This course explores the most important issues in mathematics education: How do we learn mathematics? How should we teach mathematics? What mathematics should be taught? Should we teach girls differently? Should we teach minorities differently? What is mathematical talent? Is there such a thing as `math anxiety'? How should students be evaluated? How has mathematics been taught in the past? What are the `basics' in mathematics? What is mathematics? And why do intelligent people differ so greatly and passionately about these issues?