Math Teaching, Pi out of 6

Max Tuefferd, teacher coach, writes:

I think that Paul is probably hitting the nail on the head by suggesting that students (especially those who receive less outside/parental support on their studies) are served best when we do not focus on ONE method of instruction. While constructivist approaches do seem harder to pull off well than the traditional method, it seems as though it can lead to a much deeper understanding of math. I have seen teachers attempt this and succeed and fail.

The successes seems to happen when the teacher has a masterful grasp on management and their own deep understanding of the concepts they are teaching, which, sadly, many do not have.

Can a rookie teacher pull that off? Why not? If it is harder, then it means we raise our expectations for teachers, or provide a means of supporting fledgling teachers to build their skills until they can pull it off without that support.

I often think about this: how would I want my own children to be taught? On the surface (and I may be stepping into controversial territory by saying this), many suburban parents might choose the constructivist method, and perhaps many parents in urban settings would see the value in the results achieved by the traditional approach. So at the end of the day, the question I really need to ask is what does my child need? And that may be different than what I want. So I think I would want teachers who can do both, so that my children can access whatever works for them.

I hear you Max.  My impression: suburban parents often react pretty strongly against the "new math" -- the conceptual stuff -- as well.  Also, rarely does a teacher have the luxury to say "What does one child need?"  It's typically: I've got 15 to 35 kids (or....50, 60, 70, 80 in developing world!).  I need to either start class by explaining an idea myself, or by setting kids loose to do it themselves.  Which works with this "whole room?" 

Next up, Ryan Kelly, a star school leader and former math teacher: 

It’s worth thinking not only about content, but also process – what skills and habits do our students need to be successful mathematicians now and in the future?

What I appreciate about a constructivist approach is not only that it builds stronger connections and deeper understanding, but that it also gives students regular opportunities to attempt a problem they haven’t seen before, struggle with a problem, consider multiple approaches, look for patterns, articulate their reasoning, critique the reasoning of others, etc.

These “process” skills are nicely articulated in the Common Core’s Standards for Mathematical Practice. I totally agree with Paul that a lot of the standardized test success seen from I, We, You is going to be significantly dampened by PARCC, which is a better assessment and requires deeper conceptual understanding. A constructivist approach is going to help students on PARCC (and future math classes, and life) beyond just content understanding by making sure that they can solve problems flexibly and apply concepts to situations that they haven’t seen before.

The other thing I’ll add is that the best I-We-You teachers I’ve seen are incorporating elements of a constructivist model, anyway – pushing students to make and articulate mathematical connections, guiding the “I” portion with a series of pieces that make connections and build toward the day’s key understanding, giving students opportunity to think and do during the “I” so it’s not just the teacher doing the work.

Ryan, you just stole a little of my thunder.  More on Common Core -- and how it may be stalling with traditional schools, but is generating GIANT changes in No Excuses charters, more change in math and English teaching in last 2 years than I'd seen from 1997 to 2012 -- coming in a future blog. 

Sara Schnitzer, a former star teacher, fellow alum of the Kennedy School of Gov't, and now at the MA Department of Education, writes:

As the fiancee of one of your interviewees (Ryan, a lucky man) and the former math department colleague of the other (that would be Paul if you're scoring at home), I feel compelled to comment!

Y/Y/W has more upfront costs but greater long-term benefits. 

When I read the NYT article, the phrase "you, y'all we" stuck out to me as the codification of a process that I think works really well in a math classroom. It is a natural pattern of sense-making that builds deep and long-term understanding (and as Ryan Kelly noted above, builds other important skills like perseverance, explaining thinking, and critiquing ideas, which are much harder to implement in an I, We, You classroom).

As Ryan notes, teaching a good constructivist lesson is not easy, which is why I don't believe that the Common Core mandate alone will lead to a shift in math instruction, although I wish it would. In order to succeed with You Y'all We, teachers need to know how to construct a task with multiple entry points that allows students to access prior knowledge but also struggle sufficiently. As Paul can attest, we spent a lot of our planning time trying to build or find excellent tasks/problems at Brooke. Teachers must also manage a discussion of student work in the "you" phase, which requires that the teacher understand multiple approaches to solving the problems as well as common errors.

During the entire lesson cycle, teachers also have to "be less helpful" which is really hard to do especially if you were trained in an I, We, You background. Can rookie teachers do this (constructivist math) well? I'm not sure how many teacher prep programs/charter schools have really tried to train newbies in this skill, and I did not start to teach this way until my 3rd year in the classroom. But I'd like to think it's possible (and to Mike's point on personal preference, most teachers I've known who make the transition think that You Y'all We is a more fun way to teach because it is different every time and students engagement tends to be higher).

I'd be interested to see a training program that explicitly taught the skills necessary to pull off a constructivist lesson to determine, is it that rookie teachers aren't capable of this, or just that they often aren't taught to do it this way because it's more complex?

Re: students who are far behind, when I taught 5th grade at Brooke to kids coming from BPS, we drilled them on facts. If you don't have facts, you can't do much. The rest of the gaps in knowledge we filled in conceptually. The extra investment of time on place value, conceptual understanding of fractions etc. paid off so many times down the road: when all the students knew that you couldn't add fractions with unlike denominators because the pieces aren't the same size, when they derived the algorithm for multiplying decimals on their own in 6th grade because of their prior knowledge etc. etc. etc. My opinion is that the conceptual route is totally worth it over the arc of a kid's math life because the canon of math builds so much on itself.

Good stuff; always like seeing math content on this blog.

Good stuff from all 3 of you -- thank you!