False dichotomies such as ‘proof vs. explanation’ or ‘argument vs. proof’ as described by Müller-Hill (2019) might result in encountering an impasse, when looking at practices in the mathematics classroom. Viewing mathematical practices as cultural practices reveals that explanation, argumentation and proving can all be observed and interpreted as situated practices in the context of proof and explanation in the mathematics classroom (Cobb & Bauersfeld, 1995; Krummheuer, 1995; Yackel & Cobb, 1996). Although conceptual clarity has merit, describing mathematical classroom processes and practices demands a more dialectical and integrative understanding of these concepts. The enactment of these practices by teachers and students varies considerably, reflecting cultural traditions, educational conventions, and the scripted interactions that characterize different classroom contexts (Zhuang, & Conner, 2022). These mathematical practices are thus fundamentally cultural practices, shaped by the social and institutional contexts in which they occur. The reconstruction and analysis of classroom practices offers an empirical basis for conceptual clarifications that enhance our understanding of both the practices and their theoretical underpinnings (Bredow & Knipping, 2023; Conner, Tabach, & Rasmussen, 2023; Knipping & Reid, 2019). Understanding mathematical practices such as ‘argumentation’, ‘proof’ and ‘explanation’ as cultural practices allows us to research classroom mathematical practices through an integrated educational and mathematical lens, treating these as practices that emerge from the intersection of mathematical content and social context.

References

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Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning. Erlbaum.

Conner, A.M., Tabach, M. & Rasmussen, C. (2023). Collectively engaging with others’ reasoning: Building intuition through argumentation in a paradoxical situation. Triangle. International Journal of Research in Undergraduate Mathematics Education, (9), 666–693. https://doi.org/10.1007/s40753-022-00168-x

Knipping, C., & Reid, D. A. (2019). Argumentation Analysis for Early Career Researchers. In G. Kaiser & N. Presmeg (Eds.), Compendium for Early Career Researchers in Mathematics Education (pp. 3–31). Springer. https://doi.org/10.1007/978-3-030-15636-7_1

Krummheuer, G. (1995). The Ethnography of Argumentation. In P. Cobb & H. Bauersfeld (Eds.), The Emergence of Mathematical Meaning (pp. 229–269). Routledge.

Müller-Hill, E. (2019). Explanatoriness as a value in mathematics and mathematics teaching. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11) (pp. 276–283). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

Toulmin, S. E. (1958). The Uses of Argument. Cambridge University Press.

Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458–477. https://doi.org/10.2307/749877

Zhuang, Y., & Conner, A. (2022). Teachers’ use of rational questioning strategies to promote student participation in collective argumentation. Educational Studies in Mathematics, 111. https://doi.org/10.1007/s10649-022-10160-6