These guidelines were developed by the Commission on Preservice Teacher Education of the National Council of Teachers of Mathematics to help responsible people, especially those people in colleges and universities that prepare teachers of mathematics, to find ways in which local teacher-preparation programs might be improved. The guidelines provide for general direction, generally expected levels of competence, possible evidences of the existence of essential characteristics, and indications of how the guidelines themselves help in the realization of goals. For the most part, the guidelines are stated in terms of specific competencies. Topics covered include academic and professional knowledge, professional competencies and attitudes, and institutional responsibilities. (MP)