Nothing, and I mean nothing has affected my teaching more in the last two years than an article that came from Mathematics Teaching in the Middle School titled, “Orchestrating Discussions“.
The authors share results from their research concerning the practices teachers engage in when they orchestrate mathematical discussions from which students learn.
Let’s be clear about what this means.
Imagine two teachers using the same challenging task in a classroom. Each teacher gets kids working. Kids are engaged and on task in both classrooms. And now each teacher is going to have a conversation with his students (in Connected Math, we call this the summary but it’s not a finding linked to a particular curriculum).
In one classroom, students learn more mathematics from that conversation than they do in the other. So this is not about engagement, it’s not about the task. It’s not about technology. Those things may also help, but they don’t factor into the finding in question.
Nope this is all about what the teacher does to facilitate that conversation. The research group has identified five practices that lead to productive mathematical conversations. When teachers engage in those practices, students tend to learn more than when teachers do not engage in them.
So what are these practices? I’ll summarize. But you really need to read the article.
- Anticipate. Teachers anticipate student strategies for working the task when they plan their lessons.
- Monitor. Teachers make efforts to notice what strategies their students are actually using, and to keep track of who is using which strategy.
- Select. Teachers choose which students should contribute their strategies to the conversation.
- Order. Teachers select the order that these contributions will get made.
- Connect. Teachers do the hard work of helping students see connections between the strategies that are presented.
I can’t stop thinking about it. I measure my efforts in professional development against these practices. I measure my college teaching against it. I think about these practices when I’m writing for Connected Math.
Oh. And now it’s a book.
Next post, I’ll write up some concrete changes in my teaching caused by this article.
Overthinking my teaching 
I think I actually sort of did this in my pre-calculus class yesterday – and it was pretty effective I think – so now I’m going to read the article and try to be self-aware and deliberate in using this technique – or is it a strategy?
Christopher, it seemed like your post was directed right at me. I was sitting here pondering ways to enhance Monday’s task and the subsequent discussions and could not put to paper what I wanted these pre-service elementary teachers to think about. This is perfect and I am hunting down the book!
Now I am looking at when its appropriate to have (elementary) students come to their class group having already engaged with the task, and when it might be best to have them begin the task collaboratively right there in the class. Any thoughts there?
Mary, I’ve never been clear on the difference between a technique and a strategy. I can’t wait to hear more about what you did with PreCalc. Since we’re office mates, we should be able to find time to talk about that.
Great to hear from you Neil. Is this a content or a methods course? In my third year at my present institution I have finally gotten my content course for elementary teaches onto a Tues, Thurs. 80 minute schedule (instead of MWF 50 minutes-please don’t tell anyone that I added 10 minutes/week in the process-let’s keep that our little secret). After only being back in this time slot for a week, I am pleased to report that it feels like I have returned home.
There is room to let ideas breathe in 80 minutes that there isn’t in 50. In my college courses, I feel like it often takes 10 or 15 minutes to build up some momentum. In a 50 minute period, we then only have about a half hour to use that momentum. In 80 minutes, we can let it carry us through several different tasks.
All of that is to say, Neil that I’m asking the same kinds of questions about this course that you are. And I’m answering them in a substantially different context than I was last spring.
I should write about this in a post or series of posts sometime, but I have taken more of an assignment-based than task-based approach to my content courses for future elementary teachers. I have these students write papers (about which I published a paper-let me know if you’d like a copy). Class is used to introduce the ideas that my students need to use in the papers. But those papers are the where the real learning takes place. The papers are where students apply and integrate the ideas of the course; they are where students do some original mathematical thinking.
I don’t have a lot of people in my life right now to talk through these courses with, so I’d love to hear your thoughts here or by email.
Good luck on Monday!
Thanks for posting this! I had written a note in my lesson plans for this week about ordering responses (from the article) to go over a certain concept. Look forward to getting a copy for KMS.
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Fawn gifted this to me a few weeks back. I plowed through the first half of the book no problem. However, I’ve been chipping away at the second half of the book over the past couple of weeks. There’s definitely some great insight, strategies, and examples in this book. It’s at the top of my list for books teachers (any subject/grade) MUST read.
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