Multiplicative calculus is based on a multiplicative rate of change whereas the usual calculus is based on an additive rate of change. Describes some student investigations into multiplicative calculus, including an original student idea about multiplicative Euler's Method. (Author/ASK)

Describes a 'Moore Method' course whose purpose is to teach students to create and present in class mathematically correct proofs of theorems. Discusses grading, class discussions, ways to help students, and the extent to which to encourage cooperative learning. (Author/ASK)

Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

Students in a freshmen calculus course should become fluent in modeling physical phenomena represented by integrals, in particular geometric formulas for volumes and arc length and physical formulas for work. Describes how to train students to became fluent in such modeling and derivation of standard integral formulas. Indicates that these lessons…

Shares a series of problems designed to provide students with opportunities to develop an understanding of applications of the definite integral. Discourages Template solutions, solutions in which students mimic a rehearsed strategy without understanding as the variety of problems helps prevent the construction of a template. (Author/ASK)

Compares two groups of students, one of which used writing to learn mathematics and the other which engaged thinking about mathematical ideas without writing. Indicates no significant differences between the two groups and emphasizes the importance of discussing and communicating mathematical ideas. (Contains 29 references.) (Author/ASK)

Investigates whether the use of computer algebra systems could provide a significant advantage to students taking standard university entrance calculus examinations. Indicates that supercalculators would probably provide a significant advantage, particularly for lower-achieving students. Demonstrates that it is possible to write questions in which…

Addresses the problem of poor study habits in calculus students and presents techniques to teach students how to study consistently and effectively. Concludes that many students greatly appreciate the added structure, work harder than in previous courses, and witness newfound success as a consequence. (Author/ASK)

Discusses the lack of calculus textbook improvements even though there have been complaints about them from students and professors. Argues against using commercial textbooks in calculus instruction. (ASK)

Suggests that many students with A-level mathematics, and even with a degree in mathematics or a related subject, do not have an understanding of the basic principles of calculus. Describes the approach used in three textbooks currently in use. Contains 14 references. (Author/ASK)

Discusses the role of context problems as they are used in the Dutch approach known as realistic mathematics education (RME). Uses an RME design for a calculus course to illustrate that theory based on the design heuristic using context problems and modeling, which was developed for primary school mathematics, also fits advanced topics such as…

Presents a study that examines how two teachers taught differentiation using a hand-held computer algebra system. Finds that students of the teacher who privileged conceptual understanding and student construction of meaning were more able to interpret derivatives. Highlights the fact that within similar overall attainment on student tests, there…

Probably the one "new" mathematical topic that is most responsible for modernizing courses in college algebra and precalculus over the last few years is the idea of fitting a function to a set of data in the sense of a least squares fit. Whether it be simple linear regression or nonlinear regression, this topic opens the door to applying the…

A simple and practical application of mathematics is for fairly resolving the dispute of division of items for which two parties have equal claim. Basic properties of fair division are explained, which would enable students to learn concepts on optimization without introducing calculus.

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever…