A philosophy of math education makes claims, even if only implicitly, about the nature of mathematical knowledge. As a result, philosophies of education corresponding to conflicting philosophies of mathematics must be quite different. My Thesis demonstrates this claim using the philosophies of Imre Lakatos and Alfred North Whitehead. I also show that the philosophies of education and corresponding philosophies of mathematics of both men are related in sophisticated ways, not just the naïve ways one might think at first. Finally, I give a brief account of an 'American' philosophy of education based on classroom practice, and I critique it using the two contrasting philosophies of education of Lakatos and Whitehead.
