# Math Teaching, #2 of 6

Hi folks,

1. This week we're examining the I Do/We Do/You Do format of a math class, versus the alternative Elizabeth in her NY Times Magazine article describes as “You, Y’all, We."

Up first, Ryan Holmes and Paul Friedmann.

Both have jaw-dropping results in terms of test-score gains.

Ryan taught several years at Excel Academy (he's now at Match Next).

Paul has taught for many years at Edward Brooke Charter School, and a finalist for the Fishman Prize, and was a frequent commenter on this blog until we ran into some spam issues.  (Working on it!)

Excel and Brooke are among the top charters not just in Boston, but in the nation.

Both Ryan and Paul generally agree with Elizabeth's point.

I'll post a disagreement tomorrow.

2. Ryan writes:

Big Picture: I think the most important thing you can do for students is to get them to think about the problems they approach in a reasonable and logical way.  There are many different ways to get to that end that are both what you call "constructivist" and "traditional".

The problem with traditional "I do, we do, you do" is that it can lead to a place where all you're doing is giving kids steps to solve problems.   You're not asking them to reason through anything.  This is especially true of the "I do" part of the lesson.

For example, if you wanted to talk about adding fractions an "I do" piece of that lesson could be something like teacher says:

Step 1:  First I convert the denominators so they are the same.

Step 2:  Then I add the numerators.

Step 3:  Then I keep the denominator of your sum the same."

But those "I do" steps let the teacher do all of the thinking for the students.  It  leads to a class with pretty poor ratio of student thinking to teacher thinking.  Done frequently enough, it will lead students to  approach every novel problem they see by asking themselves "What are the right steps to follow."

Instead, you want them asking themselves something like:  "What could I do next that makes sense?" or "What might work here"?  Those questions are far more likely to jog their memory later, let's say a month after the lesson, and allow them to solve the problem.

This isn't to say that modeling problem solving with kids isn't effective.  I can't imagine a good math class where you never get up to the board and reason through problems with kids.  But the conversation isn't about which steps to follow.  Good "we do's" involving asking what I (and some Excel teachers) call "metacognitive questions."  Questions that ask the whole class about the thought process they should be going through in order to solve the problem.

"What could we do here that makes sense"?

"Why did you choose to add here"?

Then, from the answers to those questions come steps.  The whole class can have the same set of steps, but every student should at least come close to being able to explain why each step is necessary or "makes sense" in order to solve the problem.  If they can't, then they aren't going to remember the steps a month later.

So if end goal is students thinking, "Constructivist" lessons lend themselves better to a higher ratio from students, but I've seen (err.....I've personally taught) really bad "constuctivist" lessons where the teacher hands out manipulatives and a worksheet with a bunch of questions; kids can't really figure it out (and don't really try); then the teacher goes to the front of the room and proceeds to try and "lead the class through it."  The teacher asks a few questions that try to get the kids thinking, but only 20% of the class raises their hand.  Then the teacher just reveals the answers.

That's just as bad (might be worse) than a "traditional" lesson where kids are just told what steps to follow.

Does it matter which groups of kids you teach?

For example, if you teach in a high-poverty school (traditional or charter), the most typical scenario is the kids are way behind grade level.

Similarly, if you teach the "entry grade" in one of the few hundred USA charters that are excellent, say Grade 6 math teacher in a Grade 6 to 12 school, the kids will arrive way behind grade level....i.e., the upper level teachers are the ones who "inherit" higher performing kids after several years of gains.

In any case: isn't it harder to teach conceptual ideas if kids have immediate and massive skill deficits?  And isn't tackling those issues better done in a non-conceptual format?

Ryan replied:

For the most part, I agree with you.  There's two goals with these kids:

-- Get as many facts (multiplication tables, etc) into their head as quickly as possible.  (Otherwise all the working memory is diverted from "thinking" to being able to follow the problem).

-- Most of them think solving math problems is a series of rule following, and so they always just want to be told what to do.  They are used to the teacher doing all the work.  You need to get them in the habit of thinking for themselves.

3. Meanwhile, Paul writes:

I think Elizabeth's NYTM article has some pretty salient points.

I love the take-down of "I Do, We Do, You Do" as the central teaching technique of American schools.  It's occasionally useful (say, teaching geometric constructions), but it's so inadequate for most areas of math teaching and it demeans learners by assuming they can't bring their prior knowledge to new problems. And it doesn't stick for most learners.

I also think the commentary on the inadequacy of most ed schools, teacher and principals to fix this problem due to lack of training is spot-on.  I went to a well-respected teaching college for my MAT.  The total instruction on math methods was 1/2 a class with an adjunct (a suburban school teacher) who had never taught the class before.

The closing quote:

The teachers I met in Tokyo had changed not just their ideas about math; they also changed their whole conception of what it means to be a teacher. “The term ‘teaching’ came to mean something totally different to me,” a teacher named Hideto Hirayama told me through a translator. It was more sophisticated, more challenging — and more rewarding. “The moment that a child changes, the moment that he understands something, is amazing, and this transition happens right before your eyes,” he said. “It seems like my heart stops every day.”

This is what I love about teaching at Brooke Charter - that we strive for this every single day.  We're certainly not perfect, but this is what we reach for every day.

We acknowledge that teaching is a demanding, intellectual pursuit. We hire teachers who we think can handle that rigor and are interested in the feedback that it requires.  We work to train our teachers to be able to do the work.

On the other hand, what concerns me about Brooke and other charters is that we turn teachers over too quickly and often to make this kind of teaching a reality.  This kind of practical intellectualism takes time to develop.  I think Match, Brooke and other networks can train up teacher to make them decent to solid classroom managers pretty quickly. And I think this is a pre-req to any deeper math teaching and a fast way to strong to excellent test scores.  But to get them really proficient in awesome math teaching takes time to develop.  I watch our teachers who regularly get kick-ass MCAS scores totally botch lessons (on the planning / discussion side of things).  And it's because of lack of experience.  I always hope they stick around to master their craft.

For Paul's thoughts on A Career Path For Every Great Teacher, read here

When we had new 5th graders here (in other words, kids who'd arrive from Boston Public Schools to fill an opening, rather than kids who started at Brooke in kindergarten), we often skipped / rushed through the geometry at the end of the year to go back and make sure the kids all knew their addition facts, number lines, and the like.

Honestly, I think if a kid is coming in to 6th grade not knowing the division algorithm, there are probably more important fish to fry - and ones that involve more conceptual work.

The reason the kid doesn't know the algorithm, in all likelihood, is that it was taught in "I-We-You" and the kid is trying to remember a series of steps in an unending series of steps that is hard to remember and really means little to them.

FWIW, I disagree on the cause of the struggling 5th graders arriving to Brooke.  Boston Public Schools for many years used precisely the sort of constructivist math (TERC) that emphasized conceptual thinking.  And the data shows (and my experience is) that the median kid left elementary school both unable to handle 12*12 and unable to explain what multiplication is.

I think this connects back to what I think is part of Elizabeth's argument: Teaching styles imposed from far away -- without taking into account the strengths/weaknesses/preferences of the teacher, or the training of the teacher, or the culture of school -- are doomed.

4. Here is a great old blog from last year, with rich comments, about math teaching.

Paul's wife Allison, an excellent elementary teacher, describes herself as exactly halfway perched between traditional and constructivist, in terms of teaching "skills" versus "concept." Comments from star math teachers Jen and Sean in there, too.

5. Overall, I'm less convinced about the takedown of I, We, You.

Tomorrow we'll explore that with Eddie Jou, a star young teacher in his own right.

My questions include:

-Can you be an excellent math teacher of either "type" -- predominantly traditional or constructivist?  Just as, for example, you can assuredly be an excellent serve-and-volleyer or an excellent baseliner in tennis.

I.e., if excellence either way is possible, it would suggest that personal preference of the teacher might play a role.  My feeling is: yes.

-Rookie teachers versus experienced teachers.  Most of us agree there are certain "moves" that experts do which, in the hands of novices, go badly.  Might that apply to math teaching?   My belief is: yes.

-To what extent does it matter if your kids are way behind grade level?  For example, if you're a 9th grade algebra teacher at a typical high-poverty American school, your typical kid cannot do fractions, decimals, or percentages....and perhaps struggles with times tables, negative numbers.  My feeling is: it matters a lot in choosing what a typical class looks like.