This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

A problem, motivated by the conversion of Fahrenheit to Celsius, is related to classical Diophantine equations. (MK)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

The general combinatorial problem of counting the number of regions into which the interior of a circle is divided by a family of lines is considered. A general formula is developed and its use is illustrated in two situations. (PK)

Presents results of an investigation of a formula for rank correlation. The exploration turned up an unexpected connection and showed the formula to be far from arbitrary. (PK)

Suggests that in the mathematics classroom the federal income tax may serve as a familiar example to illustrate several aspects of the mathematical concept of function. (PK)

Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)

This project involves devising and evaluating a sales tax schedule to meet the specific revenue needs of a hypothetical state in the United States. Conducting this unit involves many mathematical skills in a learning environment familiar to the student. The essential parts of the project consist of student preparation of a tax schedule and class…

Discusses three types of bridges to determine how best to model each one: (1) drawbridge; (2) balance bridge; and (3) bascule bridge. Describes four experiments with assumptions, analyses, interpretations, and validations. Provides several diagrams and pictures of the bridges, and typical data. (YP)