Deborah Ball and Lucy West are F*cking Masters

I recently saw some video from Deborah Ball’s Elementary Mathematics Laboratory. I actually didn’t know what she looked like so I didn’t find out till afterward that the teacher in the video was, y’know, THE Deborah Ball, but already from watching, I was thinking,

THAT IS A F*CKING MASTER. I F*CKING LOVE HER.

It put me in mind of a professional development workshop I attended 2 years ago which was run by Lucy West. Both Ball and West displayed a level of adeptness at getting students to engage with one another’s reasoning that blew me away.

One trick both of them used was to consistently ask students to summarize one another’s train of thought. This set up a classroom norm that you are expected to follow and be able to recapitulate the last thoughts that were said, no matter who they are coming from. Both Ball and West explicitly articulated this norm as well as implicitly backing it up by asking students (or in West’s case, teachers in a professional development setting) to do it all the time. In both cases, the effect was immediate and powerful: everybody was paying attention to everybody else.

The benefit wasn’t just from a management standpoint. There’s something both very democratic and very mathematically sound about this. In the first place, it says that everybody’s thoughts matter. In the second, it says that reasoning is the heart of what we’re doing here.

I resolve to start employing this technique whenever I have classroom opportunities. I know that it’ll come out choppy at first, but I’ve seen the payoff and it’s worth it.

A nuance of the technique is to distinguish summarizing from evaluating. In the Ball video, the first student to summarize what another student said also wanted to say why he thought it was wrong; Ball intercepted this and kept him focused on articulating the reasoning, saving the evaluation step until after the original train of thought had been clearly explicated. Which brings me to a second beautiful thing she did.

Here was the problem:

What fraction of the big rectangle is blue?
What fraction of the big rectangle is blue?

The first student to speak argued that the blue triangle represents half because there are two equal wholes in the little rectangle at the top right.

He is, of course, wrong.

On the other hand, he is also, of course, onto something.

It was with breathtaking deftness that Deborah Ball proceeded to facilitate a conversation that both

(a) clearly acknowledged the sound reasoning behind his answer

and

(b) clarified that he missed something key.

It went something like this. I’m reconstructing this from memory so of course it’s wrong in the details, but in overall outline this is what happened –

Ball: Who can summarize what [Kid A] said?

Kid B: He said it’s half, but he’s just looking at the, he’s just…

Ball: It’s not time to say what you think of his reasoning yet, first we have to understand what he said.

Kid B: Oh.

Kid C: He’s saying that the little rectangle has 2 equal parts and the blue is one of them.

Ball [to Kid A]: Is that what you’re saying?

Kid A: Yeah.

Ball: So, what was the whole you were looking at?

Kid A [points to the smaller rectangle in the upper right hand corner]

Ball: And what were the two parts?

Kid A [points to the blue triangle and its complement in the smaller rectangle]

Ball: And are they equal?

Kid A: Yes.

Ball [to the rest of the class]: So if this is the whole [pointing at the smaller rectangle Kid A highlighted], is he right that it’s 1/2?

Many students: Yes.

Ball: The question was asking something a little different from that. Who can say what the whole in the question was?

Kid D [comes to the board and outlines the large rectangle with her finger]

Kid A: Oh.

I loved this. This is how you do it! Right reasoning has been brought to the fore, wrong reasoning has been brought to the fore, nobody feels dumb, and the class stays focused on trying to understand, which is what matters anyway.

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11 thoughts on “Deborah Ball and Lucy West are F*cking Masters

  1. Yes. (Or maybe ‘yes!’)

    I read a post about something similar last night (can’t find it to show you, unfortunately). Before I even got to your resolution, I added a line in my ‘first day’ files to remind me to do this. I think it would be hard to do mid-semester. I hope my efforts are comfortable enough that I’ll bring this practice in permanently.

  2. Our school was labeled a “failing school” 4 years ago and we started through a process which included watching D Ball’s and D Meyer videos and asking us to see what we could do to modify our teaching. The problem we had was the Ball videos all included little, little kids (not high schoolers). And we watched the same video of her’s about 5 times over the course of 6 months.

    Questioning was the major area I tackled that first year and it is a powerful means of modifying the classroom climate and student learning.

    Thank you for reminding me.

  3. If you insist on continuing to use explicatives in your posts, I will have no option but to discontinue following you. Unfortunately, this is not appropriate for an educational setting.

    Linda Phillips Secondary Instructional Coach – Mathematics Evergreen Public Schools

    Permanently Beta… “We are all works in progress. Each day presents an opportunity to learn more, do more, be more, grow more in our lives and careers. You will need to adapt and evolve forever–that’s permanent beta.” Reid Hoffman & Ben Casnocha

    Mathematical investigation refers to the sustained exploration of a mathematical situation. It distinguishes itself from problem solving because it is open-ended. Problem solving is a convergent activity. It has definite goal the solution of the problem. Mathematical investigation on the other hand is more of a divergent activity.

    ________________________________

    1. I’m sorry you’re offended. That said, it’s tacky to issue me an ultimatum on my own blog. This is a blog about the classroom but it is not actually a classroom. I occasionally curse, especially to express ebullience / enthusiasm. I always bleep out the curses with an asterisk. This is definitely going to continue from time to time. I believe and hope that most readers will find that the thinking about the classroom is worth the occasional expletive.

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