Making Connections during Number Talks

All hands shoot up in 1M, a first grade classroom. The students strain their arms, employing arched eyebrows and pursed lips to entreat me to call on them. Of course, once I select a student to share — Sara, in the back — the hands instantly shrink, as does their collective engagement. As Sara talks and I record, the first graders lie in wait. Each one wants to be the first one to signal when it’s time for another person to share. They aren’t listening to a single word.

How do you get kids to listen to one another?

…like truly listen to one another, trying on one another’s thinking as if they are trying on hats?

It is something I expect of the upper elementary and middle school students in my school. Many of these students are able to do this innately, and for others we practice “matching our thinking,” visualizing, asking questions and making connections. It is far more challenging for our K-2 students. Many of these students want to share — urgently. Why listen?

I am completely, wholeheartedly sold on the power of Number Talks, and its variants. I have seen them open up new worlds for middle schoolers, and engage the minds of the sleepiest first graders. That does not mean that each one is enacted flawlessly. Sometimes students want to share, but they don’t want to listen. Maybe they want to feel validated, rather than opening themselves up to new ideas. I don’t know. All I know is that I saw this behavior becoming increasingly problematic in 1M… in spite of their beautiful classroom culture (lovingly crafted by our most veteran teacher on the team). The students seemed unfettered by it. They pleaded for more number talks…. more chances to solve and share.

Take 1: Talk Moves

I tried to incorporate more Talk Moves. “Can anyone explain Maxim’s thinking in your own words?” Inevitably, the same two or three kids volunteer to paraphrase, and the rest use the time to cozy up for a nap. “Turn and talk with your partner. What was one thing that Stella said that was different from your own thinking?” Crickets.

No one had the patience for listening to student after student restate one another’s strategy. Not even me. Did I yawn in front of the class?

Take 2: Making Connections

I decided to emphasize making connections: between students’ thinking and the way I record it, between two different students’ record of thought, etc.

Here was our first attempt:

After a student shared his or her thinking, I would elicit connections from the group. We paused at the end to make final connections, as well.

Students noticed that, despite having different equations, everyone arrived at the same sum. (As students introduced important vocabulary words, I recorded them in the top right). They also noticed that Devan and Lex had the same groupings, but Lex saw it as 5 + 1 + 1, which he combined to make 6 + 1, and Devan saw it as 5 + 2 (groups of 1), which made 7. Meanwhile, Elya and Devan had the same equation, but different groupings.

We were onto something.

I tried it again the following week in the same first grade class.

The students could not wait to share their connections.

“Amer and Christian both had two groups of 2, but they combined them in different ways!”

“Devan and Fei Fei both saw 5 + 4, but in different ways.”

“Lana and Fei Fei had the same group of 4. It’s on the right.”

Engagement had certainly increased, and many of the connections made helped the students think deeper about decomposition of numbers. (As with any class of live, genuine children, there were some errant comments that I recorded, nevertheless.)

We continued to work on making connections during number talks. The length of the number talk slowly crept from 10 to maybe 20 minutes… or longer. While it makes for a long routine, the classroom teacher and I were pleased that the engagement remained high in spite of the amount of “rug time.”

The following photo is of our most recent attempt, representing some of the most interesting student connections. (In many other talks, the students seemed more focused on the break down of the visuals than on truly following one another’s thinking.) For this problem, I used two different ten frame images.

I took three examples of student thinking for the first image (William, Zayne, Elya) and three for the second image (Amer, Fei-Fei, Lana).

“William and Amer had to add one on the end.”

“William and Amer kept all the parts together, but broke up one section.”

“William and Amer used doubles. William did 6 + 6 + 1 and Amer did 4 + 4 + 4 + 1.”

“Zayne and Fei-Fei didn’t break up anything. They used near doubles to add.”

“Elya and Lana used the ‘make a ten’ strategy that Ms. S taught us.”

“Elya and Lana both moved dots into empty spots in their heads.”

This was above and beyond my favorite of the connections number talks. Perhaps with so many strategies represented (usually 6 for each dot image) in previous talks, students offered more contrived connections. In this talk, I was able to place similar strategies side by side. It felt much more deliberate and intentional. It felt very “five practices.” Students noticed that both William and Amer parlayed their knowledge of doubles and near doubles to determine the quantities. Meanwhile, both Elya and Lana used similar “make a 10” strategies, showing how flexible some of these ideas are.

After finishing this particular talk, one student remarked, “I feel so smart.”

“Does that mean you felt your brain growing?” the classroom teacher, well versed in growth mindset theory, asked him.

“YES!”

So much learning can happen in the listening and looking!

In Reflection

I wonder what this would look like in older grades. Sometimes students make connections to their peer’s thinking on their own, especially if we name a strategy after a classmate (e.g. “Gabi’s Double & Halve Strategy”). Time feels more crunched in the “tested” grades, of course, and I think these extended number talks might be a tough sell unless they’re the main vehicle for instruction in the lesson. (Also: I think that the more normative number talks — short, routine — can be just as potent and valuable.)

My hope is these first graders who were pushed to make connections will adopt this as a natural lens during classroom discussions. My hope is that students will make connections even when I don’t pause between each and every student share to elicit them, and even when I don’t stretch out every number talk to twenty minutes. My hope is that students will value one another’s contributions as much as they value their own. (I do my best to share this ruthless optimism with my colleagues, and I am grateful that they share their own ambitions with me.)

Of course, I am also open to more experimentation. How else can we gets kids to listen to one another?