*In this guest post, Nate Burchell describes a sketch he uses with his students to explore parametric functions. In this process students work entirely in a graphical world, manipulating graphs directly rather than by way of equations. (Nate teaches in Seoul, Korea, where I enjoyed his family's hospitality when I attended ICME in … Continue Reading ››*

# Category Archives: Advanced Mathematics

*A Funhouse Mirror of Sketchpad Transformations*

*Did you know that The Geometer's Sketchpad is a great tool for creating funhouse mirror pictures? Sure, Sketchpad can reflect, rotate, translate, or dilate a picture, but these operations are rather tame: They transform images uniformly, producing pictures that are easily recognizable versions of the original. By contrast, Sketchpad's "custom transform" feature allows you to apply non-linear transformations … Continue Reading ››*

*Iteration in the Complex Plane*

*The cover story of the April 2014 issue of Mathematics Teacher is on "Iteration in the Complex Plane", by Robin S. O'Dell. It sounds like pretty advanced mathematics, but is surprisingly accessible with*

*The Geometer's Sketchpad.*It's all based on the surprising principle that you can multiply two complex numbers very easily if … Continue Reading ››*Eigenvectors of 2 x 2 Matrices: A Geometric Exploration*

*Shiva Gol Tabaghi obtained her PhD degree in Mathematics Education from Simon Fraser University in 2012. This guest post is based on her doctoral dissertation research. Presently, she is involved in teaching undergraduate mathematics courses at Simon Fraser University. She enjoys using dynamic geometric diagrams to influence students' ways of thinking about mathematical concepts.*If you’ve taken linear algebra, chances … Continue Reading ››*Discovering the Angle Sum and Difference Identities*

*In my Advanced Methods class at Penn’s Graduate School of Education, my students are working in groups to create shared lesson plans using an inquiry approach. For a number of reasons it can be challenging for these pre-service teachers to identify appropriate topics for student inquiry, but sometimes the brainstorming they do turns into something … Continue Reading ››*

*Wait for a Date*

*Consider the following probability question:*

*Two friends arrange for a lunch date between 12:00 and 1:00. A week later, however, neither of them remembers the exact meeting time. As a result, each person arrives at a random time between 12:00 and 1:00 and waits exactly 10 minutes for the other person. When the 10 minutes have passed, … Continue Reading ››*