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...
Angles are a thorny concept to teach because of the fundamentally different ways in which they can be used and understood. In the article What’s Your Angle on Angles?, the authors divide the concept of angle into three main groups: angle-as-figure, angle-as-wedge, and angle-as-turn. In the Web Sketchpad game below (and here), we focus on angle-as-turn. Given an angle, students...
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...
In my recent posts, I’ve introduced interactive models for comparing fractions and multiplying fractions. To continue the fraction theme, below (and here) is a Web Sketchpad model in which the need for equivalent fractions arises naturally through the rules of a game. The model displays two arrays. Dragging the four points changes the arrays’ dimensions. The goal is to drag blue squares into the...
Below is a complete list of all the interactive elementary-themed activities we’ve offered on our Sine of the Times blog. Most of these activities grew out of the work that we did during our NSF-funded Dynamic Number project. The list includes links to our original blog posts as well as links, in brackets, that take...
In my previous post, I presented an interactive Web Sketchpad model for visualizing and solving fraction multiplication problems. This week, I’d like to back up a step and focus on the more fundamental skill of visualizing and reasoning about the size of fractions. The fraction game below (and here) presents two random fractions at a time and challenges...
Last week, Scott and I attended a fraction symposium at NYU, and it made me realize how long it’s been since I’ve written about our Sketchpad work with fractions. Below is a Web Sketchpad model for displaying and solving fraction multiplication problems. Representing fraction multiplication with an area model is a common approach, but it’s challenging to sort...
Metamorphosis is a New York-based company that offers professional content coaching to transform the mindset and practice of both teachers and administrators. I recently had the pleasure to collaborate with Metamorphosis staff members Toni Cameron and Kara Levin as well as mathematics coach Ariel Dlugasch from P.S. 276 in a coaching learning community that brought...