During the past decade, mathematics education has changed rapidly, giving rise to a polarization of opinions among the community of research mathematicians. What is the appropriate balance between theory, technique, and applications? What is the role of technology? How do we fulfil the needs of students entering other fields? The purpose of this volume, the proceedings of a conference held at the Mathematical Sciences Research Institute in Berkeley in 1996, is to present a serious discussion of these educational issues, with a balanced representation of opposing ideas. Part I deals with general issues in university mathematics education; Part II presents case studies on particular projects; Part III presents a range of opinions on mathematics education in elementary and secondary schools; and Part IV presents the reports of the working groups.