The field of research in collegiate mathematics education has grown rapidly over the past twentyfive years. Many people are convinced that improvement in mathematics education can only come with a greater understanding of what is involved when a student tries to learn mathematics and how pedagogy can be more directly related to the learning process. Today there is a substantial body of work and a growing group of researchers addressing both basic and applied issues of mathematics education at the collegiate level. This volume is testimony to the growth of the field. The intention is to publish volumes on this topic annually, doing more or less as the level of growth dictates. The introductory articles, survey papers, and current research that appear in this first issue convey some aspects of the state of the art. The book is aimed at researchers in collegiate mathematics education and teachers of collegelevel mathematics courses who may find ideas and results that are useful to them in their practice of teaching, as well as the wider community of scholars interested in the intellectual issues raised by the problem of learning mathematics. This series is published in cooperation with the Mathematical Association of America. Readership Researchers in collegiate mathematics education and college level mathematics teachers. Reviews From Reviews for RCME III ... "Offers some hope for increasing the active participation of mathematicians in investigating the nature of mathematics learning and teaching ... everyone will benefit from reading the opening article ... could evolve into an important scholarly journal where both mathematicians and mathematics educators actively seek to publish ... Future developments will be of great interest."  Robert F. Wheeler, Journal for Research in Mathematics Education "Thompson's discussion on functions is very useful and illuminating both theoretically and practically."  Alfinio Flores, Journal for Research in Mathematics Education Table of Contents  A. H. Schoenfeld  Some notes on the enterprise (research in collegiate mathematics education, that is)
 P. W. Thompson  Students, functions, and the undergraduate curriculum
 T. Eisenberg and T. Dreyfus  On understanding how students learn to visualize function transformations
 S. Frid  Three approaches to undergraduate calculus instruction: Their nature and potential impact on students' language use and sources of conviction
 J. Bookman and C. P. Friedman  A comparison of the problem solving performance of students in lab based and traditional calculus
 M. V. Bonsangue  An efficacy study of the calculus workshop model
 S. Monk and R. Nemirovsky  The case of Dan: Student construction of a functional situation through visual attributes
 M. M. ShoafGrubbs  The effect of the graphing calculator on female students' spatial visualization skills and levelofunderstanding in elementary graphing and algebra concepts
 R. Zazkis and H. Khoury  To the right of the "decimal" point: Preservice teachers' concepts of place value and multidigit structures
 L. A. Steen  Twenty questions about research on undergraduate mathematics education
