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
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.
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
Hands-On Fractals and the Unexpected in Mathematics
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.