Category Archives: Educational Technology


How do you make … a pentaflake?

pentflakeA couple of days ago I got an email from my long-time friend Geri, who was spending some quality Sketchpad time with her 12-year-old grandson Niels. Geri emailed me for advice because Neils was having some trouble figuring out how to construct a pentaflake. Neither Geri … 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 ››

The Brouwer Fixed Point Theorem

According to Wikipedia, the Brouwer Fixed Point Theorem, named after mathematician and philosopher Luitzen Brouwer, states that "for any continuous function f mapping a compact convex set into itself, there is a point x0 such that f(x0) = x0. This is a deep theorem,  but one aspect of it is lovely, surprising, and entirely approachable by high-school geometry … Continue Reading ››

Danny’s Ellipse

In the early 1990s, Danny Vizcaino, a high school student at Monte Vista High School in California, wrote to Key Curriculum Press noting that Sketchpad did not come with a tool to draw an oval. Undaunted by this omission, Danny had built his own oval with the software and shared it with Key's editors. As shown in the interactive … Continue Reading ››

Logic Puzzles Made Visual

When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type: Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn't buy an apple or kale.Continue Reading ››

The Flying Squirrel-Frog Puzzle

While I enjoy reading The New York Times for its news coverage, I especially look forward to each Monday when they post a new math puzzle online in their Numberplay column. Several months ago, I shared a Numberplay puzzle from former Key Curriculum editor Dan Bennett. Now I'd like to recap the Numberplay puzzle … Continue Reading ››

From Two Dimensions to One

In my last post, I provided some dilation challenges and linked to a Dilation Function Family activity. In that activity students manipulate independent and dependent variables, observe their relative rate of change, restrict the domain, and use meaningful function notation. This and similar activities involving “technologically embodied geometric functions” … Continue Reading ››