Uses of argumentation in mathematics education
a systematic review of the literature in higher education
DOI:
https://doi.org/10.23925/1983-3156.2023v25i3p111-141Keywords:
Argumentation, Systematic review, Mathematics Education, University educationAbstract
This article aims to carry out a systematic review of selected literature on empirical studies into the use of argumentation in the field of Mathematics Education in higher education. To do so, we searched for articles on the Education Resources Information Center (ERIC) database, more specifically in Mathematics Education journals published between 2012 and 2021. This period is justified for encompassing a decade of research published until the year immediately before the beginning of this study. After selecting and reading the articles, the following categories of analysis were identified: argumentation as a tool to analyze students’ arguments, argumentation as a tool to analyze professors’ arguments and argumentation as a teaching approach. The analysis was based on literature studies, mostly from the theoretical perspective of Toulmin’s and Perelman’s argumentation theories. The results showed three ways of using argumentation in relation to the teaching approach, investigations into the teaching of proof, assessment of the relationship between argumentation and proof and investigation into students’ and professors’ argumentation quality. However, we highlight that more investigations need to be carried out to assess the potential of courses focused on argumentation for higher education mathematics subjects, especially research into Perelman’s approach, about which studies have been reasonably scarce.
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References
Almeida, W. N. C. & Malheiro, J. M. da S. (2018). A Argumentação e a Experimentação investigativa no Ensino de Matemática. Alexandria, 11(2), 57-83. https://doi.org/10.5007/1982-5153.2018v11n2p57
Anscombre, J. C., & Ducrot, O. (1983). L’argumentation dans la langue. Mardaga.
Antonini, S. (2018). Figural conceps in proving by contradiction. Quadrante, 27(2). https://quadrante.apm.pt/article/download/22967/17033/88394
Balacheff, N. (1988). Aspects of proof in pupils’practice of school mathematics. Mathematics, Teacher and children, 24, 216-235.
Boero, P., Garuti, R., & Mariotti, M. A. (1996). Some dynamic mental processes underlying producing and proving conjectures. Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, Valencia, Spain.
Can, O. S. & Isleyen, T. (2016). Teaching Probability to Pre-Service Teachers with Argumentation Based Science Learning Approach. Journal of Educational and Practice, 7(33), 109- 116. https://eric.ed.gov/?id=EJ1122873.
Can, O. S. & Isleyen, T. (2020). The effect of probability instruction through argumentation approach on the achievement of preservice teachers and the permanence of their knowledge. African Education Research Journal, 8, 540- 553. http://doi.org/10.30918/AERJ.8S3.20.072.
Eemeren V., F. H., Houtlosser, P., & Henkemans, A. F. S. (2008). Argumentative indicators in discourse: A pragma-dialectical study. Springer.
Eemeren, F. V., Garssen, B., & Meuffels, B. (2012). Effectiveness through Reasonableness: Preliminary Steps to Pragma-Dialectical Effectiveness Research. Argumentation, 26, 33-53. http://dx.doi.org/10.1007/s10503-011-9234-7.
Fukawa-Connelly, T. (2014) Using Toulmin analysis to analysis an instructor's proof presentation in abstract algebra. International Journal of Mathematical Education in Science and Technology, 45(1), 75-88.
Gabel, M., & Dreyfus, T. (2016). Affecting the flow a proof by creating presence – a case study in Number Theory. Educational Studies em Mathematics, 96(2), 187-205. http://doi.org/10.1007/s10649-016-9746-z
Gabel, M., & Dreyfus, T. (2017). The flow of a proof: establishing a basis of agreement. CERME10, 1, 155-162. https://hal.archives-ouvertes.fr/hal-01865664/document.
Galvão, T. F., Pansani, T. de S. A., & Harrad, D. (2015). Principais itens para relatar Revisões sistemáticas e Meta-análises: a recomendação PRISMA. Epidemiologia e Serviços de Saúde, 24, 335-342. http://dx.doi.org/10.1080/0020739x.2013.790509.
Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modelling mathematical argumentation: the importance of qualification. Educational Studies in Mathematics, 66(1), 3-21. http://dx.doi.org/10.1007/s10649-006-9059-8.
Kaplan, A. H., Gulkilik, H., & Emul, N. (2019). Investigating the Relationship between Argumentation and Proof a Representation Perspective. International Journal for Mathematics Teaching and Learning, 20(2), 131-148. https://eric.ed.gov/?id=EJ1237078
Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb, & H. Bauersfeld, (ed.). The emergence of mathematical meaning: Interaction in classroom cultures (pp.229-269). Lawrence Erlbaum.
Kwon, N., Younggon, B., & Hwan, O. (2015). Design research on inquiry based multivariable calculus: focusing on students’ argumentation and instructional design. ZDM: The International Journal on Mathematics Education, 47(6), 997-1011. http://dx.doi.org/10.1007/s11858-015-0726-z.
Laamena M., Nusantara, T., Irawan, B., & Muksar, M. (2018) How do the Undergraduate Students Use an Example in Mathematical Proof Construction: A Study based on Argumentation and Proving Activity. International Eletronic Journal of Mathematics Education, 13(3), 185-198. https://eric.ed.gov/?id=EJ1227508
Lichtman, M. (2010). Qualitative Reserch in Education: A User’s Guide. 2. ed. Sage.
Mariotti, M. A., & Pedemonte, B. (2019). Intuition and proof in the solution of conjecturing problems. ZDM, 51(5), 759-777. http://dx.doi.org/10.1007/s11858-019-01059-3.
Metaxas, N., Potari, D., & Zachariades, T. (2016). Analysis of a Teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes. Educational Studies in Mathematics, 93(3), 383-397. http://doi.org/10.1007/s10649-016-9701-z.
Nunes, J. M. V., & Almouloud, S. A. (2013). O modelo de Toulmin e a análise da prática da argumentação em matemática. Educação Matemática Pesquisa: Revista do Programa de Estudos Pós-Graduados em Educação Matemática São Paulo, 15(2), 487-512. https://revistas.pucsp.br/emp/article/view/14592.
Pedemonte, B. (2002). Étude didactique et cognitive des rapports de l'argumentation et de da démonstration dans l'apprentissage des mathématiques. [Tese de Doutorado em Educação, Université Joseph Fourier-Grenoble I/Université de Genova, Genova, Itália]. https://theses.hal.science/tel-00004579.
Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66(1), 23-41. http://dx.doi.org/10.1007/s10649-006-9057-x.
Pedemonte, B. (2012). L’argumentation en mathématiques et sa relation avec la démonstration. Quadrante, 21(2), 5-28. https://doi.org/10.48489/quadrante.22882.
Perelman, C. (1993). O império retórico: retórica e argumentação. Edições ASA.
Perelman, C., & Olbrechts-Tyteca, L. (2005). Tratado da argumentação: a nova retórica. Martins Fontes.
Plantin, C. (2008). A Argumentação: História, teorias, perspectivas. Tradução Marcos Marcionilo. Parábola.
Silva Júnior, G. A. (2019). Elementos de exploração argumentativa docente na sala de aula: uma proposta de análise à luz de teoria de Perelman e Olbrechts-Tyteca [Tese de Doutorado, Universidade Federal do Rio Grande do Norte, Natal]. https://repositorio.ufrn.br/handle/123456789/28638
Simpson, A. (2015). The anatomy of a mathematical proof: implications for analyses with Toulmin’s scheme. Educational Studies in Mathematics, 90(1), 1-17. http://dx.doi.org/10.1007/s10649-015-9616-0
Staples, M., & Newton, J. (2016). Teachers' Contextualization of Argumentation in the Mathematics Classroom. Theory Into Practice, 55(4), 294-301. https://doi.org/10.1080/00405841.2016.1208070
Teixeira, E. S., Freire Júnior, O., & Greca, I. M. (2015, mar.). La enseñanza de la gravitación universal de Newton orientada por la historia y la filosofía de la ciencia: una propuesta didáctica con un enfoque en la argumentación. Enseñanza de las Ciencias, 33(1), 205-223. http://dx.doi.org/10.5565/rev/ensciencias.1226
Teixeira, E. S., Greca, I. M., & Freire, O. (2012). The history and philosophy of science in physics teaching: a research synthesis of didactic interventions. Science & Education, 21(6), 771-796.
Toulmin, S. (2006). Os Usos do Argumento. Martins Fontes.
Toulmin, S. E. (1958). The uses of argument. University Press.
Tristanti, B., Sutawidjaja, A., Abdur, R., & Muskar, M. (2016). The construction of deductive warrant derived from inductive warrant in preservice-teacher mathematical argumentations. Educational Research and Reviews, 11(17), 1696-1708. https://files.eric.ed.gov/fulltext/EJ1116653.pdf
Uygun-Eryurt, T. (2020). Conception and Development of Inductive Reasoning and Mathematical Induction in the Context of Written Argumentations. Acta Didactica Napocensia, 13(2), 65-79. https://eric.ed.gov/?id=EJ1280349
Walton, D. N. (2012). Lógica Informal: manual de argumentação crítica. Martins Fontes.
Wawro, M. (2015). Reasoning About Solutions in Linear Algebra: the case of abraham and the invertible matrix theorem. International Journal of Research in Undergraduate Mathematics Education, 1(3), 315-338.http://dx.doi.org/10.1007/s40753-015-0017-7.
Yopp, D. A., & Ely, R. (2015). When does an argument use a generic example? Educational Studies in Mathematics, 91(1), 37-53. http://dx.doi.org/10.1007/s10649-015-9633-z.
Zazkis, D., Weber, K., & Mejía-Ramos, J. P. (2016). Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context. Educational Studies in Mathematics, 93(2), 155-173. http://doi.org/10.1007/s10649-016-9698-3.
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