Suggests structured investigations as a method of teaching mathematics to preservice elementary school teacher. Presents an example problem that asks students to determine the maximum number of regions that can be created by connecting any two points around the circumference of a circle. (MDH)

Discusses the rate of fall of a wooden beam or a chimney by examining the fall of a highway lamp pole when it is sheered off at its base upon impact by a vehicle. Provides the mathematical formulas to explain and an experiment to illustrate the phenomenon. (MDH)

Described is a programing application of the software, Mathematica, which allows students to explore the various cases involved in minimizing the sum of squares for the best fit of a regression line. Several examples are included with appropriate software commands. (JJK)

This Australian document is a guide to teaching mathematics as it relates to specific work situations. After a brief introduction, chapter 1 looks at problem solving, advises teachers to lower the reading level and thus raise the understandability of written math problems, and describes a four-step problem-solving process. Chapter 2 outlines a…

Defines arithmetic, harmonic, and weighted harmonic means, and discusses their properties. Describes the application of these properties in problems involving fuel economy estimates and average rates of motion. Gives example problems and solutions. (CW)

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)

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,…

The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

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)

Presents a motion problem that students in a college physics class are asked to solve and later asked to continue to analyze until they have stopped learning from the problem or the problem itself is finished. (MDH)

Many common objects can provide numerous opportunities for students to develop mathematical concepts and skills. The lesson described in this article provided an excellent opportunity for middle school students to discover how real-life situations do not always present obvious "right" answers. As students explored a question related to the…

Research in goal theory has often relied on the general linear model, ignoring some central assumptions of the theoretical framework under investigation. The purpose of the two studies reported here was to illustrate how the Rasch model can supplement traditional statistical analyses when evaluating the effects of goal orientations on persistence.…

The elements of statistical formulae that cause people to perceive them as difficult were studied, working from theoretical bases that involve cognitive load, motivational perception, and impasse driven learning. In a pilot study conducted to identify difficulties that novices perceive while learning statistical formulae, 22 students in an…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

Presents three teaching ideas: (1) investigating patterns in the sum of four numbers in a square array, no two from the same column or row; (2) using three-dimensional coordinates to generate models of three tetrahedra; and (3) applying the K=rs area formula for a triangle to other polygons. (MDH)