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February 2009, Volume 102, Issue 6

FEATURES

Sacred Cows Make the Best Hamburger
Rita Barger, Ann McCoy
A description of the authors’ attempts to make a college mathematics class more hands-on and interactive. The authors challenge other college mathematics instructors to try similar approaches to enhance the learning and understanding of their students.

Examining Cylindrical Dice
Dustin L. Jones
An activity where prospective mathematics teachers made hypotheses about the dimensions of a fair cylindrical die and conducted experiments with different cylinders. He also provides a model that estimates the probability that a cylinder would land on the lateral surface, depending on the height and diameter of the cylinder.

Playing with Dominos: Proof by Induction
Gail Kaplan
A hands-on approach to learning proofs by induction. Students create patterns of dominos so that when the first domino is pushed, the entire design collapses, one domino at a time. Students then build designs that do not work. By constructing a list of conditions that ensure a given pattern will collapse, students discover the basis for proofs by induction. A discovery worksheet leads students through mathematical examples.

Exploring and Writing Geometry
Cathleen Sanders
When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject.

Mathematics Skills and NAEP Results over a Generation
Zachary Rutledge, Peter Kloosterman, Patricia Kenney
The performance of seventeen-year-olds on the Long-Term Trend program of the National Assessment of Educational Progress. The analysis focuses on a selection of questions from the assessment on which performance has changed significantly between 1982 and 2004.