Discusses the use of mathematical modeling. Describes types, examples, and importance of mathematical models. (YP)

Discusses a misconception about the cycloid that asserts the final point on the path of shortest time in the "Brachistochrone" problem is at the lowest point on the cycloid. Uses a BASIC program for Newton's method to determine the correct least-time cycloid. (MDH)

Develops the formulas for the sum of the numbers from 1 to n and for the squares of the numbers from 1 to n geometrically by utilizing the formulas for the area of a triangle and the volume of a pyramid. (MDH)

Discusses the use of scaling test scores for an algebra class. Provides example data, several equations used in scaling, and graphs. (YP)

Describes a theoretical development to explain the shadow patterns of an object exposed to an extended light source while held at varying distances from a screen. The theoretical model is found to be accurate in comparison with experimental results. (MDH)

Presented is a method for factoring quadratic equations that helps the teacher demonstrate how to eliminate guessing through establishment of the connection between multiplication and factoring. Included are examples that allow the student to understand the link between the algebraic and the pictorial representations of quadratic equations. (JJK)

This paper presents a model for compensating school districts for implementing effective prereferral programs, in order to promote the most appropriate service delivery for all students. The model develops formulae based upon changes in regular and special education enrollment, and includes state monies allocated to special education. Variables in…

Addresses the problem that students balk at the notion velocities do not add algebraically. Offers a geometric model to verify the algebraic formulas that calculate velocity addition. Representations include Galilean relativity, Einstein's composition of velocities, and the inverse velocity transformation. (MDH)

This section provides mathematical activities in reproducible formats appropriate for students in grades 8-10. The activity is designed to provide an experience in model building while developing the concept of slope. (PK)

Sprinting is described by a simple physical model. The model is used to predict the differences between the recorded times for races on a straight track and on a curve. It is shown that the choice of the running lane makes a nonnegligible difference. (Author/SK)

Described is a graduate level engineering course on functional analysis offered at Purdue University. The course restricts itself to linear problems, specifically analysis of linear operators on vector spaces. Key applications in the course demonstrating the utility of abstract formulations are presented. (BT)

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)

Discussion of guaranteed college tuition programs first explores their origins and reasons for continuing high inflation rates for tuition. The relationship between tuition increase and enrollment is examined, and many current guaranteed tuition plans are reviewed. Basic considerations in developing a model for a multiyear plan are outlined and a…

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)

Introduces a method of examining college enrollment patterns that is unlike the traditional cohort models currently used. The student flow matrix model can track student retention and attrition within the institution, and can also help the administrator identify key relationships between and among specific student-flow characteristics. (MSE)