The Math Education Blog
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...
News alert! Scott and I wrote the cover story, Connecting Functions in Geometry and Algebra, in this month’s Mathematics Teacher. You can read the article in print, but better yet, go to the free online version. This is the first time Mathematics Teacher has incorporated live dynamic-mathematics figures into its online offerings, allowing readers to manipulate the mathematical objects in...
For the past few years, Scott Steketee and I have collaborated with the author team of Everyday Mathematics to integrate Web Sketchpad deeply into their curriculum. As part of that work, I just completed a websketch that nicely mixes practice with logical reasoning. Students are challenged to find a hidden treasure on the coordinate plane by...
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...
Can mathematical curves be beautiful? Most certainly! Precalculus students glimpse the connection between mathematics and art when they graph roses, cardioids, limaçons, and lemniscates. But these curves give just a taste of the beauty that can be achieved when graphing equations. In a recent article from the online science magazine Quanta, Pradeep Mutalik reviews a gorgeous new math book, Creating Symmetry:...