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History of mathematics in the context of mathematics teachers’ education: a dialogical/ethical perspective

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Abstract

This paper deals with the use of original sources in mathematics education, with emphasis on preservice teachers’ education and the exploration of historical texts. In this context, there is a real challenge, for both teachers and learners, to conduct both ‘synchronic’ and ‘diachronic’ reading. As reported extensively in research, learners seem to have a strong propensity to focus on and to ‘translate’ the texts into modern mathematics, which makes it difficult to deepen both their understanding of history and their own set of conceptualizations. Rather than propose practical solutions, in the paper we explore a theoretical positioning that may help us think differently about these difficulties and, ultimately, provide articulated and different avenues for interventions. Drawing on the philosophy of language of Mikhaïl Bakhtin and Valentin Voloshinov, the idea is to question the Saussurean perspective that underpins the notions of synchrony and diachrony. From this theoretical perspective, we propose to think about the challenges associated with the reading of historical texts in terms of the ethical stance of answerability and engagement in the context of preservice mathematics teachers’ education, and we suggest envisioning a third possible reading, namely, that of the educator.

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Notes

  1. HPM is the International Study Group on the Relations between the History and Pedagogy of Mathematics, affiliated with the International Commission on Mathematical Instruction (ICMI) (see International Mathematical Union, 2022).

  2. More details on this Saussurean analyses of the prospective teachers’ tendency to deploy a reading based on a modern synchronic plan can be found in the report by Guillemette (2016). These analyses are part of a larger empirical study concerning the description of the prospective teachers’ lived experiences when engaging in the reading of historical texts (see Guillemette, 2017).

  3. As de Saussure contends: “In separating language from speaking we are at the same time separating: (1) what is social from what is individual; and (2) what is essential from what is accessory and more or less accidental” (1916/1959, p. 14).

  4. On the one hand, it is important to be aware that Bakhtin and his close collaborators do not propose a unified and precise theory, but an articulated epistemological position which is applied in quite heteroclite domains. On the other hand, it is also important to be aware of the important polemic around the authorship of this corpus. The origin of the various texts that appeared under the name of Bakhtin and the existence of a single and homogeneous Bakhtinian corpus are now discussed among literary scholars (see Bronckart & Bota, 2011).

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Acknowledgements

We would like to acknowledge the support of the Fond de Recherche du Québec—Société et Culture and the Conseil de Recherches en Sciences Humaines du Canada/Social Sciences and Humanities Research Council of Canada.

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  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, Canada

    David Guillemette

  2. École d’éducation, Université Laurentienne, Sudbury, Canada

    Luis Radford

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Correspondence to David Guillemette.

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Guillemette, D., Radford, L. History of mathematics in the context of mathematics teachers’ education: a dialogical/ethical perspective. ZDM Mathematics Education 54, 1493–1505 (2022). https://doi.org/10.1007/s11858-022-01437-4

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