias e modelos praxeológicos institucionais: o caso da álgebra linear. Tese (Doutorado em Educação em Ciências e Matemáticas) - Instituto de Educação Matemática e Científica, Universidade Federal do Pará, Belém.
Nesselmann, G. 1842. Die Algebra der Griechen. Berlin: Reimer
Pereira, J. C. S. (2017). Alterações e recombinações praxeológicas reveladas por professores de matemática do ensino básico em formação continuada: a partir de um modelo epistemológico alternativo para o ensino da álgebra escolar. Tese (Doutorado em Educação em Ciências e Matemáticas) - Instituto de Educação Matemática e Científica, Universidade Federal do Pará, Belém. Recuperado de: https://drive.google.com/file/d/1S5hyeh8l_NpB3KaJjZbxg_5M6Ouh3h56/view.
Ruiz-Munzón, N. (2010). La introducción del álgebra elemental y su desarrollo hacia la modelización funcional. Tese (Doutorado em Matemática) - Departament de Matemàtiques, Universitat Autònoma de Barcelona.
Sodré, G. J. M. (2019). Modelagem matemática escolar: uma organização praxeológica complexa. Tese (Doutorado em Educação em Ciências e Matemáticas) - Instituto de Educação Matemática e Científica, Universidade Federal do Pará, Belém.
Stevin, S. (1634). Les oeuvres mathematiques de Simon Stevin. Leyde.
Viète, F. (1630). Introduction en l'art analytic ou nouvelle algèbre. Paris. Recuperado de: http://dx.doi.org/10.3931/e-rara-4788.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Revista Eletrônica de Educação Matemática
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors hold the copyright and grant the journal the right for their articles' first publication, being their works simultaneously licensed under the Creative Commons Attribution License (CC BY), which allows the sharing of such works with its authorship acknowledged and its initial publication in this journal.
Authors are allowed to enter into separate additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or as a book chapter, with an acknowledgment of its initial publication in this journal).