Discards the blinders that have hampered the traditional teaching of calculus and reexamines some of the intuitive ideas that underlie this subject matter. Analyzes the various indeterminate forms that arise through the blind application of algebraic operations. (Author/ASK)

Explores first-year students' understanding of fundamental calculus concepts using written tests and interviews. Analysis of the written and verbal responses to the test items revealed significant misconceptions on which students' mathematical activities were based. Describes some of those misconceptions and errors relating to students'…

Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…

Describes a test using 155 third-year undergraduates in 15 different institutions to examine the extent to which certain core first-year material is retained and understood. Includes an analysis of the answers given by students to each question as well as some of their comments. Students' misconceptions indicate that foundations laid in the first…

The calculus of finite differences and finite sums is used to create a context in which the computer can be incorporated into calculus courses. Analyses of the experimental implementations are included. (MP)

Reports on ongoing developmental research efforts to adapt the instructional design perspective of Realistic Mathematics Education (RME) to learning and teaching of collegiate mathematics using differential equations as a specific case. Focuses on the RME design heuristic of guided reinvention as a means to locate the starting point for an…

Considered are the main elements of computational chemistry problems and how these elements can be used to formulate the problems mathematically. Techniques that are useful in devising an appropriate solution are also considered. (Author/TG)

Describes a scheme for testing and assisting students with the mathematical skills essential for math courses. Discusses the aims and philosophy of the scheme and describes the logistics of running such a scheme. Reviews student performance and discusses those skills that students are strong in or have difficulty mastering. (Author/ASK)

A calculus course was designed to give students an appreciation of mathematics as a social process rather than a set of techniques. Group activities, problem solving sessions, and a new approach to testing were used. (SD)

Provides an overview of recent changes in calculus education at Chinese colleges and universities. Focuses on the changes parallel to the development of computer-assisted instruction (CAI) technology and software. Discusses how the wide application of mathematical CAI software has greatly facilitated mathematical experimentation and offerings of…