Beyond Epistemology and Axiology: Locating an Emerging Philosophy of Mathematics Education
This paper explores the need to move beyond epistemological and axiological discussions in philosophy of mathematics education by reframing the inquiry to include an ontological perspective. The main goal of this work is to envision a new relationship between philosophical discourse and mathematics education, one that takes into account ontological assumptions in mathematics and relates it to axiological objectives and epistemological claims. I begin with a description of the dominant view of mathematics education as depicted in U.S. policy reform discourses and contrast it with critical views of philosophy of mathematics education. I show that the deficiency of both perspectives is their lack of attention to the ontological assumptions inherent in mathematics education. Lastly, I provide a preliminary sketch of a new type of philosophy of mathematics education, which brings ontological inquiry to the forefront, and I speculate on how this emerging philosophy of mathematics education might impact the field.