The Math Education Blog
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 another puzzle of mine called Mystery Number that focuses on multiples. Here’s how the Web Sketchpad...
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 Ryan E.B. Mruczek from the University of Nevada,...
From 2009 to 2013, I had the pleasure of working with the elementary teachers at the School for Discovery and Exploration in Brooklyn, New York as they field tested Sketchpad materials for the Dynamic Number project. Although the project has ended, I still keep in touch with a few of the teachers, and they continue to...
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...
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...
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...
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...
There are certain topics in mathematics education not appropriate for polite discussion. Number bases other than 10 fit this category well, perhaps because of their association with the maligned “new math” of the 1960s. That’s a shame because there is a lot to learn from them, especially when presented as interactive puzzles. Below (and here) are...
In my prior post, I presented an interactive Web Sketchpad odometer that is a great tool for introducing young learners to place value. Well, technology moves fast these days, and the latest odometers are more powerful than ever. While our prior odometer featured ‘+’ buttons above each digit, our newest innovation in number-tracking technology features ‘+’ and (gasp!) ‘–’...
Below (and here) is an interactive odometer built with Web Sketchpad. Press each of the ‘+’ keys and observe their effect on the odometer’s value. Also notice how your button presses are tracked in the table below the odometer. I built this model as a way to support students’ development of place-value concepts. Here are...