The psychology of mathematics: A journey of personal mathematical empowerment for educators and curious minds

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Acknowledgments

I am grateful to Paul Dawkins and Eirini Geraniou for helpful comments on earlier drafts of this manuscript.

Notes

1 Some mathematics educators might blanch at this claim, but I find De Toffoli’s (2021) argument in favor of it to be compelling.

2 See De Toffoli (2021) for strong refutations of this position.

3 See Benacerraf’s (1965) classic argument against the claim that numbers are “really” sets.

4 I am grateful to Pat Thompson for encouraging me to make this suggestion. It should be noted that there is a strong body of empirical support that arithmetic develops in children as Norton describes it, with the author of POM contributing important work in the area (e.g., Norton & Wilkins, 2009). However, the role of empirical evidence itself in supporting conceptual analyses is underspecified.

5 A more sophisticated and detailed version of this dilemma is given in the famous paper by Benacerraf (1973).

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Notes on contributors

Keith Weber

Keith Weber is a professor of mathematics education at Rutgers University. His research has focused on the epistemology, cognition, and practice of advanced mathematical reasoning, with a focus on mathematical proof in particular. In his recent work, Dr. Weber has analysed how mathematical text supports students’ and mathematicians’ reasoning and understanding of mathematical ideas.