Volume III of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem solving - included here are three different articles analyzing aspects of Schoenfeld's undergraduate problem-solving instruction. The articles provide new detail and insight on a well-known and widely discussed course taught by Schoenfeld for many years. Understanding concepts - these articles feature a variety of methods used to examine students' understanding of the concept of a function and selected concepts from calculus. The conclusions presented offer unique and interesting perspectives on how students learn concepts.Understanding proofs - this section provides insight from a distinctly psychological framework. Researchers examine how existing practices can foster certain weaknesses. They offer ways to recognize and interpret students' proof behaviors and suggest alternative practices and curricula to build more powerful schemes. The section concludes with a focused look at using diagrams in the course of proving a statement.
Teaching mathematical problem solving: An analysis of an emergent classroom community by A. Arcavi, L. Meira, J. P. Smith III, and C. Kessel On the implementation of mathematical problem solving instruction: Qualities of some learning activities by M. Santos-Trigo Reflections on a course in mathematical problem solving by A. H. Schoenfeld A cross-sectional investigation of the development of the function concept by M. P. Carlson Honors students' calculus understandings: Comparing calculus&mathematica and traditional calculus students by D. E. Meel Supplementary methods for assessing student performance on a standardized test in elementary algebra by A. Baranchik and B. Cherkas Students' proof schemes: Results from exploratory studies by G. Harel and L. Sowder Students' use of diagrams to develop proofs in an introductory analysis course by D. Gibson Questions regarding the teaching and learning of undergraduate mathematics (and research thereon) by A. Selden and J. Selden.