The 17th-century Dutch mathematician Frans van Schooten developed "hands-on manipulatives" centuries before the term became popular in math education circles. Below are two images of ellipse-drawing linkages from van Schooten's manuscript, Sive de Organica Conicarum Sectionum in Plano Descriptione, Tractatus (A Treatise on Devices for Drawing Conic Sections). Continue Reading ››
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 ››
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. … Continue Reading ››
Dan Anderson commented on my Pentaflake post to observe that the pentaflake can also be created by a random process, sometimes called the Chaos Game. In this game you start with an arbitrary point and dilate it toward a target point that's randomly chosen from some set … Continue Reading ››
The study of multiples and factors is ripe with opportunities to engage students in intriguing mathematical puzzles. In prior posts (When Factoring Gets Personal, and Open the Safe), I've given some examples of what can be done. Now I'd like to introduce you to … Continue Reading ››
A 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 nor Niels had any idea that I'd never even … Continue Reading ››
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. … Continue Reading ››
Nathan Dummitt teaches mathematics and statistics at Columbia Preparatory School in New York, NY. He teaches all four years and is interested in sharing low-threshold, high-ceiling activities with his students. — Guest post by Nathan Dummitt I teach Geometry at a high school in New York City, and I like to start the school year … Continue Reading ››
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