"There is no one way"

Sunday, February 26, 2017

Free workshop: Connecting the Dots

Regular visitors to this blog probably know about my interest in a tool-rich pedagogy.  I have developed much curriculum based on manipulative and technological tools, as well as some pencil-paper tools such as function diagrams and the ten-centimeter circle. Typically, the purpose of learning tools is to make mathematical concepts more accessible and more interesting to students.

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 Dots
Saturday, March 4 
San Francisco Math Teachers Circle.
Proof School, 555 Post St.
Free. (Lunch included.)
RSVP here.
My 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.

And yes, most of the questions we will explore can be adapted for use in the classroom.