Abstract
The development of students’ mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR, this research project aimed to qualify it from a theoretical perspective, with an elaboration that would not only indicate its ways of being thought about and espoused but also serve as a tool for reflection and thereby contribute to the further evolution of the cultures of the teaching and research communities in mathematics education. To achieve such an elaboration, a literature search based on anasynthesis (Legendre, 2005) was undertaken. From the analysis of the mathematics education research literature on MR and taking a commognitive perspective (Sfard, 2008), the synthesis that was carried out led to conceptualizing a model of mathematical reasoning. This model, which is herein described, is constituted of two main aspects: a structural aspect and a process aspect, both of which are needed to capture the central characteristics of MR.
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Notes
The epistemic value of a proposition refers to the notion that an utterance can be true, probable, likely, or false.
In French, the word raisonnement is usually translated as reasoning (see, e.g., Duval, 1991).
Formal proving is referred to in French as démontrer.
Formal proving, an action derivative of formal proof (a term widely used in the mathematics education research literature), should not be construed as reasoning that operates only syntactically.
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Acknowledgments
The authors express their appreciation to the Social Sciences and Humanities Research Council of Canada for its financial support of this research and to the reviewers for their helpful comments. In addition, the first author wishes to thank the members of her doctoral research committee for their academic support and encouragement during the years of this project.
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Jeannotte, D., Kieran, C. A conceptual model of mathematical reasoning for school mathematics. Educ Stud Math 96, 1–16 (2017). https://doi.org/10.1007/s10649-017-9761-8
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DOI: https://doi.org/10.1007/s10649-017-9761-8