Last summer, I taught a workshop on “Hands-On Geometry”, as part of the Center for Innovative Teaching. It was successful in some respects, but the participants were almost unanimous in letting me know I had not managed to get across the “authentic approach to proof” I had promised in the course description. Part of the problem was that it is not easy to do a workshop on this with a mixed group of high school and middle school teachers, given the vastly different brains of their respective students, and the vastly different backgrounds of the teachers at those levels. (The hands-on activities, on geometric puzzles, pattern blocks, Zome, and the like, do not suffer of this, which is one reason they work well in the classroom.) But the other part of the problem is that the approach is quite nonstandard. It will take me some time and practice to figure out how to best present this material.
In the meantime, I have added a brand-new page on teaching proof to my site, plus two new proofs “without words” (sum of the angles of a triangle, completing the square), and an overview of how proof figures in the Math 2 (geometry) course at my school. The latter includes a key unit (both worksheets and teachers’ guide) where students prove and disprove conjectures they make about quadrilaterals.
(I’ll probably need to edit that page as I get more clarity on this!)
Of course posting new pages led to the addition of a bunch of links here and there on the site.