This paper reviews some of the basic issues and concerns which are reflected in the literature and which either directly or indirectly influenced the development of a syllabus for a mathematics methods course for preservice elementary teachers. These issues include: (1) What should be the content in mathematics for elementary school children? (2) What should be the content in mathematics for elementary school teachers? (3) What should be the goals of the mathematics methods course? (4) What objectives should be included in the mathematics methods course? (5) What is the role of individualized instruction in the mathematics methods course? (6) What is the competency-based mathematics methods course? (7) What is the content-methods approach to the mathematics preparation of preservice elementary teachers? (8) What is the laboratory approach to teaching a methods course? (9) What is the role of professional laboratory experiences in a methods course? and (10) Who should teach the methods course? The syllabus, prefaced by a set of explanatory statements, is included in an appendix. (JN)