With this professional development program, teachers work with colleagues and experience a manner of teaching that embeds habits of mind.
Miriam Gates, Tracy Cordner, Bowen Kerins, Al Cuoco, Eden Badertscher, and Gail Burrill
Susan R. Popelka
Students investigate the geometrical properties used to design reflective safety garments and road signs.
Robert L. Devaney
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.
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.
Younhee Lee, Qi Lu, and Woong Lim
Translation by a vector in the coordinate plane is first introduced in precalculus and connects to the basic theory of vector spaces in linear algebra. In this article, we explore the topic of collision detection in which the idea of a translation vector plays a significant role. Because collision detection has various applications in video games, virtual simulations, and robotics (Garcia-Alonso, Serrano, and Flaquer 1994; Rodrigue 2012), using it as a motivator in the study of translation vectors can be helpful. For example, students might be interested in the question, “How does the computer recognize when a player's character gets hit by a fireball?” Computer science provides a rich context for real-life applications of mathematics-programmers use mathematics for coding an algorithm in which the computer recognizes two objects nearing each other or colliding. The Minkowski difference, named after the nineteenth century German mathematician Hermann Minkowski, is used to solve collision detection problems (Ericson 2004). Applying the Minkowski difference to collision detection is based on translation vectors, and programmers use the algorithm as a method for detecting collision in video games.
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.
Ellipses are the focus of photographs and mathematical equations.
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.