In his article Simply Symmetric, Michael de Villiers observes that symmetry is a powerful but often overlooked tool for formulating proofs:
Most primary geometry curricula around the world introduce the concept of line symmetry fairly early, and sometimes also that of rotational, translational and glide reflective symmetry. … Continue Reading ››
In a prior blog post, I presented an uncommon method for solving the well-known Burning Tent problem. My solution, modeled on the approach in the Connected Geometry curriculum, used a dynamic ellipse to pinpoint the optimal solution. Now, I'd like to offer a related problem from Connected Geometry where … Continue Reading ››
This post is a follow-up to Sarah Stephens' guest post of a week ago, in which she described a lesson using embodied cognition to help students make sense of the interior angle sum theorem for triangles, not just as an abstract concept, but as a property grounded in their concrete physical experiences.
[This guest post by Sarah Stephens, a senior at Pennsylvania State University, describes a lesson she created as part of her Senior Honors Thesis on leveraging embodied cognition to help students develop abstract mathematical concepts.]
As a soon-to-be classroom mathematics teacher, I have taken special interest in the field of … Continue Reading ››
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped.
In this post, I'll describe a Web Sketchpad activity … Continue Reading ››
This past January, we introduced the Web Sketchpad Tool Library and Viewer. The Tool Library is a collection of over 60 mathematical tools for customizing a Web Sketchpad model, making it possible for teachers to decide which tools students have available to them on an activity-by-activity basis. The Viewer is a site … Continue Reading ››
Geometry tends not to receive much love in elementary curricula, and that's a shame. In this post, I'll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.
On page 1 of the websketch below (and here), begin by asking students to drag … Continue Reading ››
David Henderson, the author of Experiencing Geometry, died this past December. I wrote about David in a prior post, and in particular, his approach of asking us to grapple with a small number of rich problems, allowing us to find our own, often non-traditional, ways of … Continue Reading ››