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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.

We started the UCSB Mathematics Project this past summer. About 30 participants, most of whom are school teachers, attended a one-week workshop in late July and will continue to gather for three days during the school year.

While the Project's focus is on the new Common Core Standards in Mathematics, we also present and discuss leadership and equity issues, engage teachers in math activities that model the new standards, and 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. 

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 by telling students what tools are available and what type of task products they can expect.

  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 students may develop.

    2. Monitor—The teacher needs to pay close attention to students 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 (It's no fun if the group with the "best" strategy shares first!)

    5. Connecting—The teacher is responsible for asking students to connect the solutions presented by the different groups and identify the key mathematical ideas 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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