http://mathdemos.gcsu.edu/mathdemos/domainrange/domain_range_piecewise.html

Also, sometimes it helps them to visualize the zero as a big ball and the fraction line as a tabletop. It’s possible to balance a ball on a tabletop, so it’s possible to put zero above the fraction line. But it’s not possible to balance a tabletop on top of a ball, so you can’t put a zero below the fraction line. It’s kind of weird, but it works!

Basically, Dr. Susan Wagner Cook divided 3rd and 4th graders into three groups and taught them how to solve equivalence problems. One group was taught a phrase to say out loud, another group was taught a gesture, and the third group was taught a phrase and a gesture.

4 weeks later, the kids got a pop quiz on equivalence problems. Only 10% of the students who learned the phrase remembered how to do the problems. But 90% of those who learned the gesture remembered how to do the problems– even though it had been a whole month!

I wonder if that’s part of why “pop it out” is so effective — because of your “raise the roof” gesture.

I think now that we math educators know how powerful gestures are in helping students remember things, we can come up with all kinds of awesome new ways of doing that!

By the way, I’ve been a fan of your blog for a few months now, and I’m currently a first year Algebra 2 teacher in Philadelphia through the Teach for America program. I only recently figured out, however, that you teach at Packer, where I graduated from in 2005! (Those SMARTboards and SFJC stuff did sound awfully familiar.) If you get a chance, do say hi to Ms. Danforth (my 7th grade math teacher!) and some of the administration (Feibelman, Genaro, etc.) who’ve been around for a while for me, and maybe I’ll get to meet you at my 5 year reunion (yikes…) next May.