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March 2000, Volume 93, Issue 3

FEATURES

Liquid Assets: Increasing Students' Mathematical Capital
Mary Winter, Ronald Carlson
Laboratory-type activities are one way to involve students in collecting data. The laboratory experiment in such a setting includes collecting meaningful data, guided mathematical analysis, and interesting extensions. Moreover, the agreement of the analysis and the actual data give valuable feedback to the student.

Functioning in a World of Motion
Juli Dixon, Cynthia Glickman, Terri Wright, Michelle Nimer
A graduate class on methods of teaching secondary mathematics set out to investigate the roller-coaster questions so that its members could make forming and testing conjectures about the measurement of motion interesting and accessible to students. The goal was to give these teachers the know-how to offer secondary school students opportunities to model real-world phenomena through a variety of functions and to construct and draw inferences from tables and graphs that summarize data from these situations.

The Prisoner Problem-a Generalization
Gerald Gannon, Mario Martelli
The "prisoner problem" is a good example of a problem that most students enjoy thinking about and solving. We recommend this problem as a way to emphasize to students the final step in a problem solver's tool kit—considering possible generalizations when a particular problem has been solved.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student
Greg Fiore
The theory of relativity and some of the developmental mathematics involved. It furnishes motivational classroom material to use when discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations.

Bingo Games: Turning Student Intuitions into Investigations in Probability and Number Sense
Jennifer Bay, Roberts Reys, Ken Simms, P. Taylor
The large-number activities with the bingo card serve as a springboard to a host of mathematical topics, including volume, measurement, ratios, and rates. If you or a colleague have been looking for an exciting investigation full of meaningful mathematics, we hope that you can say, "Bingo! We found it"!

Getting to the Root of the Problem
Peter Vanden Bosch
A root-approximation method using fixed points: it converges quickly for most functions, and it works even on discontinuous functions and functions of several variables. More important for the classroom, it can be used to illustrate a number of important concepts and is a natural lead-in to chaos theory and fractal geometry.

Using The Geometer's Sketchpad to Visualize Maximum-Volume Problems
David Purdy
Using this featured sketch and others like it, whether constructed by the teacher or by the student, can clearly aid in visualizing maxima in volume problems. Students gain practice in, and motivation for, such skills as polynomial multiplication. They see strong connections among technology, algebra, and geometry.

The Coefficient of Determination: Understanding r squared and R squared
Gloria Barrett
Fitting least-squares lines to bivariate data is a topic traditionally discussed in introductory statistics courses, often in a unit of study that includes correlation. Recently, because calculators that graph bivariate data sets and compute regression equations have become widely available, this topic has also been included in many algebra and precalculus courses.

The Test of Time
Rick Norwood
We have at least three reasons for trusting mathematics, three reasons to believe that mathematics gives answers more reliable than many a pronouncement of pundit and sage. This article considers each in turn.