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.

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