Not from Nowhere History and Philosophy behind Mathematical Education

Summary In this paper I discuss some of the historical and philosophical aspects of mathematical education, especially in foundational subjects where many of the principal issues seem to lie. Historical examples are chosen from the calculus, mathematical analysis, set theory and logic, but the philosophical points discussed also apply to other branches of mathematics. The paper falls into four parts, which are alternately mainly historical and philosophical. The first part is motivated partly by problems arising in school mathematics (although the subject matter is treated from a more advanced viewpoint), and the second attempts to develop some general methodological considerations. The third part is relevant mainly to university mathematics, while the final part contains a number of broad conclusions, including the question of the role of the history of mathematics in mathematical education.