Abstract
This paper the sub-field of study the philosophy of mathematics education from one perspective. The field is characterised in both narrow and broad terms, and from both bottom-up (questions and practices) and top-down perspectives (in terms of philosophy and its branches). From the bottom-up one can characterize the area in terms of questions, and I have asked: What are the aims and purposes of teaching and learning mathematics? What is mathematics? How does mathematics relate to society? What is learning mathematics? What is mathematics teaching? What is the status of mathematics education as knowledge field? I have characterized the sub-field using a ‘top down’ perspective using the branches of philosophy. Looking briefly into the contributions of ontology and metaphysics, aesthetics, epistemology and learning theory, social philosophy, ethics, and the research methodology of mathematics education reveals both how rich and deep the contributions of philosophy are to the theoretical foundations of our field of study. But even these two approaches leave many questions unanswered. For example: what are the responsibilities of mathematics and what is the responsibility of our own subfield, the philosophy of mathematics education? I conclude that the role of the philosophy of mathematics education is to analyse, question, challenge, and critique the claims of mathematics education practice, policy and research.
