The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based calculus instruction. The next study uses technology and the van Hiele framework to help students construct concept images of sequential convergence. The volume continues with studies on developing and assessing specific competencies in real analysis, on introductory complex analysis, and on using geometry in teaching and learning linear algebra. It closes with a study on the processes used in proof construction and another on the transition to graduate studies in mathematics. Whether they are 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 that they can use. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.
An image of calculus reform: Students' experiences of Harvard calculus by J. R. Star and J. P. Smith III Effects of concept-based instruction on calculus students' acquisition of conceptual understanding and procedural skill by K. K. Chappell Constructing a concept image of convergence of sequences in the van Hiele framework by M. A. Navarro and P. P. Carreras Developing and assessing specific competencies in a first course on real analysis by N. Gronbaek and C. Winslow Introductory complex analysis at two British Columbia universities: The first week-complex numbers by P. Danenhower Using geometry to teach and learn linear algebra by G. Gueudet-Chartier Investigating and teaching the processes used to construct proofs by K. Weber The transition to independent graduate studies in mathematics by J. Duffin and A. Simpson.