A model for evaluating proof arguments in teaching contexts based on collective argumentation
DOI:
https://doi.org/10.37001/ripem.v14i1.3859Keywords:
Mathematics Education, Proof Argument, Empirical Proof, Conceptual ProofAbstract
This study presents a theoretical-methodological model to evaluate the quality of a proof argument in a teaching context based on collective argument. The model combines the elements of an argumentative structure with a theory involving the types and levels of proof in Mathematics Education. The test was conducted with a class of first-year students in a course of Mathematics teacher training at the Instituto Federal do Sul de Minas, in 2023. Data was collected through written and video records of groups' collective production. The results show that the model presented allowed for an efficient quality evaluation of the proof argument. Therefore, it is a tool to analyze future research data. Furthermore, it is a useful instrument for Mathematics teachers to evaluate their students' proof level in the classroom.
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Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18(2), 147-176.
Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics (ODD). Mathematics, teachers, and children, 215-235.
Bicudo, I. (2002). Demonstração em Matemática. Boletim de Educação Matemática, 15(18), 79-90.
Cervantes-Barraza, J. A.; Hernandez Moreno, A. & Rumsey, C. (2000). Promoting mathematical proof from collective argumentation in primary school. School Science and Mathematics, 120(1), 4-14.
Conner, A. M.; Singletary L. M.; Smith, R. C.; Wagner, P. A. & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401-429.
Dede, A. T. (2019). Arguments constructed within the mathematical modelling cycle. International Journal of Mathematical Education in Science and Technology, 50(2), 292-314.
Erkek, Ö. & Bostan, M. I. (2019). A different look at the reasoning process of prospective middle school mathematics teachers: Global argumentation structures. Egitim ve Bilim, 44(199), 1-27.
Erkek, Ö. & I?iksal Bostan, M. (2019). Prospective Middle School Mathematics Teachers’ Global Argumentation Structures. International Journal of Science and Mathematics Education, 17(3), 613-633.
Fiallo, J. & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145-167.
Garnica, A. V. M. (2002). As demonstrações em Educação Matemática: um ensaio. Boletim de Educação Matemática, 15(18), 91-99.
Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1-3), 5-23.
Kollar, I.; Ufer, S.; Reichersdorfer, E.; Vogel, F.; Fischer, F. & Reiss, K. (2014). Effects of collaboration scripts and heuristic worked examples on the acquisition of mathematical argumentation skills of teacher students with different levels of prior achievement. Learning and Instruction, 32, 22-36.
Kosko, K. W. & Zimmerman, B. S. (2019). Emergence of argument in children’s mathematical writing. Journal of Early Childhood Literacy, 19(1), 82-106.
Lakatos, I. (1978). A Lógia do Descobrimento Matemático: Provas e refutações. Rio de Janeiro, RJ: Zahar Editores.
Lin, P. J. (2018). O Desenvolvimento da Argumentação Matemática por Estudantes de uma Turma do Ensino Fundamental. Educação & Realidade, 43(3), 1171-1192.
Lourenço, M. L. (2002). A demonstração com informática aplicada à Educação. Boletim de Educação Matemática, 15(18), 100-111.
Monteiro, M. A. A. & Teixeira, O. P. . B. (2019). Contextos argumentativos e processos interativos em sala de aula. In: F. C. Bozelli & O. P. B. Teixeira. (Org.). Contextos argumentativos e discursivos no ensino de Ciências. (pp.27-44), São Paulo, SP: 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.
Nordin, A. K. & Boistrup, L. B. (2018). A framework for identifying mathematical arguments as supported claims created in day-to-day classroom interactions. Journal of Mathematical Behavior, 51, 15-27.
Rodrigues, F. C. & Monteiro, M. A. A. (2021). Modelo para avaliação do argumento de prova em um contexto de ensino baseado em modelagem. Revista Ensenanza de la Física, 33(2), 143-151.
Rodrigues, F. C. (2023). Da argumentação à prova: produção e avaliação de argumentos matemáticos produzidos por alunos ingressantes em um curso de formação de professores. 315f. Tese (Doutorado em Educação para a Ciência). Universidade Estadual Paulista. Bauru, SP.
Solar, H.; Ortiz, A.; Deulofeu, J. & Ulloa, R. (2020). Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms. International Journal of Mathematical Education in Science and Technology, 52(12), 1-29.
Staats, S. (2017). The poetics of argumentation: the relevance of conversational repetition for two theories of emergent mathematical reasoning. Research in Mathematics Education, 19(3), 276-292.
Toulmin, S. (2001). Os usos do argumento. São Paulo, SP: Editora Martins Fontes.
Vigotski, L. S. (2009). A construção do pensamento e da linguagem (2. ed.). São Paulo, SP: WMF Martins Fontes.
Walter, J. G. & Barros, T. (2011). Students build mathematical theory: Semantic warrants in argumentation. Educational Studies in Mathematics, 78(3), 323-342.
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