This fifth volume of ""Research in Collegiate Mathematics Education"" (RCME) presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: advancing our understanding of collegiate mathematics education, and readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.The volume begins with a study from Mexico of the cross-cutting concept of variable followed by two studies dealing with aspects of calculus reform. The next study frames its discussion of students' conceptions of infinite sets using the psychological work of Efraim Fischbein on (mathematical) intuition. This is followed by two papers concerned with APOS theory and other frameworks regarding mathematical understanding. The final study provides some preliminary results on student learning using technology when lessons are delivered via the Internet. Whether specialists in education or mathematicians interested in finding out about the field, readers will obtain new insights about teaching and learning and will take away ideas they can use.
First-year undergraduates' difficulties in working with different uses of variable by M. Trigueros and S. Ursini Cooperative learning in calculus reform: What have we learned? by A. Herzig and D. T. Kung Calculus reform and traditional students' use of calculus in an engineering mechanics course by C. Roddick Primary intuitions and instruction: The case of actual infinity by P. Tsamir Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle by K. Weller, J. M. Clark, E. Dubinsky, S. Loch, M. A. McDonald, and R. R. Merkovsky Models and theories of mathematical understanding: Comparing Pirie and Kieren's model of the growth of mathematical understanding and APOS theory by D. E. Meel The nature of learning in interactive technological environments: A proposal for a research agenda based on grounded theory by J. Bookman and D. Malone.