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April 2006, Volume 99, Issue 8


An Engaging Puzzle to Explore Algebraic Generalizations
Tod Shockey, David Bradley
The connection between a novel puzzle and uses of algebra to generalize the fewest moves to solve it. Includes discussion of solutions from the point of view of a math educator, a preservice mathematics teacher, and a research mathematician. Includes suggested assessment activities following investigation activities.

Advice for Solving Equations
Michael Stueben, Shane Torbert
The rich thinking that can go into solving a difficult equation. Includes a discussion of solving difficult equations by inspection, algebraic manipulation, and by substitution. Includes a set of hueristics for solving difficult equations and resources for challenging mathematical equations.

From Classroom Discussions to Group Discourse
Azita Manouchehri, Dennis St. John
The attributes of discourse of a learning community. Article discusses and compares the differences between traditional classroom discussions and discourse within learning communities. Includes a framework for analyzing the discourse of the classroom.

Hands-On Perspective
Marc Frantz, Annalisa Crannell, Dan Maki, Ted Hodgson
The mathematics underlying the construction of perspective images of three-dimensional objects. Discussion of hands-on applications and the use of algebraic reasoning to create perspective art in a way that is accessible to secondary teachers and their students. Includes procedures for drawing a perspective cube.

Hands-On Fractals and the Unexpected in Mathematics
Alan Gluchoff
A hands-on project in which fractal images are produced using a photocopy machine and office supplies. Article discusses how the resulting images are an example of the contraction mapping principle. Includes questions for extension investigations.