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December 1999, Volume 92, Issue 9

FEATURES

Grasping Graphing
Anne Patterson
Active involvement and infusion of mathematics into familiar, everyday experience are essential elements in challenging students to engage in true thinking. The concept of graphing is a natural vehicle for achieving this objective.

Developing Mathematical Reasoning Using Attribute Games
Anne Quinn, Robert Koca Jr., Frederick Weening
Students' investigative work that has resulted from playing Set, in an attempt to show how such games can be used to develop mathematical reasoning.

Making the Black Box Transparent
Lawrence Lesser
Focusing on a common example in technology-rich mathematics curricula, namely, the line of best fit, followed by a discussion of two additional examples—interpolating polynomials and complete graphs. In each case, connections between theory and technology do not appear to be as widely known and used as they could be.

Astronomical Math
Robert Ryden
The NCTM's Standards stress the importance of connections among various branches of mathematics and between mathematics and other disciplines; the astronomy problems that follow combine algebra, geometry, trigonometry, data analysis, and a bit of physics. My geometry and algebra students have seen most of these problems and could understand them. They have also been able to experience making distance measurements themselves by using the method of parallax, which is explained in this article.

Service Learning: Taking Mathematics into the Real World
Johnny Duke
This article introduces service learning, explores how it can be used in mathematics education, and relates the author's personal experiences in using service learning in his mathematics classes.

Geometry's Giant Leap
Alan Brown
A major goal of the project was for the students to use this new technology in studying geometry. Each student group compiled its project report on a computer word processor with appropriate visual examples from the calculator.

Triangular Numbers in Problem Solving
Walter Szetela
A surprising number of mathematics problems have solutions that involve triangular numbers. This article gives some of these problems, as well as many of their interesting extensions. It also suggests other extensions for further investigation.

______ and the Volume of a Cone
Cedric Greive
The first part of this article derives the volume of a right circular cone, and the second part describes a teaching approach that can make this exercise a valuable problem-solving activity for upper secondary students.

A Mathematical Study of the Game Twenty-Four Points
Yixun Shi
A mathematical analysis of the game "twenty-four points". Although the author derived the mathematics in this article, high school students can easily appreciate it.

Maclaurin Taylor Series for Transcendental Functions: A Graphing-Calculator View of Convergence
Marvin Stick
Most calculus students can perform the manipulation necessary for a polynomial approximation of a transcendental function. However, many do not understand the underlying concept. Graphing-calculator technology can be used to bridge this gap between the concept of an interval of convergence for a series and polynomial approximations.