The Math Education Blog
Did you know that The Geometer’s Sketchpad is a great tool for creating funhouse mirror pictures? Sure, Sketchpad can reflect, rotate, translate, or dilate a picture, but these operations are rather tame: They transform images uniformly, producing pictures that are easily recognizable versions of the original. By contrast, Sketchpad’s “custom transform” feature allows you to apply non-linear transformations to pictures, resulting in images that...
Welcome back to my ongoing series in which I feature interactive Web Sketchpad models that draw conic sections. Today’s installment, like the previous one, focuses on ellipses, and dates back to the 17th-century Dutch mathematician, Frans van Schooten. Below is an image from van Schooten’s manuscript, Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus (A Treatise on...
I first encountered the kinetic sculptures of Arthur Ganson nearly 20 years ago at the MIT Museum. Ganson is an engineer, artist, and inventor whose machines, when set in motion, display a grace you would not expect from metal, gears, and other industrial objects. Below is a video of one of my favorite Ganson sculptures called...
This will be the first in an occasional series of posts that offer interactive Web Sketchpad models for drawing conic sections. My interest in conic sections dates back to the mid 1990s, when I authored Exploring Conic Sections with The Geometer’s Sketchpad for Key Curriculum Press . You can read more about it in my prior...
Guest blogger Juan Camilo Acevedo is part of the University of Chicago’s Center for Elementary Mathematics and Science Education (CEMSE) digital team, where he develops Sketchpad-based activities for Everyday Mathematics. Currently, he teaches undergraduate language classes at the University of Chicago and is writing his doctoral dissertation on Digital Humanities. Juan holds a BA in...
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 for the early introduction of simultaneous...
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,...
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,...
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...
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....