Investigated the behavior of college mathematics professors as they taught a basic course. It was found that all of the teachers typically taught the class as a unit using a teacher centered approach. Compared to less effective teachers, the more effective teachers asked more product questions and covered more content. (PK)

Describes a college-level course that develops an awareness and understanding of environmental issues through instruction of mathematical concepts and processes, presenting sample mathematical problems which illustrate how environmental issues are used as themes for teaching mathematical skills. Also provides a list of annotated references for…

Describes a course (Introduction to Numerical Techniques of Physics) which can be adapted to such courses as applied mathematics, numerical analysis, mechanical or electrical engineering, chemistry, and biomathematics. Course goals (including emphasis on the distinction between computing, programming and coding) and instructional strategies are…

The following ideas are presented: (1) an approach to exploring some of the patterns of prime numbers as a junior high activity; and (2) an informal introduction to continuity functions that uses pictures to represent simple physical situations, with suggestions for follow-up exercises. (MP)

That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)

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)

The implementation of the first phase of a project involving the use of computer software in a course on the mathematics of finance is discussed. Results of a controlled experiment indicated that the techniques employed seemed to have positively impacted the performance of the students. (CW)

A nonconventional graphical way to represent functions (the Parallel Axes Representation) is discussed. A computerized environment designed to support the exploration of the representation of linear functions is described. The didactical potential of this representation is illustrated. (CW)

Presents perspectives from students and teachers about project work in mathematics. Presents a theoretical framework consisting of problem-centered studies, interdisciplinarity, participant-directed studies, and the exemplarity principle. Contrasts theoretical conceptions with practice. (MKR)

Discusses an activity-based, exploratory-centered model of instruction based on the Piagetian theory of developmental learning that bridges the gap between the expected and actual levels of student reasoning. Applies the method to learning the mathematical concepts of circumference, area and volume, and division by zero. (22 references) (MDH)

Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is…

This paper reports on initial results from an ongoing evaluation study of a National Science Foundation project to implement reform-oriented teaching practices in college science and mathematics courses. The purpose of this study was to determine what elements of reform teaching are being utilized by college faculty members teaching undergraduate…

A mathematician's work consists of proving theorems, calculating, and making mathematics understandable. An assistant for all three components is a Computer Algebra System. We describe and discuss various CAS-assisted processes for proving theorems, and discuss the constraints which can appear regarding efficiency, confidence in the result and…

We present a project for a differential equations class: an analysis of an H. G. Wells story in which is given a submersible's descent time, its ascent time, and its eruption from the surface before splashdown. (Contains 5 figures.)

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the…