In this article, the author suggests that to improve the teaching of mathematics in elementary schools, we must, when teaching content courses to prospective teachers, model the kind of teaching we want them to engage in. The author suggests ways to model this kind of teaching, which include the following: (1) challenge "all" students; (2) encourage different solutions; (3) explain in more than one way, including a way appropriate for elementary children; (4) include in each lecture something that students find exciting, and (5) connect mathematics with its history and with mathematicians. (Contains 3 tables and 5 figures.)