One of the most wonderful ways to introduce students in middle school or secondary school to the beauty and excitement of contemporary mathematics is to involve them in the many variations of the “chaos game” which produces such intriguing fractal patterns as the Sierpinski triangle and the Koch curve.
Robert L. Devaney
Susan R. Popelka
Students investigate the geometrical properties used to design reflective safety garments and road signs.
Miriam Gates, Tracy Cordner, Bowen Kerins, Al Cuoco, Eden Badertscher and Gail Burrill
With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.
Lynn Mitzel and Mark Spanier
When it was released in the mid-1980s, Tetris jump-started the video game craze, but many students of the current generation have never even seen this game, much less played it. Now, with the flood of mobile device applications, Tetris has made a comeback, and today's students have a chance to use it, too. We have found Tetris to be an engaging tool for high school geometry students to apply an isometry in context and to learn the composition of isometries. The game allows a player to rotate and translate moving pieces to create full rows anywhere on the screen.
Mika Munakata and Leslie A. Cheteyan
The walls along the walkway leading to Shanghai's Guilin Garden are lined with geometric panels. The following questions refer to the wall panels shown in photographs 1–8. When answering these questions, assume that the patterns continue in all directions.
Robin S. O'Dell
Graphing orbits using linear iteration rules inspires enjoyment and artistry.
Christopher J. Bucher and Michael Todd Edwards
In the introductory geometry courses that we teach, students spend significant time proving geometric results. Students who conclude that angles are congruent because “they look that way” are reminded that visual information fails to provide conclusive mathematical evidence. Likewise, numerous examples suggesting a particular result should be viewed with skepticism. After all, unfore–seen counterexamples render seemingly valid conclusions false. Inductive reasoning, although useful for generating conjectures, does not replace proof as a means of verification.
Ellipses are the focus of photographs and mathematical equations.
My favorite lesson is based on a problem my geometry students encounter. When we study similar triangles, students use indirect measurement to determine the height of an object.
Jonathan Dick and Maria Childrey
With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding.