Math Teaching, #4 out of 6

Hi folks,

I'm 45 years old today.  Taco night with Pru's family at our house.  I suspect they'll bring a cake.  It'll probably be from Rosie's.  Rosie's is waaaay better than all other bakeries in the world.  I'm not exactly sure why.  I wonder what the baking equivalent is of the math teacher question we've been discussing, which is I-We-You versus You-Y'all-We. 

Sean works on schools in Kenya, for Bridge International Academies.  Before that he taught math in NYC and was a star coach at Match Teacher Residency.  MTR gets every trainee to rate every single coaching session, so the result is a database that notices outlier coaches, and Sean was high on that list. 

Sean knows Ryan and Eddie, and he knows Paul's school (Brooke), so I wondered about his opinion on this matter.  He says:

Might be easy to frame my own thinking on a 1-10 scale.  I think you I-We-You has ceiling of 8/10.   Kids plugging away, teacher generating lots of effort.  It's an easy structure for kids to understand. (I pay attention, then we do some together, then I'm on my own, then we regroup).   I also think the floor on a reasonably tight I-We-You is like a 5/10 if you have classroom management tight.

I think the ceiling for the type of instruction Paul describes is 10/10.  The best teachers I've seen do lean more towards the teacher described in Elizabeth Green's NYT Magazine piece. But I think the fundamental misunderstanding about that kind of teaching is that it's "open-ended." It's in fact incredibly structured and tight -- the questions are moving along at just the right pace, inefficient conversations are elegantly re-routed, kids misconceptions are brought out and then corrected.

The floor on these kinds of lessons is like 1/10. Disaster. Kids confused, way too much pressure on working memory, no clear takeaways, random conversations.

A 7/10 classroom -- which is easier to get in I-We-You -- leads to good gains on simpler tests like MCAS.  (That is a meaningful gain, it's a real gain, and it's not easy to accomplish -- just easier.  A typical classroom doesn not even yield these gains). 

However, I think if you have an 7/10 classroom, you won't do as well on the new tests, where the questions are  harder and require a much different kind of thinking. (That may explain why some top charters faced some trouble in NY last year on the next Common Core aligned exams. The Success Charter Network in Harlem (and elsewhere now) is a notable outlier -- and from what I've read, they do a lot more of what Paul Friedmann and NYT Magazine piece describe.)

I asked Sean some follow-up questions. 

Q: I believe I-we-u is helpful for a beginner teacher.  You don't teach a beginner player how to do a reverse layup.  In fact, you might not insist that he use his left hand on left side - because a kid's left hand isn't strong enough to heave ball at basket yet.  Perhaps you don't expect novices to do We-Y'all-You. 


100% agree.  Many teachers I've observed in Rhode Island, New York, takes perhaps 4 years to start moving towards the "Times teacher," though no doubt it varies by teacher.  I'd recommend starting with I-We-You, and then evolving from there.

(Note tomorrow Randall will weigh in on what Match's teacher prep program does).

Q: But in Kenya, the context changes.  I We You is troubling because the "I" always lasts way too long, and because kids just try harder there on the "You."


I agree.  I'd call the Bridge 7th grade setup You-We-You-I. 

It's you (study the worked example independently), we (let's work through a worked example together), you (do a bunch of these on your own while I walk around), I (let me show you how to do the hardest one). 

Constructivist has  high risk -- I struggle to recall even one good lesson that I'd characterize as purely constructivist.  Working memory gets slammed and kids are just unclear on what to do.  I recall watching a classroom with this task: "here's some string and circular objects. Figure out pi by measuring the circumference and diameter for each. Go." It didn't go well. So many places where you can get confused. There needs to be 10-20 questions in between the launch and the desired outcome for that to work.

"Guided discovery" -- what Canada's John Mighton espouses (of JUMP math) -- is very good in capable hands. Where you're walking through kids micro-step by micro-step and allow them to intuit what the next step might be.  It's a scaffold play, always. If you give kids too much, it's overwhelming and they don't where to begin.

But there's also some language here where constructivist versus traditional means different things to different people. 

I'd change the binary to "procedural versus conceptual." And yes -- possible to be excellent leaning towards either, so long as you have some of both.  I think 10/10 "wow" lessons often comes from 60 procedural, 40 conceptual.