All posts by Daniel Scher

Daniel Scher, Ph.D., is a senior digital strategist at McGraw-Hill Education. He worked as a senior scientist at KCP Technologies, co-directing the NSF-funded Dynamic Number project.

A Funhouse Mirror of Sketchpad Transformations

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 … Continue Reading ››

Playing with Triangular Decompositions

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 … Continue Reading ››

Simultaneous Equations in Elementary School? You Bet!

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 … Continue Reading ››

Eigenvectors of 2 x 2 Matrices: A Geometric Exploration

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 Puzzles

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 ››

Factor Patterns at Your Fingertips

Take a look at the interactive model below. 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. You'll see that … Continue Reading ››