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.
Comment (from this Blueprint): While this paper by Hamami & Morris is not a necessary reading, it provides a fairly broad overview of the practical turn in mathematics. Since it was aimed at mathematics educators, it is a very accessible piece, and provides useful directions to further reading beyond what is included in this blueprint.