A friend of mine tweeted about his experience running a Number Talk and through follow-up conversations, we realized that I run mine a little differently than the format shared in the books. Although I talk briefly about my process in my Parent Night blog post "What are these stupid strategies kids are learning days? Why can't they just learn the #@$#* way I learned it?", I thought I would focus a single blog post on it so that I can go into my process in more detail.
How many of you have students who are effective at communicating their mathematical thinking? They won't be amazing at communicating their thinking in the beginning (unless they have been practicing this a lot in previous years) and that's ok. This is a skill that students develop over time. They must be provided with opportunities to practice it in meaningful settings.
You can use number talks at any point in students' learning and understanding. Maybe you are introducing 3 digit addition and want to see what strategies they have for 2 digit addition. Maybe you have been exploring 3 digit addition for a while and want to see what they will do if given a 3 digit plus 4 digit number.
I typically have students complete their work using as much mental math as possible, although they know they can always access manipulatives if they need it or use a mini whiteboard to record their thinking as they work through it. However, I have noticed that people often use different strategies when given paper and pencil versus solving it mentally. When I ask adults to solve an addition question in their head, they often use alternate strategies but admit that if I had said to use paper and pencil, they would have used the traditional algorithm instead.
Everything written below in normal text is something that I say during the process. If it is in italics, then it is something I do or notice.
Step 1: Post a meaningful question for students to solve on the board so that all can see it. This might be a "How many dots are there?" or "Add 324 + 493" or pretty much anything else that you would like to focus on.
I am going to give you 2 minutes to work on figuring it out. It's only 2 minutes though so will everyone finish? (No.) Is that ok? (Yes as long as you keep working on it the entire time.) If you figure it out and still have time left, see if you can confirm your answer by solving it a different way.
While you are thinking, place a closed fist in front of your chest. That will tell me you are thinking. When you have solved it one way, put your thumb up. If you have time, solve it a different way. If you do, put another finger up.
Step 2: Students work. My "2 minutes" are up when I see that almost every student has their thumb up.
Turn to your partner and explain to them how you solved the question on the board. If you didn't finish, that's ok. Share as far as you got. I should hear things like "First I did this. Then I did this."
Students have time to share their strategies with their partner. During this time, I wander around the classroom listening for a variety of strategies that I would like to have shared during the group sharing time. I will let students know that I think they have explained an interesting strategy and will ask them to share it with the rest of the class. I try to focus on the students who may not typically share in class and the students who don't often feel success.
Step 3: Class Sharing. During this time, I will call upon students to share strategies, starting with the least efficient / easiest strategy first and then moving onto more complex strategies. I will ask students who want to share their strategies, and of course the students whom I talked with earlier always put their hands up because they know I am going to call on them anyways.
Who would like to share how they solved this question or how their partner solved this question? If you didn't have enough time to finish, that's ok. You can still share your thinking as far as you got.
I phrase the first statement that way so that students know they have permission to talk about the strategy that their partner used. I started saying it that way because, especially in the beginning, I would have students who didn't / couldn't solve it on their own until after they talked to their partner. This gave them permission to share even if it wasn't their own original idea. In fact, after students have had experience with Number Talks, I will require them to explain the strategy their partner used rather than their own strategy. This really helps them focus on listening to understand and to ask clarifying question.
I phrase the second statement this way because it's important that students realize that it's not about solving it quickly. Even if you didn't finish, you still have ideas and strategies you can share.
As students are explaining their strategy, I am asking them clarifying questions, ensuring that they are being very specific and clear about their thinking. For example, if they are solving 24 + 95 and they say 3 + 9 = 12, I will ask them - Where did the 3 came from? They will tell me that it's from 1 + 2. I will ask them - is that really a 9? They will tell me - No, that's 9 tens - or - No, that's 90. As they are explaining their strategy, I am writing it out the board. This helps students see the thinking represented symbolically.
Step 4: After a student has finished explaining their strategy:
Who else solved it the same way?
Students are going to say - I solved it that way too - so you might as well ask. This also shows this student that other people thought about the question the same way they did.
Step 5: Does it make sense to others?
Let's take a moment to think about that strategy. If that strategy made complete sense to you, give me a thumbs up. If that strategy made no sense to you, give me a thumbs down. If that strategy makes some sense to you, give me a thumb in the middle. It's ok to give me a thumbs up, thumbs down, or thumb in the middle.
Having students self assess this way gives you an opportunity to see how students feel about this particular strategy. Does it make sense to most students? Who doesn't it make sense to? When students see a strategy for the first time, you might see a lot of thumbs down. The next time they hear it, you will probably see some more thumbs in the middle. The more they see it or hear it, the more their thumbs will move.
Step 6: Repeat with the other strategies. Don't do too many strategies, though. Focus on about three. Any more than three and students tend to lose focus.
Step 7: Reinforce the idea that there are many ways to solve a single question.
We just heard 3 ways to solve this question. Which way was correct? (They all are). Take a moment to think about the one that makes the most sense to you today. Wait a few seconds. Turn to your partner and tell them which one makes the most sense for you today and tell them why. Give students a minute or two at most to share.
Number talks shouldn't take up more than 10 minutes in the class. I wouldn't do these every day but I like using them about 2-3 times per week, regardless of the grade level. They have so many benefits to them that the time invested is well spent. Every student shares their thinking with their partner so every single student is practicing communicating their thinking. They are seeing their thinking represented symbolically. They are listening for understanding to others' strategies. They are seeing strategies move from less complex to more complex. They are reinforcing the idea that there are many strategies for solving the exact same question.
Reflection Question for you: Have you ever used a process similar to Number Talks in your classroom? What benefits have you seen? Are there parts of the process you have struggled with?
I would love to hear your thoughts in the comment section!