Model for evaluating the proof argument in a model-based teaching context

Authors

  • Fredy Coelho Rodrigues Instituto Federal do Sul de Minas Gerais. Passos-MG, Brasil, CEP: 37901-078
  • Marco Aurélio Alvarenga Monteiro Universidade Estadual Paulista (UNESP). Faculdade de Engenharia. Guaratinguetá-SP Brasil. CEP: 12.516-410

DOI:

https://doi.org/10.55767/2451.6007.v33.n2.35196

Keywords:

Physics education, Argumentation, Argument proof, Mathematical modeling, Quality of the argument

Abstract

The study starts from the general characterization of the stages that compose the process of mathematical modeling, emphasizes in a
special way the stage to which our approach is focused (obtaining and validating models) and then addresses the structure of the
argument proposed by Toulmin (2006) as well as the theory of types and levels of proof in mathematics by Nicolas Balacheff
(1987,1988). This last study, when placed in the context of the use of TAP (Toulmin's Argument Pattern) in a model-based teaching
context configures a theoretical and methodological approach that allows analyzing the nature of the justifications and supports
employed in said argumentative process as well as classifying the data and evaluating the conclusion. This tool also allows a diagnostic
evaluation of the student's level of knowledge regarding the use of proof and demonstration in Physics Teaching. It is, therefore, a tool
that allows combining all the elements of TAP with Nicolas Balacheff's (1987, 1988) theory of the types and levels of proof.

References

Almeida, L. W., Silva, K. P e Vertuan, R. E. (2012). Modelagem Matemática na Educação Básica (1ªed). São Paulo : Contexto.

Balacheff, N. (1987). Processus de Preuve et situations de Validation. Education Studies in Mathematics,18 (2), 147-176.

Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. Pimm D. (ed.) Mathematics, Teachers

and Children. 230-316.

Bassanezi, R. C. (2019). Ensino-aprendizagem com modelagem matemática (4ª ed.). São Paulo: Contexto.

Biembengut, M. S., Hein, N. (2007). Modelagem matemática no ensino. (4ª ed.). São Paulo: Contexto.

Boavida, A. M. R. (2005). A argumentação em Matemática Investigando o trabalho de duas professoras em contexto de

colaboração. 975f. Tese (Doutorado em Educação) - Faculdade de Ciências, Universidade de Lisboa.

Conner, A. (2012). Warrants as indications of reasoning patterns in secondary mathematics classes. In Proceedings of

the 12th International Congress on Mathematical Education (ICME-12), 2819–2827. Seoul, Korea, Disponível em:

http://www.lettredelapreuve.org/pdf/ICMI-12/TSG14_Conner.pdf. Accesso em 24 jul. 2020.

Conner, A. M., Singletary, L. M., Smith, R. C., Wagner, P. A. e Francisco, R. T. (2014). Identifying Kinds of Reasoning in

Collective Argumentation, Mathematical Thinking and Learning, 16(3), 181-200.

https://doi.org/10.1080/10986065.2014.921131

Dede, A. T. (2019). Arguments constructed within the mathematical modelling cycle, International Journal of

Mathematical Education in Science and Technology, 50(2), 292-314, https://doi.org/10.1080/0020739X.2018.1501825

Erduran S., Simon S. e Osborne J. (2004). TAPping into Argumentation: Developments in the Application of Toulmin's

Argument Pattern for Studying Science Discourse. Science Education, 88(6), 915–933. DOI:10.1002/sce.20012

English L. D. e Sriraman B. (2010). Problem solving for the 21st century. In: English L. D., Sriraman B., editors. Theories of

mathematics education: seeking new frontiers. (263–285). Berlin: Springer.

Inglis, M., Mejia-Ramos, J.P e Simpson, A. (2007). Modelling mathematical argumentation: the importance of

qualification. Educ Stud Math, 66, 3-21. https://doi.org/10.1007/s10649-006-9059-8

Kelly, G.J e Takao, A. (2002).Epistemic levels in argument an analysis of university oceanography student’s use of evidence

in writing. Science Education, 86(3), 314-342. https://doi.org/10.1002/sce.10024

Lin, Pi-Jen. (2018). O Desenvolvimento da Argumentação Matemática por Estudantes de uma Turma do Ensino

Fundamental. Educ. Real. 43(3), 1171-1192. https://doi.org/10.1590/2175-623676887

Monteiro, M.A.A., Santos, D.A., Teixeira, O. P. B. (2007). Caracterizando a autoria no discurso em sala de aula.

Investigações em Ensino de Ciências, 12(2), 205-225. Recuperado de:

https://www.if.ufrgs.br/cref/ojs/index.php/ienci/article/view/472/274. Acesso em 20 de maio de 2021.

Monteiro, M.A.A., Teixeira, O.P.B. (2019). Contextos argumentativos e processos interativos em sala de aula. In: Bozelli,

F.C.; Teixeira, O.P.B. Contextos argumentativos e discursivos no ensino de ciências (1ª ed.). São Paulo: Espelho D’alma.

Nardi, E., Biza, I., Zachariades, T. (2012). “Warrant” revisited: Integrating mathematics teachers’ pedagogical and

epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157–

173, 2012. https://doi.org/10.1007/s10649-011-9345-y.

Sá, L. P. e Queiroz, S. L. (2011). Argumentação no ensino de ciências: contexto brasileiro. Ens. Pesqui. Educ. Ciênc. (Belo

Horizonte) [online], 13(2), 13-30. https://doi.org/10.1590/1983-21172011130202.

Toulmin, S. (2006). Os usos do argumento (2ª ed.) Trad. Reinaldo Guarany. São Paulo: Martins Fontes.

Vaz, R. (2004). O uso das isometrias do software Cabri-Gèométre como recurso no processo de prova e demonstração.

Dissertação (Mestrado em Educação Matemática). São Paulo: PUC/SP

Published

2021-11-05

Issue

Section

Investigación en Enseñanza de la Física

How to Cite

Model for evaluating the proof argument in a model-based teaching context. (2021). Journal of Physics Teaching, 33(2), 143-151. https://doi.org/10.55767/2451.6007.v33.n2.35196