All posts by Daniel Scher

Daniel Scher, Ph.D., is a senior scientist at KCP Technologies. He co-directed the NSF-funded Dynamic Number project (http://dynamicnumber.org). He has developed Sketchpad activities across the entire mathematics curriculum, from elementary school through college. He received his Ph.D. in Mathematics Education at New York University.

Can Computer-Based Assessment Model Worthwhile Mathematics?

Several weeks ago, Dan Meyer described his experience of completing 88 practice sets in Khan Academy's eighth-grade online mathematics course. His goal was to document the types of evidence the Khan Academy asked students to produce of their mathematical understanding. Dan's findings were disappointing: He concludes that 74% of the Khan Academy's eighth-grade questions were either multiple choice or required nothing more than … Continue Reading ››

Exploring Factor Rainbows

This week, I'm going to describe one of my favorite activities for introducing young learners to multiplication and factors. It comes from  Nathalie Sinclair, a professor of mathematics education at Simon Fraser University. In the interactive Web Sketchpad model below, press Jump Along to watch the bunny take 2 jumps of 4 … Continue Reading ››

Refutation in a Dynamic Geometry Context

Michael de Villiers teaches courses in mathematics and mathematics education at University of KwaZulu-Natal in South Africa. His website features a wealth of Dynamic Geometry-related books, articles, and sketches. He is the author of the Sketchpad activity module Rethinking Proof with The Geometer's Sketchpad. This blog … Continue Reading ››

A Quartet of Ellipse Constructions

It's the season for NCTM regional conferences, and I'm presenting sessions on conic section construction techniques in both Richmond and Houston this month. For those of you who can't attend, here's a peek at what I'm demonstrating. The 17th-century Dutch mathematician Frans van Schooten developed "hands-on manipulatives" centuries before the term became popular in math education circles. Below … Continue Reading ››

Isosceles Triangle Puzzles

As readers of this blog can probably tell, I like puzzles. I especially enjoy taking ordinary mathematical topics that might not seem puzzle worthy and finding ways to inject some challenge, excitement, and mystery into them. This week, I set my sights on isosceles triangles. It's common to encounter isosceles triangles as supporting players in geometric proofs, but … Continue Reading ››

Dancing Unknowns: You Haven’t Seen Simultaneous Equations Like These!

When it comes to simultaneous equations, I like to push the bounds of conventional pedagogical wisdom. In an earlier post, I offered a puzzle in which elementary-age students solve for four unknowns given eight equations. Now, I'd like to present a puzzle that might sound even more audacious: Solving for ten unknowns. Oh, and … Continue Reading ››

The Dynamic Ebbinghaus Illusion

We've all seen amazing examples of illusions, but did you know that there is a fertile community of researchers creating new ones? The Best Illusion of the Year contest and website provide a showcase for celebrating illusions. This year's winner for best illusion was created by Christopher D. Blair, Gideon P. Caplovitz, and … Continue Reading ››