A course in the philosophy of mathematics for future high school mathematics teachers

In this paper, I discuss a course in the philosophy of mathematics designed to help future high school mathematics teachers develop an understanding of philosophical questions about mathematics. Throughout the course, our discussions link core philosophical questions to particular theories of mathematics teaching and learning. Thus the course mixes traditional philosophy of mathematics with the study of everyday embodied mathematical habits, offering a kind of descriptive and synthetic approach more often associated with continental traditions of philosophy. This paper describes some of the key theoretical themes and issues, and argues that such courses offer future teachers important insights into the nature of mathematics.