The Math Education Blog
The title of this post is a nod to the Sketchpad activity module Pythagoras Plugged In by Dan Bennett. Dan’s book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more: The Pythagorean Proposition, published in 1928 by Elisha Scott Loomis, contains over 350 proofs, 255 of which are geometric. Wow! I revisited the Pythagorean...
I began this post on Friday night in Hamburg Germany, near the end of ICME, the quadrennial international math-education conference that’s been both exhilarating and exhausting. I’m now finishing it on the airplane headed back home. As interesting as many of the presentations have been, they’ve also been almost entirely lecture format with Q&A at...
I’m currently attending the 13th International Congress on Mathematics Education (ICME) in Hamburg, Germany, with well over 1000 math educators from around the world. Professor Gabriele Kaiser opened the conference with a statement of solidarity with Turkish mathematics teachers and researchers who at the last minute were unable to attend due to newly imposed government...
Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the article* where I found...
Four years ago, my colleague Scott Steketee and I set out to develop an interactive game to help students develop strategies for thinking about and solving multiplication problems. As we examined the existing apps on the market, we discovered that most focused on the drill aspect of learning one’s multiplication facts. We set our goals higher. We...
The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points...
March 2023 UPDATE: If the dilation games below whet your appetite for challenges based on transformations, check out these Reflection and Rotation games as well. What does dilation feel like? I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what I call geometric...
One of the aspects I like best about Dynamic Geometry software like Web Sketchpad is its ability to illustrate concepts that cannot effectively be represented with static media. Take, for example, a number line that we draw on a white board. Showing the number line labeled with integers is easy. Adding tenth-mark divisions to the...
With Web Sketchpad, it’s easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics. My goal was to design a lesson focusing on the triangle area formula, A = bh/2. In particular,...
Dan Meyer has posted a number of “What Can You Do With This?” activities on his blog. (Activities is probably too prescriptive a word; they’re more in the nature of prompts for student thinking, noticing, and wondering.) One of the first was the image below, which he made by superimposing frames from a video camera....