Thursday, March 31, 2016

NCTM Essential Mathematics Teaching Practice #4—Facilitate Meaningful Mathematical Discourse

Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. 

For years I have listened to the cries of those who hate mathematics.  The most common thread of complaint is that math doesn’t make any sense and in school they fail to learn the rules.  I remember days in the student seat, feeling lost, trying to follow the teacher’s train of thought as she jotted on the blackboard.  I often wonder how these same folks would feel about mathematics if they were fortunate enough to sit in a math classroom with a deep focus on sense-making.  At the core of these powerful classrooms is a community of learners who contribute to the intellectual capacity of the room.  The strength of these communities stems directly from the power of great classroom discourse.

Leading a great classroom conversation around mathematics is a complicated task.  It is far more than a mathematical show and tell.  Teachers have to consider the mathematics that they want students to learn and select student work and questions that will help move the class’ understanding of the concept forward.

Here are some things to keep in mind to help make your next classroom conversation high-leverage:
  1. Plan ahead.  Start with a rich task that promotes problem-solving and reasoning.  Selection of the right task is important.  If there is only one obvious solution or strategy you may not get the diverse ideas that make for great classroom debate.  Discussion designed around steps in a procedure are not likely to produce the deep conceptual understanding you’re hoping for.                      
  2. Anticipate student responses.  If possible have a team teacher solve the problem.  The better prepared you are beforehand, the better equipped you will be to guide students to the mathematics from the student strategies.                                                                                                 
  3. Of course there will always be the one unanticipated strategy.  The art is to honor student thinking while ensuring that the underlying mathematical ideas are the common thread in the conversation.                                                                                                                                             
  4. As students are working, circulate and make note of students’ strategies.  You should be planning who you would like to have share.  Think about which students’ work makes clear connections to the mathematical ideas central to your lesson.  Keeping that in mind, you want the samples that you select to have variations to provide talking points for students to contrast the strategies.                                                                                                                                           
  5. Select the order in which you would like students to share.  Plan to go from the least to most sophisticated strategy.                                                                                                                               
  6. While students share, think of what questions you will ask to help the class connect the strategies to each other as well as to the mathematical ideas.  Guide students to ask questions.  Students should be encouraged to defend their thinking, question one another, and critique the reasoning of others.  This purposeful, deep conversation develops higher-level thinking skills as students make sense of a variety of strategies.

Having students reflect on their learning is a great way to end a lesson focused around discourse.  It can also be an effective formative assessment.  If you use learning targets you may wish to wait until the students end their conversation to share the target and allow time for students to connect their discussion to the target. 

If you haven’t used this type of instruction in your classroom before it can be a bit of a shift.  To think that one or two tasks can elicit as much learning as 50 practice problems is a major change in thinking.  The power of the learning comes from the ideas that students present and the connections they make, not solely on answer getting.  For students who are proud of quick answers, taking time to debate the process can be frustrating at first.  Through these rich experiences students will come to see the value in exploring mathematical concepts deeper.  Often teachers who are shifting to this level of discourse will comment that they saw a deeper level of insight or thoughtful work from particular students that they did not typically see.  This just validates that this focus on sense-making is so powerful in student learning and has great potential to assist our struggling learners.

Already implementing mathematical discourse in your classroom?  Take your class to the next level by facilitating student to student classroom conversations.  Use of accountable talking stems or other statement/question starters help empower students to communicate clearly with peers to critique the reasoning of others and defend their thinking. 

Want tools to help you get started?  Number Talks by Sherry Parrish is an excellent resource which includes a DVD with sample lessons.  These 5-10 minute classroom discussions can help you perfect your technique and build your confidence for larger discussions.  When you’re ready to implement more challenging tasks, start with some from Illustrative Mathematics or from the Coherence Map at

We'd love to hear how you are implementing classroom discourse in your classrooms!  Share with us on Twitter (@KYCenterForMath) using #KCMTalks or on Facebook at Kentucky Center for Mathematics.

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