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1 Introduction This ICME-13 Topical Survey is designed to provide an overview of contemporary research in the philosophy of mathematics education. This is a broad cluster of overlapping but at times disparate themes. In the first instance, this publication exposes some of the problems and questions in mathematics education that the philosophy of mathematics education clarifies, illuminates and sometimes helps to solve. A metaphor for what is offered is a three tier pyramid. At the apex is this publication, presenting an abbreviated ‘problematique’ of the subfield, that is, the cluster of problems and issues at the heart of the area. At the next level, is the breadth of problems, issues and research results that will be shared when the group of authors of this publication meet with the ‘public’ at the ICME 13 conference in Hamburg, July 2016. Finally, at the base level is the full spread of research and its results, books, journals, papers, conference presentations and other activities that make up the subfield, the philosophy of mathematics education, which is beyond the scope of this publication and conference. This publication thus briefly sketches some of the topics, problems and areas of active research (the apex) and through this point to some of what will be offered at the conference (the middle level). In doing so it serves as an introduction to the extent of the sub-field overall, through references to current publications and classic literature (the base of the pyramid). Why the philosophy of mathematics education? What does it offer? The philosophy of any activity comprises its aims or rationale. Given our shared commitment to the teaching and learning of mathematics it is vital ask: What is the purpose of teaching and learning mathematics? What do we value in mathematics and its teaching and learning? Why do we engage in these practices and what do we

© The Author(s) 2016 P. Ernest et al., The Philosophy of Mathematics Education, ICME-13 Topical Surveys, DOI 10.1007/978-3-319-40569-8_1

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The Philosophy of Mathematics Education

hope will be achieved? The sub-field can also help us uncover whatever implicit assumptions and priorities underlie mathematics education. These can including paradigmatic assumptions of which we may be unaware, but that can be identified through, let us say, a philosophical archaeology. The philosophy of mathematics education applies philosophical methods to a critical examination of the assumptions, reasoning and conclusions of mathematics education, systematically enquiring into fundamental questions: • • • • • • • • • •

What is mathematics? How does mathematics relate to society? Why teach mathematics? What is the nature of learning (mathematics)? What is the nature of mathematics teaching? What is the significance of information and communication technology in the teaching and learning of mathematics? What values underlie these activities, overt and covert? How and to what extent is social justice promulgated by these activities and this field of study? What is the status of m