But certain tools are actually more than tools, and provide rich environments for exploration and learning, once known as microworlds. The microworld concept originated in the Logo movement in the 1980s. Logo was a programming environment where children could explore programming and geometry, but it was also a place for teachers to do interesting math and create lessons for their students. A microworld is accessible ("low threshold"), but at the same time it offers near-limitless possibilities ("high ceiling".) Contemporary descendants of Logo include MIT's Scratch and UC Berkeley's Snap. Interactive geometry (GeoGebra, for example) is another type of microworld.
I maintain that the geoboard, as well, is more than a learning tool: it is a microworld. Yes, it can be used for excellent lessons on slope, area, distance, the Pythagorean theorem, and simplifying radicals (as you can see in my Geometry Labs.) But it is also a wonderful arena for mathematical explorations, including some fun puzzles and some unsolved problems. I will focus on such teacher-level questions as I co-lead a workshop on
Connecting the DotsMy co-presenter will be Paul Zeitz, of the University of San Francisco, the co-founder of Proof School, the Bay Area Math Olympiad, and the SF MTC.
Saturday, March 4
San Francisco Math Teachers Circle.
Proof School, 555 Post St.
Free. (Lunch included.)
And yes, most of the questions we will explore can be adapted for use in the classroom.