Clara:

Dan- could you make more videos like the one with the penny pyramid?

Noted!

As a math coach, I frequently field candid requests for training on the things that you and I take for granted in this activity (class discussion, group work, student conjecture, manipulatives, varying responses, improvisation, etc). Most of us reading this post would take Nicole Paris’ photo and run with it. The vast majority of teachers cannot.

With that said, this post and Bryan’s comment have me thinking how to offer what is best for both students and teachers.

Jeffrey Choppin at University of Rochester has looked into how teachers use the CMP teachers’ editions. It is case study work, though, so it does not pretend to inform us on how widespread the usage he finds is.

One of the important contributions that CMP has made in US math curriculum is a set of teacher materials that go beyond answer keys and teaching tips. It is a curriculum in which the student edition really isn’t enough to get the whole picture.

Do you have a sense of how much teachers took their cues from the student edition vs. the teacher edition?

Dan writes:

My primary question about the CMP version is “how much help should we offer and when?” CMP has answered that question with “lots and right away!”

Yes and no.

It is absolutely the case that the student pages we see here answer that question in that way. Dan is not wrong at all here.

The teacher’s edition talks about this problem in a somewhat different way, though.

You can use a Rubik’s Cube to launch the problem…Also having small unit cubes or sugar cubes around so students can build some of the smaller cubes of length 2, 3, or 4 will be very helpful…

[Ask students] Suppose we paint a cube with edge length of 10 cm and then separate it into 1,000 small centimeter cubes. How many of the small cubes will have paint on three faces [etc.]? (Let students make some conjectures. Some might notice that the cube on a corner will have three faces painted.)

If I were given a stab at writing that TE text today, I would definitely include some language that explicitly asks teachers not to over-organize things for kids, that explicitly encourages teachers to launch the problem without the student edition in front of them.

One of the important contributions that CMP has made in US math curriculum is a set of teacher materials that go beyond answer keys and teaching tips. It is a curriculum in which the student edition really isn’t enough to get the whole picture.

The ongoing tension in every bit of CMP work I have been involved in has been between open and structured. How much structure do teachers need in order to get kids into a place where they notice and work on the important mathematics? Too little structure creates a problem (viz. the basketball game breaking out on the checkerboard in the present discussion). Too much structure creates a problem (this is the premise of the critique here).

I think two questions are in play here:

(1) How much structure/direction do we want the lesson to have in an ideal implementation?

and

(2) How much structure/direction do student materials need to have in order to get as many classrooms as possible as close as possible to this ideal?

These are really difficult questions. They are asked regularly among CMP authors, writers, teachers and professional development folks. I am glad that you are asking them, too, Dan.

That student page deserves the critique you give it. And yet the curriculum’s goals are more nuanced than the student page suggests.

I am sad to report that I am 40 minutes away from my office where my CMP1 books are housed (the image here is from CMP2). Thus I cannot produce for you an image of the CMP1 version of this problem, and I cannot recall whether it had the same structure. It is absolutely the case that publisher and classroom feedback pushed the writing team to make many problems more structured in CMP2 than they had been in CMP1.