Daniel Scher, Ph.D., is a senior academic designer at McGraw-Hill Education. He has co-directed two NSF-funded projects: the Dynamic Number project and the Forging Connections project.
Algebra classes devote considerable time to equations in a single variable before solving multiple equations in two or more unknowns. But just because elementary-age students are not familiar with algebraic symbolism doesn't mean they can't solve simultaneous equations, too! The mathematician and educator W. W. Sawyer makes a compelling argument … Continue Reading ››
Shiva Gol Tabaghi obtained her PhD degree in Mathematics Education from Simon Fraser University in 2012. This guest post is based on her doctoral dissertation research. Presently, she is involved in teaching undergraduate mathematics courses at Simon Fraser University. She enjoys using dynamic geometric diagrams to influence students' ways of thinking about mathematical concepts. If you’ve taken linear algebra, chances … Continue Reading ››
Arranging Addends is an interactive puzzle that I designed on a long bus ride through Alaska. The goal of the puzzle is to arrange the circles and the six numbers (1, 2, 4, 8, 16, and 32) so that three conditions are met simultaneously: The sum of the numbers in the green circle is 21, … Continue Reading ››
In the 1970s, my childhood friend Tim owned an Activision console and a variety of game cartridges. Tim was the envy of our block, but no matter how much I enjoyed a rousing game of Pong, I knew that my electronic toy was even better. No, I didn't own the rival Atari game system: I … Continue Reading ››
Take a look at the interactive model below (and here). Most of the numbers in the array are shaded orange, but several are blue. What is special about these blue values? They are the factors of 32, the largest number in the array. Try dragging the red point to change the dimensions of the array. … Continue Reading ››
Take a look at the two groups of shapes below. Both groups contain an equilateral triangle and a square. Now imagine that you showed students each group and asked them to identify the shapes. Do you think students would do equally well in naming the shapes in group A and group B? Continue Reading ››
Consider the following probability question: Two friends arrange for a lunch date between 12:00 and 1:00. A week later, however, neither of them remembers the exact meeting time. As a result, each person arrives at a random time between 12:00 and 1:00 and waits exactly 10 minutes for the other person. When the 10 minutes have passed, … Continue Reading ››
A little over a year ago, the Museum of Mathematics opened in the heart of New York City. One of my favorite exhibits at the museum is the Human Tree. When you stand in front of the Human Tree screen and wave, your arms are replaced by images of … Continue Reading ››
Yesterday, I led a webinar that demonstrated how Sketchpad and Web Sketchpad can be a powerful tools for exploring Common Core algebra topics. My examples included solving for unknowns with a pan balance, exploring the slopes of lines, maximizing the area of a fixed-perimeter rectangle, and graphing trigonometric functions. I touched only briefly on each example during the … Continue Reading ››
Today's guest post is from Marta Venturini, a PhD student in Mathematics Education at Simon Fraser University under a "Cotutelle Agreement" with the University of Bologna, where she's a PhD student in Mathematics. While looking for some tasks that would be suitable for Sketchpad, I found the “dog leash” problem in a March 2007 Continue Reading ››
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