First, the usual description of “traditional unproductive.” Why, why is the “traditional” way of doing things always deemed “unproductive”? It’s incredibly unscientific to start that way. Can we not learn from the Evil Traditional Way?
The slide itself just called ’em unproductive vs. productive… first unproductive one being “Students can learn to apply mathematics only after they have mastered the basic skills.” Well, we’ll see.
…. I’ve seen, and I really like. They left half an hour or so for questions… and there’s a real emphasis on building the basics and directly teaching how to think about math. Now, all of it was attacking problems at GED level — but there was even mention that something could be used with basic numeracy as well as GED level, so they aren’t of that group who can’t fathom anything below “GED.”
An answer to a question included introducing algebra by giving groups of students a jigsaw puzzle with a piece missing, and recognizing that they could put the puzzle together even without all the pieces, and that variables in algebra were those “missing pieces,” and that you could figure out all kinds of things about it from pieces you had.
I’ll be back for those folks. (Now, I’m not saying I like the GED test… just that I liked what these folks were saying about math…)