The Math Education Blog
[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 embodied cognition and integrating it...
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...
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 for students to...
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 point P and...
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 solving them over weeks at a time. In this...
At a recent meeting of mathematics content coaches (many from the organization Reimagined) we investigated the following problem: What is the perimeter of the polygon below? It appears at first that there isn’t enough information to solve the problem. Indeed, the lengths of only three of the polygon’s eight sides are provided. But as the...
In his 1947 book, One, Two, Three…Infinity, physicist George Gamow poses a pirate treasure problem that has since become a classic. Below is my reworded statement of the puzzle. Among a pirate’s belongings you find the following note: The island where I buried my treasure contains a single palm tree. Find the tree. From the...
Below are two maps of the United Sates, with the smaller map a 50 percent scaled copy of the original. The edges of the two maps are parallel. Imagine that the maps are printed out, with one resting on top of the other. Believe it or not, you can stick a pin straight through both...
The picture below on the left shows a right triangle JML with altitude KM. This altitude is defined as the geometric mean of JK and KL. Using similar triangles, you can prove that JK × KL = KM². Another way to think about this construction is shown below on the right. Start with segments JK and...