Highlighting Ideas from Making Number Talks Matter by Cathy Humphreys and Ruth Parker
Many educators are familiar with the beauty of Number Talks—a short routine in which students solve problems using mental math and share their strategies with the classroom community. Many of us love Number Talks for the ways they help students develop social and mathematical agency, for the opportunities to uncover big mathematical ideas over time, and for conversations that make student-to-student discourse and navigating mistakes part of the classroom culture.
And yet, anyone who has spent time facilitating Number Talks knows they don’t always go exactly as we might have planned. As Cathy Humphreys and Ruth Parker write in Making Number Talks Matter, “At first, they [Number Talks] appear to be deceptively easy…all we have to do is put a problem on the board and ask students how they got the answer, right? But every Number Talk takes on a life of its own when students start to explain their reasoning and there is no road map for us to follow. We need to think on our feet about what to ask and how to respond. We need to consider who is talking, who isn’t, what and how to write on the board--and we need to keep all of these things in our head at once. It is no wonder that it can be hard to know what to do next…” (2015, 163).
For educators looking to not just navigate the math behind Number Talks in grades 3–10, but to also manage the bumps in the road along the way, Making Number Talks Matter offers us a guide for developing a vibrant Number Talk practice.
Let’s take a look at two of these common bumps in the road in these excerpts from Making Number Talks Matter.
Q: What if I don’t understand what a student is saying?
A: This is an important issue for all of your students. If one student’s explanation is hard for you to understand, other students probably don’t understand it, either. And, since your ultimate goal is for students to listen to and respond directly to one another, it is important that all students learn to communicate clearly about mathematics so they can understand one another. This does not happen overnight. Before the adoption of the Common Core State Standards for Mathematical Practice (NGA/CCSSO 2010), for example, most students did not have regular opportunities to express their reasoning or present a mathematical justification. It is understandable that they would have a hard time expressing their ideas clearly during initial Number Talks.
When you find yourself in the position of not understanding what a student is saying, keep asking and rephrasing to see if you have interpreted their words correctly. You might say something like “Let me see if I really understand what you’re saying. I think you. . . .”
Strategies That Have Worked for Us
• Ask, “What I think I heard you saying was _______. Is that what you are saying?” Just be careful to express what you actually heard them say.
• Ask, “I want to make sure I understand what you mean. Could you please repeat that last part?”
• Ask, “Who can explain what _______ said in your own words?”
Finally, if the preceding strategies haven’t helped you, you can say, “I need some more time to
think about your strategy, and I’ll get back to you.” Then do think about it and do talk to the
student. In giving yourself time to think about an idea, you are also giving the student time
to think about how they might express the idea more effectively. This way, you don’t have
to feel nervous about not understanding what is being said, and you won’t have to worry
about losing other students who can’t follow a cumbersome or inarticulately expressed idea
or procedure.
Q: I know we are supposed to use mistakes as sites for learning, but what should we do when a student’s answer—or method—is wrong?
A: Sometimes as many as four—or more—different answers emerge from a Number Talk.
Some arise from small computation errors, while others indicate misconceptions about how
a property or operation works. These latter errors are the ones that offer the greatest opportunity for moving students’ understanding of mathematics forward. Our goal here is to get our students to the point where they are genuinely curious, rather than embarrassed, about their mistakes.
Strategies That Have Worked for Us
• We establish a class norm that any answer, right or wrong, must be justified. A student
explaining a strategy should begin with identifying the answer he or she is defending. “Which answer are you defending?” is a good prompt for this and communicates that the logic of the mathematics will determine whether a strategy is sound.
• Usually it becomes apparent early on which answer is “right.” There are several possible ways to approach the other answers if you decide it would be valuable to discuss them. You can ask, “Is the person who answered ______ willing to tell us how you thought about this?” If no one volunteers, you can just let it go, or you might want to ask, “How might someone arrive at this answer?” If there is a lingering question about which answer is right, you might want to say about the strategy or strategies, “Let’s try this with
smaller numbers that we know the answer to and see if it works.”
Are you curious about how to navigate other bumps in the road with Number Talks? You can check out a chapter from Making Number Talks Matter all about that issue, and find out more about the book on our website.
Until next time, may your Monday be mathematically marvelous!
