A recent post on the my NCTM discussion group
asked about tools to help students visualize and understand addition and subtraction of integers. I always found this confusing for some of my Algebra 1 students, mainly because they had been told to memorize some rules about whether to add or subtract the two integers and … Continue Reading ››
I was delighted that Daniel recently posted our Binomial Multiplication
sketches in Web Sketchpad format. I thought about those sketches when I noticed a fairly new myNCTM thread on "When and How do we phase out the body in math education?"
This thread raises a very important question for us as … Continue Reading ››
The four Web Sketchpad
activities below from our Dynamic Number project provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.
Dynamic Algebra Tiles, Part One
In the first websketch
, … Continue Reading ››
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 … Continue Reading ››
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 … Continue Reading ››
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 functions
). I got lots of good ideas for improving the activities not only by watching the students, but also but also from their suggestions … Continue Reading ››
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 … Continue Reading ››
For this year’s Pi Day post, I thought I’d continue our Web Sketchpad
(WSP) construction theme. But rather than adapting the visualizations from last year’s Pi Day post
to the new construction capabilities, I decided to take a different approach. Some time ago, I built a set of custom tools … Continue Reading ››
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 … Continue Reading ››
On November 6 I had the honor of being one of the panelists in a Symposium Honoring Zalman Usiskin
, held to honor Zal’s many years of contributions to mathematics education, from his groundbreaking 1971 textbook Geometry: A Transformation Approach (GATA)
to his continuing activities today. My panel was supposed to discuss his work on … Continue Reading ››