Philosophy of mathematical practice: A primer for mathematics educators

ZDM Mathematics Education 52:1113–1126 (2020)
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Abstract

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education.

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Author Profiles

Rebecca Morris
Independent Scholar
Yacin Hamami
ETH Zurich

Citations of this work

The Practice-Based Approach to the Philosophy of Logic.Ben Martin - forthcoming - In Oxford Handbook for the Philosophy of Logic. Oxford University Press.
What Is the Basic Unit of Scientific Progress? A Quantitative, Corpus-Based Study.Moti Mizrahi - 2022 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 53 (4):441-458.
Rationality in Mathematical Proofs.Yacin Hamami & Rebecca Lea Morris - 2023 - Australasian Journal of Philosophy 101 (4):793-808.
Mathematical Explanation in Practice.Ellen Lehet - 2021 - Axiomathes 31 (5):553-574.

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References found in this work

The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.
Explanatory unification and the causal structure of the world.Philip Kitcher - 1989 - In Philip Kitcher & Wesley Salmon (eds.), Scientific Explanation. Minneapolis: University of Minnesota Press. pp. 410-505.
Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
Wandering Significance: An Essay on Conceptual Behavior.Mark Wilson - 2006 - Oxford, GB: Oxford: Clarendon Press.

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