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The Philosophy of Mathematics Education

Paul Ernest, et al.
Springer Open
Publication Date: 
Number of Pages: 
ICME-13 Topical Surveys
[Reviewed by
Brian P. Katz
, on

This pamphlet is framed as an overview of the field of philosophy of mathematics education, and it lives up to that promise. There are four main essays, written largely independently. The first, by Paul Ernest, articulates many questions in the field (with special attention paid to disciplinary hygiene for mathematics education research) while making a case that education researchers need to engage these questions in their work at some level. The second, by Ole Skovsmose, offers a more detailed view of critical mathematics education as an approach to making the hidden assumptions of mathematics education research visible. The third, by Jean Paul Van Bendegem, is a nice history of the introduction and evolution of paradigms in philosophy of mathematics education, ending with a metaphor about researchers switching between registers in this work. The final essay, by Maria Aparecida Viggiani Bicudo and Roger Miarka, is a case study that describes the growth of a tradition of philosophy of mathematics education research in Brazil and some of the mechanisms (mostly conferences and working groups) that help sustain this community.

While I found this short book interesting and engaging, its readership might be narrow because of its original purpose: to survey the field to build a shared foundation for discussions among scholars working in the field at ICME-13. On one hand, to get much more than a summary out of this piece, the reader may need to be familiar with the works of scholar such as Freire and Kuhn from outside of mathematics and many others inside this field.

On another hand, it has been my experience that the mathematics education (and social science in general) research community has a strong tradition of engaging the philosophical issues in its work to some extent, so many of these scholars will already be loosely aware of the ideas in this pamphlet at the level of that summary. As a result, this piece is a particularly good read for (i) young scholars who are just starting their work in this area and (ii) other education researchers who know they have a gap in their perspective on the philosophical issues in their own work but do not know how to start addressing this gap. I think it could also be effective in the context of a methods or, with careful framing and support, in a research seminar for graduate students or advanced undergraduates.

I have been party to discussions recently of whether the general value placed on justice in education research means that we should expect all mathematics education research to engage questions of equity and identity, perhaps by asking authors or reviewers to comment on the justice implications for each piece of research. This issue, which seems to be looming larger and larger, does not appear explicitly in this pamphlet as I expected, but reading it is a good way to prepare to engage those discussions.

Brian P. Katz is an associate professor at Augustana College (IL). He teaches courses across the undergraduate curriculum, with a preference for courses that meet students at transition points in their mathematical justification processes, that highlight philosophical issues in mathematics, and that prepare teachers to bring the two previous themes into their future classes; his research interests are similar. With Michael Starbird, Brian has published Distilling Ideas: An Introduction to Mathematical Thinking.

1 Introduction

2 An Overview of the Philosophy of Mathematics Education, by Paul Ernest
2.1 Introduction: What Is the Philosophy of Mathematics Education?
2.2 A ‘Top Down’ Analysis of the Philosophy of Mathematics Education
2.3 Conclusion

3 Critical Mathematics Education: Concerns, Notions, and Future, by Ole Skovsmose
3.1 Some Concerns in Critical Mathematics Education
3.2 Some Notions in Critical Mathematics Education
3.3 Critical Mathematics Education for the Future

4 The Philosophy of Mathematical Practice: What Is It All About?, by Jean Paul Van Bendegem
4.1 Lakatos as the Starting Point
4.2 Kitcher as the Next Step.
4.3 A Tension Is Introduced to Stay
4.4 Enter the Sociologists, Educationalists and Ethnomathematicians
4.5 Brain and Cognition Complete the Picture
4.6 Conclusion: Working in Different “Registers”

5 The Philosophy of Mathematics Education in Brazil, by Maria Aparecida Viggiani Bicudo and Roger Miarka

6 Summary and Looking Ahead