Why We Number TalkFebruary 15, 2022 | By Lauren Woll, Lead Fellow, Oakland
Blueprint Math Fellows facilitate Number Talks to improve students’ mental math and computational strategies. In this narrative piece, one of our Lead Fellows gives us a behind-the-scenes look at what it means to orchestrate a number talk.
I write the problem on the board. It almost doesn’t matter what it is. A discussion can grow out of 19 + 2, or 17 + 25: students can see multiple paths through those problems. But this time, let’s say, I write 4 x 5 or 4 x 10. The first problem has to be easy enough that everyone gives an answer pretty quickly. Once they’ve started answering, they’ll keep going.
Once the problem is on the board, my teacher hat is off: I’m the game-show host. The students know it too: the girl who is doodling in her notebook sits up straight, the boy who had craned his head to watch the eighth graders on the other side of the room fixes his eyes on the whiteboard. First one holds up a fist in front of them to show they have an answer, then another. Now they are the teachers, the talkers, the game show contestants. They know the answers, and it’s their job to say them.
Everyone gives an answer to that first question. Somebody gets it wrong and corrects themselves quickly. I write down all the answers and praise the self-correction. If they don’t agree on the answer, I don’t correct them: I ask for explanations. Sometimes two or three students want to be first to say how they solved the problem, but whoever goes first, there are always more explanations. If no one offers a second way of seeing it, I prompt them: “Did you see it the same way?”
I write each student’s name on the board and take notes of their solution. Sometimes I draw diagrams or number lines to illustrate what they are telling me. Often they name their strategies. “I used skip counting”; “I used the traditional algorithm, but I want to try a place value strategy.” They comment on each other’s strategies, taking note of one they want to use next time, or remarking that one is easier or faster than another.
I put another problem on the board, 4x50 this time. The students take a moment longer to consider the math before holding up their fists. I wait, and then check in with students who haven’t signaled that they have an answer yet. “Do you need a little longer? Can I call on you?”
As the problems get a little harder, I’ll ask for more explanations. Someone will announce, “Eerily similar!” – the name they gave the strategy of using the answer to the last question to find the answer to the next: this means they see a pattern forming in the problems. I can ask them now: “What do you think the next question will be?”
Their answers show the multiple ways they’re thinking about the math: “4 times 100” – “4 times 500” – “4 times 55”. Their quickness to answer shows their confidence, the degree to which they own this process. I acknowledge their answers, and write up the final problem, the dessert of the number talk: 4x49
Somebody frowns. This is a little harder. But then the fists come up again. They offer answers, some wrong, some right, then talk through it until they agree on the right answer. I don’t tell them which it is, although I’ll ask questions if they seem lost. One by one, they try the strategies they used on the earlier problems. Maybe someone offers a new strategy to grapple with the differences in the final problem. When they’re done, I stop to admire the board, noting everyone’s name next to a strategy, commenting on how many different ways they found of looking at and solving the math. I finish by checking off the completed number talk under each of their names on the grading sheet, but the pride I see on their faces doesn’t come from the check that means 10% of their grade – they have solved another problem string. They feel smart and ready to conquer whatever math I give them in the lesson.
Again and again, students have told me – and written in their anonymous feedback on the class – that the number talk is their favorite part of the class. It embodies the values that I believe in most about learning: that there are many right ways to find an answer, and that learning happens when the students are talking instead of the teacher. I hope that they’ll remember the number talks when they find a problem that seems too hard – I hope they’ll try again even if they don’t get it right the first time, try what feels comfortable to them and know that they have multiple tools to solve even the most challenging problems. And I know they can.
A note on the author: Lauren is a lead math fellow in Oakland. This is her third year working with Blueprint Schools Network.