This monograph presents personal insights gained during the teaching of a course in elementary mathematics teaching methods. The class was developed on the premise that children are active constructors of mathematical meaning. The course consisted of teaching sessions, action research projects, and demonstrations. To assess student learning from these teaching experiences, a portion of the final exam required that each student identify the ten most important things learned during the course. Analysis of student responses led to the identification of five clusters: instructional strategies, planning for teaching, teaching for understanding, teacher interactions, and issues in mathematics education. These clusters matched the instructional goals of the course. An important finding was that 13 students out of a total enrollment of 19 indicated gender equity as one of their most important discoveries from this course. Included are assignments, informal mathematics interview format, coaching form, verbal interactions observation form, verbal interactions explanation, math lesson assessments, and the final exam. (JRH)