The importance of visual representation, usually a geometric figure presented in words and in mathematical symbols that is frequently found on high-stakes standardized tests is evaluated. The study shows that mathematics teachers can help prepare students to solve mathematical problems containing a figure not drawn to scale by looking for and…

Although the phase plane can be plotted and analyzed using an appropriate software package, the author found it worthwhile to engage the students with the theorem and the two proofs. The theorem is a powerful tool that provides insight into the rotational behavior of the phase plane diagram in a simple way: just check the signs of c and [alpha].…

This research focuses on the graphics calculator in calculus and its impact on students' abilities to work with graphical, numerical, and symbolic representations. Three courses are compared, two of which are taught with less emphasis on the use of graphing calculators. The format of the course emphasizing calculator use is more traditional than…

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

This document is a compilation of abstracts of 28 research papers presented at the 52nd Annual Meeting of the National Council of Teachers of Mathematics. The major portion of the reports concerned methods of instruction; nine were related to college mathematics, ten on secondary school mathematics, and two at the elementary school mathematics…

Provides a simplified, synoptic overview of the area of thermodynamics, enumerating and explaining the four basic laws, and introducing the mathematics involved in a stepwise fashion. Discusses such basic tools of thermodynamics as enthalpy, entropy, Helmholtz free energy, and Gibbs free energy, and their uses in problem solving. (JM)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Presented is an example of a question that can be used to investigate probability and random triangles. Included is the question, analysis, and procedure for solving the question. (KR)

Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)

Given are instructions for teaching spreadsheet use for problem solving in mathematics. Examples of relevant problems from algebra through calculus are provided. The advantages of using computer spreadsheets in this application are stressed. (CW)

Deficits common among secondary students with learning disabilities or mathematics deficiencies are considered, along with a strategy to teach upper level mathematics, such as algebra or calculus. The strategy involves use of a mentor to help students to comprehend mathematics vocabulary, develop their own problem-solving strategy, and create a…

Presents one model for a liberal arts mathematics course that combines probability and calculus. Describes activities utilized in the course to heighten students' interest and encourage student involvement. Activities include use of visualization, take-home tests, group problem solving, research papers, and computer usage with DERIVE computer…

Describes an experiment to determine which of four objects, hollow cylinders, solid cylinders, hollow balls, and solid balls, will reach the bottom of an inclined plane first when released simultaneously. Provides solutions to the problem and supplementary exercises. (MDH)

Describes the mechanics of group work in the college mathematics classroom specifically group formation, preliminary class work, class and group discourse, individual and group assignments, and impact on test taking. Includes examples from a first-semester calculus course. (JJK)