The field of research in collegiate mathematics education has grown rapidly over the past twenty-five 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 college-level 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.
Some notes on the enterprise (research in collegiate mathematics education, that is) by A. H. Schoenfeld Students, functions, and the undergraduate curriculum by P. W. Thompson On understanding how students learn to visualize function transformations by T. Eisenberg and T. Dreyfus Three approaches to undergraduate calculus instruction: Their nature and potential impact on students' language use and sources of conviction by S. Frid A comparison of the problem solving performance of students in lab based and traditional calculus by J. Bookman and C. P. Friedman An efficacy study of the calculus workshop model by M. V. Bonsangue The case of Dan: Student construction of a functional situation through visual attributes by S. Monk and R. Nemirovsky The effect of the graphing calculator on female students' spatial visualization skills and level-of-understanding in elementary graphing and algebra concepts by M. M. Shoaf-Grubbs To the right of the "decimal" point: Preservice teachers' concepts of place value and multidigit structures by R. Zazkis and H. Khoury Twenty questions about research on undergraduate mathematics education by L. A. Steen.