It is noted that all graphs of cubic equations are symmetric about their inflection points. This is proven through the use of some calculus and the fundamental theorem of algebra. A table sums up the nature of symmetry for polynomials of any degree. (MP)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

This discussion deals with the question, are there integral rectangles such that a box of maximum volume is obtained by removing an integral-sided square from each corner? An equation to solve the problem is generated and a table of values presented. The material appears suitable for beginning calculus students. (MP)

Results are presented of an impromptu exploration of polar formulas for volumes of revolution for certain plane regions. The material is thought to be unique, and to offer room for student exploration. It is felt pupil investigation can lead to increased pupil interest in both polar coordinates and calculus. (MP)

A logically and empirically valid structure of knowledge for differential calculus was made by textbook analysis and by collecting data from a first semester college calculus course. (MP)

Examples of some geometric illustrations of limits are presented. It is believed the limit concept is among the most important topics in mathematics, yet many students do not have good intuitive feelings for the concept, since it is often taught very abstractly. Geometric examples are suggested as meaningful tools. (MP)

Detailed examples of the kind of interdisciplinary activity involving differential equations and the computer that are highly motivating to many pupils and can be easily integrated with current materials are provided. It is felt the projects illustrated can work well within courses and are not excessively time-consuming. (MP)

An experimental program in Calculus I at the University of Southern California (USC) is described. It is concluded that it is possible to give a meaningful program in which computer use is incorporated. The intent is to set up all USC calculus courses with some use of microcomputers. (MP)

During the summers of 1978 and 1979, mathematics classes sponsored by SMPY (Study of Mathematically Precocious Youth) were held for seventh graders with the goal that participants learn as much precalculus mathematics as was feasible during the eight-week program. (SB)

Using covarient harmonic oscillator formalism as an illustrative example, a method is proposed for illustrating the difference between the Poincare (inhomogeneous Lorentz) and homogeneous Lorentz groups. (BT)

Considers the results of a study supported by the American Educational Research Association (AERA) and the National Science Foundation (NSF) that focuses on the impact of different environments on students' abilities to learn calculus. (DDR)

Reports on part of a study that was conducted with individual students (n=5) and five groups of students who worked together in the first course of experimental calculus classes. The goal of the study was to discover how the concept of inverse function can be learned. (26 references) (DDR)

Describes a research study that determined that calculus educators are slow to use technologies in instruction because they perceive a lack of clarity regarding the use of technology, technology is rapidly changing, and using technology requires too much time and effort. (DDR)

Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Uses Muybridge's sequence of photos of a moving cat to examine how one might picture changes in the cat's velocity. Classroom implications include building on personally enacted physical experience and recognizing uncertainty as fundamental. Concludes that carefully examined case examples are essential in teaching students to learn and reason…