In this paper we provide a detailed account of how to implement a peer role model (PRM) program similar to the one that we developed at San Diego State University (SDSU) to broaden participation of college women in science, technology, engineering, and math (STEM). In particular, we summarize our findings of the PRM program's best practices,…

Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)

Nonstandard Analysis gives an alternative approach to teaching elementary calculus. This paper hopes to communicate to the reader the ideas of this recent development in mathematics and its implications in teaching undergraduate students. The development of the approach is first briefly traced. Then a method of constructing on ordered field…

Discusses the teaching of mathematics to engineers in Italy. The four courses (usually taught during the first two years), the role of computers, and related ongoing activities (such as meetings and the suggestion of conducting mathematical research in an engineering environment) are described. (JN)

A project is described that provides explicit instruction on the skills necessary for solving word problems. An informal inventory of such skills is being developed, intended for diagnostic use. It contains six sections, each keyed to the problem-solving skills of understanding the problem, representing the unknown, writing the equation, and…

Arguing that college mathematics education must be made more effective, especially for technology, engineering, mathematical sciences, and physical sciences students, this paper presents nine general principles to enhance math instruction for all students. Introductory material argues that changes in perception, attitudes, and role models are…

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…

This paper discusses the problems associated with mathematics anxiety, and provides detailed information on the history and structure of the Mathematics Anxiety Program at the University of Minnesota. The seven parts concern: (1) the Continuing Education for Women Program, (2) the development of the Math Anxiety Program, (3) the symptoms of…

Discusses (in 10 sections) some problem-solving techniques that are typically encountered in a first course in discrete mathematics. Sections (which include exercises) are titled: draw a figure; search for a pattern; mathematical induction; one-to-one correspondence; recurrence relations; generating functions; calculus; finite differences; and…

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)

A program designed for students who enter the teacher education program with a strong academic background in mathematics is described. However, there is a significant gap between academic course completion and depth and breadth of understanding of mathematics. Teachers' practices reflect their view of mathematics. Therefore, students in the…

Described is a statistical methodology course offered at the University of Nebraska at Omaha. The course covers descriptive statistics as well as some procedures for estimating and testing hypotheses. Students use computer statistical packages and write a computer program for some statistical procedures. (RH)