"De-tracking" Versus Mastery: Is This Our Dirtiest Little Secret...?

There has been so much heat and noise (and not very much light) on all sides of the so-called "de-tracking" debate, it has made me want to raise a question I have been thinking a lot about:

What is the difference between "tracking" (i.e., ability grouping, as in "high-," medium," or "low") and an SBG-style measure of mastery?

I ask because as someone who thinks about classroom instruction in a deeply Vygotskian way, I value the Zone of Proximal Development (ZPD) above almost all else in figuring out how to ensure that all my students receive meaningfully differentiated instruction.

But if there IS no reasonably common ZPD, there's no way I can see to differentiate — apart from simply allowing everybody to work at their own pace... in which case, what good am I in the room?

How do you make sense of this distinction?

NCTM 2016 — Talk Moves and Talk Structures for MP 3 (introducing and using Talking Points)

All the files for my session are available for download at this folder:          

https://goo.gl/I1O2R4

Volume of a Pyramid: Proof by Play-Doh

This is the best idea I never had.

My colleague, Tom Chan, asked me in the Math Office this morning, "Where are you guys at?"

I told him, "We're on volume of a pyramid."

"Me too!" He's usually a pretty cool cucumber, so this caught me by surprise. He said, "We're doing proof of the volume formula by Play-Doh. Wait here a minute."

He dashed out and came back within a minute with a fist-sized cube made of three different colors of Play-Doh.

"Each table gets three little tubs (so three colors) and they have to make three identical pyramids that fit together into a cube. Then they can move on and do the next piece."

I was dumbfounded. The best I'd been able to do for today was to produce tiny, helpful diagram handouts to fit into our INBs.

But I'm bookmarking this for myself for next year by blogging it, and by giving full credit.