NCTM is the forward-thinking younger sibling of NCSM and was, therefore, much more progressive about wireless Internet access.
How to Develop Computational Skills without Drill, During Problem Solving. Jerry Becker.
So Here Are A Few Interesting Problems That Permit Constructive Solutions While Still Assessing Basic Skills
Becker brought out two problems that a) assessed both computation and reasoning and b) scaled all the way from basic counting through limits, which isn't a small trick.
First, arithmogons. Add adjacent circles to get the middle rectangles. Then do it in reverse. Develop a rule for solving them quickly. They scale from easy to algebra at whatever speed your students want.
Second, the Christmas problem, which goes from counting all the way up to limits as you add more and more rows to the pyramid.
The Really Curious Part
The session was remarkable mostly for the one hundred copies Becker made of a 55-page handout he spread across ten chairs. "Take one from each pile," he said as I walked in.
He only used (conservative estimate here) seven of those pages. When he ran out of packets, he promised the remaining attendees he would mail them a copy (as in postal mail) if they left him their addresses. I swear I am not making this up.
Here's an excerpt of an e-mail Becker sent out to the group several days after the conference:
I apologize for running short of the handouts at our session. But I will have the handouts duplicated in the next couple days and then put them in the U.S. Postal Services mail to you – snail mail, so it might take a few days. But I am working on it already. The address labels will be typed up tomorrow.
So I don't know.
It struck me several times throughout both conferences that we need to counter-program a session across from the "Newcomer's Orientation." I'm not talking about "Rolling Your Own Backchannel with Twitter." Scale that back. Way back. Something more like, "How to Make National Presentations a Lot Less of a Chore for Presenters," featuring URL shorteners, Delicious, PDFs, basic FTP. maybe drop.io. You name it.
(BTW: here's a PDF of Becker's handouts.)