Towards a shared reference epistemological model?

Authors

DOI:

https://doi.org/10.23925/1983-3156.2024v26i3p462-492

Keywords:

Epistemology, Teaching, Limit, Model

Abstract

This text was written to disseminate proposal of Calculus in Secondary and Higher Education Study Group, headed by researchers Dr. Pierre Job (ICHEBrussels Management School-Belgium) and Dr. Luiz Márcio Santos Farias (UFBA-Brazil), whose objective is to create a joint work Brazil-Belgium in search of a Reference Epistemological Model for Calculus and Analysis teaching. In 2023, at the Integrated Studies Seminar-Calculus in Secondary and Higher Education, at PUC/SP, Professor Job presented aspects of the research carried out in Belgium, based on a Reference Epistemological Model, Theory of Didactic Situations and Anthropological Theory of the Didactic, regarding the limit concept. In order to motivate Calculus teachers to engage in this research, events of two of the Seminar three days are summarized. In text first part, questions proposed on the first day are reported, followed by a reflection on some of them. Those questions serve as a model for the initial survey of difficulties that could provide answers to three open questions: “Are the premises used in Belgium valid in Brazilian context?”, “Is it possible to build a common theoretical framework that allows us to question the status of epistemological obstacles and the main difficulty encountered in teaching the concepts of limit, derivative and integral?”, “What kind of experiment can we plan together to test this model?”. Text second part presents a summary of Prof. Job's presentation on the second day, about the research carried out in Belgium.

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Author Biographies

Ana Maria Velloso Nobre, PUC/SP

She holds a degree in Mathematics from the University of São Paulo (1968) and a
Master's degree in Mathematics Education from the Pontifical Catholic University
of São Paulo (1995). She is currently an assistant professor at the Pontifical
Catholic University of São Paulo. He has experience in the area of ​​Mathematics,
with an emphasis on Mathematics Teaching, working mainly on the following topics:
teacher training, teaching Algebra, teaching Calculus, textbooks.

 

Vera Helena Giusti de Souza, Universidade de São Paulo

Doutora em Educação Matemática

References

Adam, A. & Lousberg, F. (2000). Espace Math 56, Livre de l'élève. De Boeck-Wesmael.

Anjos, I. M. dos et al. (2023) O Quiz Interativo Digital na identificação de dificuldades de aprendizagem em conceitos nucleares do Cálculo I. Revista de Ensino de Ciências e matemática, 14(2), 1-26.

Artigue, M. (1990) Ingénierie didactique. Recherches en Didactique des Mathématiques, 9(3), 281-308.

Artigue, M. (2020). Didactic Engineering in Mathematics Education. In S. Lerman (Eds.), Encyclopedia of Mathematics Education (pp. 202-206). Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_44

Brousseau, G. (1998) Théorie des situations didactiques. La Pensée Sauvage.

Cauchy, A.-L. (1821). Analyse algébrique. Cours de l’École Polytechnique.

Chevallard, Y. (1985). La transposition didactique : du savoir savant au savoir enseigné. La Pensée Sauvage.

Chevallard, Y. (1999). L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en didactique des mathématiques, 19 (2), 221-266.

Chevallard, Y. (2011). Quel programme pour l’avenir de la recherche en TAD? In Bosch et al. (Eds.), Un panorama de la TAD (pp. 33-55). Centre de Recerca Matemàtica.

De Guzmán, M. et al. (1998). Difficulties in the Passage from Secundary to Tertiary Education. Documenta Mathematica. ICM-Invited Lectures, III, 747-762. http://eudml.org/doc/230779

Fishbein, E. et al. (1979). The intuition of infinity. Educational Studies in Mathematics, 1, 3-40.

Fourez, G. (1988). La construction des Sciences. De Boeck-Wesmael.

Garcia, L. M. L. da S., & Gomes, R. S. (2022). Causas da evasão em cursos de ciências exatas: uma revisão da produção acadêmica. Revista Educar Mais, 6, 937-957. https://doi.org/10.15536/reducarmais.6.2022.2970

Godoy, E., & Almeida, E. (2020). Evasão nos cursos de engenharia: um olhar para os trabalhos do COBENGE de 2000 a 2014. Revista Brasileira de Ensino de Ciências e Tecnologia, 13(3), 50-74. https://periodicos.utfpr.edu.br/rbect/article/view/8583

Igliori, S. B. C., & Silva, B. A. da. (2001) Concepção dos alunos sobre os números reais. In J. Lachini & J. B. Laudares (Orgs.). A prática educativa sob o olhar de professores de Cálculo, 1 (1ª Ed., pp. 39-67). Fumarc.

Job, P. (2011). Étude du rapport à la notion de définition comme obstacle à l'acquisition du caractère lakatosien de la notion de limite par la méthodologie des situations fondamentales/adidactiques. [Doctorat d´État, Docteur en Sciences, Didactique des Sciences Mathématiques, Faculté des Sciences, Université de Liège]. https://hdl.handle.net/2268/98996

Lachini, J. (2001) Subsídios para explicar o fracasso de alunos em cálculo. In J. Lachini & J. B. Laudares. (Orgs.). A prática educativa sob o olhar de professores de Cálculo, 1. (1a ed., pp. 146-190). Fumarc.

Lakatos, I. (1984). Preuves et Réfutations. Hermann.

Popper, K. (1973). La logique de la découverte scientifique. Payot.

Popper, K. (2014). Conjectures and réfutations: the growth of scientific knowledge (2nd ed.). Routledge.

Projet Euclide. (2007). L’interaction entre compétences disciplinaires et langagières dans l’apprentissage des mathématiques: détection des difficultés et pistes de remédiation au 3e degré. Comment sensibiliser les élèves du 3e degré aux exigences de l’enseignement supérieur? Formation I.F.C. Université de Liège. http://www.ulg.ac.be/sectmath/Euclide.htm

Schneider, M. (2009). Ingénieries didactiques et situations fondamentales. Quel Niveau praxéologique?. In Margolinas et al. (Org.), En amont et en aval des ingénieries didactiques, XVª École d´Été de Didactique des Mathématiques (pp. 172-202) - Clermont-Ferrand. Recherches em Didactique des Mathématiques. La Pensée Sauvage, v. 2.

Schneider, M. Note de cours de didactique des mathématiques. Facultés Universitaires Notre-Dame de la Paix.

Schneider, M. (2008). Traité de didactique des mathématiques. Éditions de l' Université de Liège.

Schneider, M. (2019). Quels usages du concept de modèle epistémologique de référence pour la recherche? Et pour la formation? In I. J. Pilet (Ed.), Actes du séminaire de didactique des mathématiques de l'ARDM (pp. 72-86).

Thomas, M. et al. (2012). Survey Team 4: key mathematical concepts in the transition from secondary to university. In Sung Je Cho (Ed.), 12th International Congress on Mathematical Education (pp. 90-136). COEX.

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Published

2024-11-03

How to Cite

NOBRE, A. M. V.; SOUZA, V. H. G. de . Towards a shared reference epistemological model?. Educação Matemática Pesquisa, São Paulo, v. 26, n. 3, p. 462–492, 2024. DOI: 10.23925/1983-3156.2024v26i3p462-492. Disponível em: https://revistas.pucsp.br/index.php/emp/article/view/66635. Acesso em: 21 nov. 2024.

Issue

Vol. 26 No. 3 (2024): Epistemological reference model - Calculus

Section

Epistemological reference model (ERM) for teaching calculus

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