# The Polar-Cartesian Connection

The Web Sketchpad model below (and here) shows the function f(θ) = 1 – cos 2θ in both Cartesian and polar form. For each graph, the independent variable appears as a red bar that corresponds to a particular value of x (for Cartesian) or θ (for polar). The red bar has … Continue Reading ››

# The Cowgirl Problem

In a previous post, I described two different approaches to solving the Burning Tent optimization problem. Now I'd like to offer a related problem that I assigned many years ago to my pre-service mathematics teachers at New York University.

A cowgirl wants to give her horse some food and … Continue Reading ››

# A Follow-Up to the Interior Angle Sum

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.

# The Interior Angle Sum: An Embodied Investigation

[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 ››

# Race to the Burning Tent

How can you identify a lover of math? Casually mention a burning tent and notice if her first thought is how to minimize her path to a river and then to the tent to douse the flames. Here is a full statement of this classic geometry problem:

Ah, the great … Continue Reading ››

# Pirate Treasure Awaits

In a 2018 blog post, I presented George Gamow's pirate treasure problem, which can neatly be solved by capitalizing on the geometry of complex numbers. There's more treasure to be had, however, so get ready for another adventure!

An island contains a giant boulder, a lighthouse, a cave, and a jail. Among … Continue Reading ››