This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

To achieve the vision of mathematics set forth in "Crossroads" ("AMATYC," 1995), students must experience mathematics as a sensemaking endeavor that informs their world. Embedding the study of mathematics into the real world is a challenge, particularly because it was not the way that many of us learned mathematics in the first place. This article…

This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included…

For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

Most two-year mathematics faculty initially won't gravitate toward the chapter on stakeholder involvement in implementing Beyond Crossroads. Faculty most likely will search out the chapter on curriculum and instruction. In fact, some mathematics faculty may not consider the relevancy of other stakeholders as an important factor for improving their…

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Presents a theorem and its converse to generate all of the primitive Pythagorean quadruples. Provides a BASIC program generating them. (YP)

Discusses numerical methods to compute approximate solutions of a differential equation. Provides a Pascal program for the extended Euler-Heun method. (YP)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

To demonstrate concepts or rapidly create quizzes, teachers commonly encounter the need to quickly create mathematical examples. Unfortunately, by producing undesirable or overly complex solutions, extemporaneously created examples can become problematic, create tense learning environments and become more confusing than they are worth. Experience…

This article traces some of the events leading up to the call for reform, differing aspects of the suggested reform, steps taken, and possible future directions for the reform of calculus instruction. (CW)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

Provides four examples for testing the validity of logical arguments by using the method of truth trees. (YP)

Describes the "Buffon's Needle" problem, which is calculating the probability that a needle will cross one of two separated lines. Calculates the probability when the length of the needle is greater than the space of the two lines. Provides an analytic solution and the results of a computer simulation. (YP)

Discusses the need for a geometry course in a two-year college mathematics program. Provided are guidelines for developing the geometry course separately or integrally with current curricular pattern. (25 references) (YP)