Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Much of what is taught, especially in college, is designed to support other disciplines. To determine the current mathematical needs of twenty-three partner disciplines, the Mathematical Association of America (MAA) conducted the Curriculum Foundations Project (Ganter and Barker 2004; Ganter and Haver 2011), as discussed in the appendix…

In mathematics, as in baseball, the conventional wisdom is to avoid errors at all costs. That advice might be on target in baseball, but in mathematics, avoiding errors is not always a good idea. Sometimes an analysis of errors provides much deeper insights into mathematical ideas. Certain types of errors, rather than something to be eschewed, can…

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is…

The Fundamental Theorem of Calculus is discovered based on the use of data analysis techniques applied to a variety of common families of functions. (Contains 8 figures and 6 tables.)

The placement tests used at most colleges represent what is probably the biggest hurdle in the transition between school and collegiate mathematics. This article looks at different aspects of the problems and suggests some strategies for attempting to resolve the difficulties.

Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)

Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)