Computer algebra systems are frequently used for research. In addition, some instructors have based entire advanced courses around these systems. One benefit is that they allow students to become familiar with the methods of calculus by individual experimentation. However, instructors have generally seen computer algebra systems as unsuitable for…

Although dogs seemingly follow the optimal path where they get to a ball thrown into the water, they certainly do not know the minimization function proposed in the calculus books. Trading the optimization problem for a related rates problem leads to a mathematically identical solution, which, it is argued here, is a more plausible model for the…

Using the problem of determining where a Flatland artist was standing, this article takes another look at perspective.

What may have been the birth of a new calculus problem took place when the author noticed that two coffee cups, one convex and one concave, fit nicely together, and he wondered which held more coffee. The fact that their volumes were about equal led to the topic of this article: complementary surfaces of revolution with equal volumes.

This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

A major source of challenging problems for students is the use of higher mathematics to derive elementary problems. Several examples are given. (MP)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

An interesting comparison of the techniques of geometry and calculus used to solve the same problem. (JP)

Examines the effects of two teaching techniques on college liberal arts majors' ability to solve calculus problems; concludes that instruction involving a modified directed reading-thinking activity followed by peer tutoring may improve problem-solving ability in calculus. (DD)

As times change, so has the role of algebra in the educational program. The Interactive Mathematics Program (IMP) offers secondary students an opportunity to learn algebra in a college preparatory sequence that combines basic skills, problem solving, and conceptual understanding while integrating algebra into a problem-based program. Designed for…

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)