This fourth volume of ""Research in Collegiate Mathematics Education"" (""RCME IV"") reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning.
Teaching and learning calculus: What can be learned from education research and curricular changes in France? by M. Artigue Evaluating calculus reform: A review and a longitudinal study by B. Darken, R. Wynegar, and S. Kuhn The need for evaluation in the calculus reform movement. A comparison of two calculus teaching methods by S. L. Ganter and M. R. Jiroutek A longitudinal study of the C$^4$L calculus reform program: Comparisons of C$^4$L and traditional students by K. E. Schwingendorf, G. P. McCabe, and J. Kuhn Understanding sequences: A tale of two objects by M. A. McDonald, D. M. Mathews, and K. H. Strobel A theoretical framework for analyzing student understanding of the concept of derivative by M. J. Zandieh Why can't calculus students access their knowledge to solve non-routine problems? by A. Selden, J. Selden, S. Hauk, and A. Mason Lasting effects of the integrated use of graphing technologies in precalculus mathematics by W. O. Martin Visual confusion in permutation representations by J. Hannah Factors, divisors, and multiples: Exploring the web of students' connections by R. Zazkis On student understanding of AE and EA quantification by E. Dubinsky and O. Yiparaki.