• Carrie S. Cutler

Four Talk Moves to Elicit Student Thinking in a Number Talk

I love number talks! They are one of my go-to practices for helping children develop appropriate, flexible, and efficient strategies for solving problems using mental math.


Rather than focusing on memorization or robotically following rote procedures,

number talks emphasize reasoning in math and connections

between numbers and operations.


If you're not familiar with number talks, here is a short video of one I did with my sons Quinn (6) and McGregor. (8) In this video, I ask the boys to explain how the number 120 can be made of other numbers. Watch how they use addition, multiplication, subtraction, place value, and known facts to share their thinking.



As you saw in the video, the sequence of interaction we use during a number talk goes a bit like this:

  1. Pose a problem that can be solved using mental math.

  2. Allow students time to think. Students place their thumb up against their chest to show when they’re ready.

  3. Several students share solutions, and the teacher writes them on the whiteboard.

  4. Ask questions to probe student thinking about the strategies or relationships between the ideas.

  5. If desired, highlight an efficient strategy for discussion or ask students to try a related problem to help them generalize the ideas.

  6. Begin the sequence again but wrap it up after about 5-10 minutes. Number talks are meant to be brief.

This interaction is prime real estate for a rich mathematical discussion,

but what if the kids don’t engage?

Crickets!


How do we get kids to talk during a number talk? It can be tough, especially if our students are used to a classroom where math is a quiet, individual exercise.


One of the Effective Mathematics Teaching Practices (NCTM 2014) is Eliciting and Using Evidence of Student Thinking. Effective mathematics teachers use evidence of student thinking to ASSESS progress and PLAN or ADJUST instruction accordingly. Here we see it in action:

Notice how the figure is cyclical. We follow the cycle numerous times during a discussion. This requires a teacher to be on his/her toes listening, scribing, responding, and providing feedback.


Sound complicated? It is! And it takes practice!

Add to that the need for on-the-spot brilliant questioning and whoa—overwhelming!


For me, thinking of the perfect question in the moment is tough. I can never think of what to say! I get in a rut asking the same questions:

How did you get that?

Did anyone do it a different way?

Boring!


But never fear; Talk Moves to the rescue!


Talk moves are ways a teacher can facilitate the progression of a discussion among students without being the one doing all the talking. Seriously, some of my best teaching has happened when I have just been quiet and let the students build the ideas, make a connection, or create their own ah-hah moment.


Here are 4 talk moves that are helpful for guiding discussion

and easy to implement during a number talk.


1. Wait Time


Consider that children (and adults too) need time to think. After giving the initial computation problem (and throughout the discussion) allow time for children to gather their thoughts. This is respectful and sends the message that the problem is worth their thought and effort.


When I started teaching in the age of purple dittos and newsprint worksheets, the recommendation for adequate wait time was 30 seconds. It felt painfully looooooooong. Today, experts suggest giving children 5-15 seconds to formulate a response to a question for which they should know the answer. Give more time for students to respond to a question for which you anticipate divergent thinking.


What the teacher can say:

  • I’m going to give you a few moments to think about this.

  • It’s okay to think for a moment.

  • Good ideas take time.

  • Put a silent thumb against your chest when you have one idea. Put up a second finger when you have a second idea.

  • When I see you have lots of fingers up, I know you're taking your time to think deeply.


2. Clarify or Repeat


Children’s limited vocabulary sometimes (though not always) affects their ability to articulate their ideas with precision. When you ask children to clarify their thinking by restating their ideas, they often self-correct or speak with greater clarity during the second go-round.


The teacher can also repeat what children have said to model precise mathematical language and correct vocabulary and usage. And check out the 4th bullet below. Orienting students to one another is a great way to improve equity and send a message that students should listen to one another's ideas.


What the teacher can say:

  • Can you say that again?

  • Are you saying that you think __________?

  • Let me see if I understand what you mean.

  • Who can tell us what (child’s name) said?


3. Reason


Emphasizing reasoning in mathematics is essential to learning conceptually. Further, a child’s reasoning may be strong, even if they don’t necessarily arrive at the correct conclusion. If you sense that a student is on the right track, prompt them to justify their reasoning. They may self-correct as they explain. This is good not only for the child who is doing the explaining but also for those listening. When children hear the reasoning behind one another’s strategies, they are more willing to accept them as valid, can compare them to their own, and can make connections between problems and strategies.

What the teacher can say:

  • Why do you think that?

  • Can you tell me more about why you decided that?

  • How is your strategy alike/different from Knox's?

  • How did you figure that out?

4. Add On


Asking other children to add on to what a classmate has said helps everyone feel part of the conversation. Like I pointed out earlier, orienting students to one another's ideas encourages active listening while classmates are explaining. And when kids hear other kids talk about math, it sends a message that math is for everyone!

What the teacher can say:


Who can give us another example?

Who can add on to what (child’s name) said?

Who can rephrase what Duncan said and add on to it?

Zeb, can you give us an example different from the one Sybil gave?


Let me know what you think of these ideas, add your own suggestions in the comment section, or send me a Tweet. I'd love to hear how you are orchestrating discussion in your classroom. Whether during a number talk, a discussion about 3 Act Tasks, or in small groups discussion builds math-positive mindsets.

If you like these ideas, hit subscribe. And find many more tips in my book Math-Positive Mindsets: Growing a Child's Mind without Losing Yours.

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