Virtually every college or university training elementary school teachers offers a course in mathematics content with a title similar to “Mathematics for the Elementary School Teacher”, the title we use at the University of Cincinnati. The course is usually a year long and in most states it is a certification requirement for grades kindergarten through eight; it evolved from the recommendations of the Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematical Association of America in the early 1960s. Little, however, has appeared in journals such as the Arithmetic Teacher about the experiences various universities or instructors have had with this course. This paper describes some aspects of such a course at the University of Cincinnati, and I have had two major purposes in mind in writing it. One is to communicate some successful ideas to others who teach similar courses, and the other is to encourage others to submit their ideas, experiences, and suggestions so that all of us can share and profit from each other's successes and failures. A third possibility is to generate some comments from teachers in elementary and middle schools who once took such a course and now, in retrospect, have suggestions to make to those of us who teach it.