5 Practices for Orchestrating Productive Mathematics Discussion

The post title is a book by Margaret S. Smith and Mary Kay Stein.  It’s a wonderful little book that can make a big impact in a math classroom.


I’m lucky to be part of a team of presenters — there are four of us: Chris is a math professor at UCSB, Maria is a high school math teacher, Jeff is a district math coach, and then there’s me.

This past summer we started an Institute called “UCSB Mathematics Project — California Common Core State Standards (CaCCSS).”  We have about 30 participants, most are schoolteachers, who attended a one-week workshop in late July and will continue to gather again for three days during the school year.

While the Institute’s focus is on the new Common Core Standards in Mathematics, we also present and discuss leadership and equity issues, we engage teachers in doing math activities that model the new standards, and together we examine the 5 Practices for Orchestrating Productive Mathematics Discussions chapter by chapter. I was assigned to cover the Introduction, Chapter 1, Chapter 5, and Chapter 7.  (Hey, there are only 8 chapters, how did I get so many?)

The book persuades and guides teachers to lead more thoughtful and productive discussions during a math activity.  It outlines the necessary steps:

  1. Find a math problem that is high-level with multiple strategies.
  2. Launch the task to students by telling them what tools are available and what the nature of the task products are to be expected from students.
  3. Discuss and summarize by using these “5 Practices”:
    1. Anticipate — the teacher must do the problem ahead of time and anticipate the different strategies and solutions that students may come up with.
    2. Monitor — the teacher needs to pay close attention when students are working in groups, listen to their mathematical thinking and observe their strategies.
    3. Select — the teacher needs to select which groups or which member(s) of a group will share with the whole class.
    4. Sequence — the teacher must arrange the order in which the selected people will share.  (No fun if the group with the “best” strategy shared first!)
    5. Connecting — the teacher is responsible for asking students to connect the solutions presented by the different groups and what the key mathematical ideas are in the problem.

I like to practice what I preach, so I’ve been using the 5 Practices whenever appropriate.  My algebra kids were working on a problem involving systems of inequalities.  I monitored closely to learn the following:

  • Luis’ group was talking about so-and-so-dude-on-YouTube,
  • Bella’s group was on task but they were too focused on one strategy that may not take them to the solution they needed,
  • Miranda’s group was drawing graphs, but everyone focused on the same graph instead of branching out to get more done,
  • Martin’s group smiled at me and covered up their empty papers,
  • Eliana’s group had the first part completed correctly but had a hard time going further,
  • and Dean’s group was… “Dean, what are you doing over there?…  Did you ask me if you could get out of your seat?…  Nobody cares that your back is hurting right now, Dean!”

What step was after monitoring?

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  1. Anne
    Posted July 18, 2015 at 7:01 pm | Permalink

    Thank you for your honest experience. I will work on being a better monitor too!

  2. Posted August 16, 2016 at 10:56 pm | Permalink

    Your style is so unique in comparison to other folks I’ve read
    stuff from. Many thanks for posting when you’ve got the
    opportunity, Guess I’ll just book mark this web site.

  3. Rebecca Rouse
    Posted January 11, 2019 at 3:30 am | Permalink

    Hi Fawn,
    I’m a mid-life career changer about to start my first teaching position to high school in 3 weeks (which will be the start of the school year here in Australia). As you can imagine, I’m desperately searching for tips for implementing group work as I really want to give it a good crack rather than fall back into the easy traditional direct teaching. How do you get and keep a new class of students on task??? Any tips for a newbie starting with new year classes will be greatly appreciated :-)
    Cheers, Bec

    • Fawn
      Posted January 13, 2019 at 10:11 pm | Permalink

      Hi Bec! That’s very exciting that you’re starting your first teaching soon! And yet, I can imagine that it’s also very scary. But, being yourself is the most important (and easiest), so I’d start there. I always say that successful group work begins with a great task, that’s half the battle. A great task gets them hooked and engaged. Sure, you need to set norms for group work, but you can set these as you go along and they need reminders each time you do the task anyway. If you can observe a colleague or someone directly who does this successfully is the best way to really get a sense of it. Also, group work can happen daily and all the time, from warm-ups to exit tickets. Group work just means kids talking and sharing their mathematical thinking, so build this into your routines. Pose a question, ask them to think about it quietly first, then have them turn to a neighbor or group and discuss. Find as many opportunities as you can for kids to talk with one another, but put a timer on, one-minute quick talk, or 3 to 5 minutes within a small group. When you stay on top of the timer, it indicates that you are managing the time and want students to be efficient and maximize this time. It should not mean that they must have an answer (to anything) when the timer goes off.

      Everything takes time to develop. But, please, start it on day one, not so much with rules and procedures (I vote that you don’t do any of it, except for fire drill procedure), but with a great task. Get them going with doing mathematics for the love of doing maths. Get them to take pleasure in thinking slowly and deeply. Also, please remember to take small bites and go easy on yourself. Things will likely NOT go as you had planned, they might be worse, they might be better. Only through actual practice that we learn this. Best to you, Bec! And thank you for stopping by.

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