July 10, 2020

Playful Home Learning Series: #10

We return to our home learning series with this second post from the Atrium School, an independent school in the Boston area. During the past school year, Atrium participated in the PoP: USA research along with 5 other schools. As the next year may include online or blended teaching for many, how the Atrium teachers maintained their commitment to playful learning in math is instructive.


Ten plus ten plus ten…plus ten is a big number!: A 1st grade math small group

by Ben Mardell

In a breakout room* Bader and Julia are discussing adding and multiplying groups of tens. Bader exclaims, “These are big numbers!” Because it gets them past one hundred quickly, first graders are intrigued by counting up by tens. They love big numbers.

Learning different strategies for grouping tens, gaining automaticity in adding and multiplying by ten, and enjoying math are the learning goals 1st grade teacher Bob Dowling has for Bader, Julia, and their classmates, Oliver and Maya. In a half hour small group zoom call, Bob provides a variety of activities and discussions with all four students and in pairs in the breakout rooms.

The lesson begins with Bob displaying cards, each of which has ten dots. He asks the children how they can figure out how many dots there are in total. After children tell him that for four cards you can use multiplication to get forty, he asks them, "What are you doing when you multiply?"

Maya answers immediately: "You’re basically doing ten, four times." Bob follows up: "What are you doing with the tens?"

Maya: We are doing ten plus ten plus ten plus ten basically. And 4 x 10 is a short way to write it.
Bob: You could have four tens. What else could you use?
Maya: Ten fours equals forty.

Bob’s next question -- Which way is more efficient? -- creates an enthusiastic response from all the children, who call out: Tens! Then in quick succession:

Maya: The multiplication way.
Bader: The least efficient way is ones.
Oliver: Or zeros!

A few minutes later Bob sends the children to break out rooms to consider the problem: There are ninety fingers. If everyone has ten fingers, how many people are there? In their group Bader and Julia struggle, but remain positive. Julia notes, “I know I can ask for help.”

Bader and Julia in the breakout room

Bob brings the group back together but does not ask for the answer. Rather, he asks, "who can tell me how they solved the problem?"

Bader: There were ninety fingers and each person has ten. Ninety is you get a nine and then a ten. So it’s nine people because everyone has a ten. Bob illustrates Bader’s solution on a white board for all to see.
Bob illustrating Bader’s comment

There is time for one more breakout group where the children use playing cards to compare the size of numbers. Bob generally has them use concrete objects—pebbles or even blades of grass—in these virtual lessons.

Returning to the main room, Maya notes, “There are no grownups here. No one can tell us what to do. Let’s go and have a party!” Julia adds, “Play with your backgrounds.” But before the party can start Bob returns. Bader asks if they can have a party after the lesson. Bob answers, "Not today, but I do have a question. The other math groups were asking if we could have a math group with the whole class where we just play games.” There is a chorus of yeses, with Maya declaring it a math party. Bob agrees with the gathering's new name to the delight of all.

Transitioning to distance teaching, Bob and his co-teacher Melissa Burns were initially skeptical that first graders could manage online learning. They have been heartened by how resilient their children have been in meeting the challenges the transition dealt the group. While they found whole group gatherings less successful, small groups, both in math and writing and reading were generally positive. As in the lesson described here, the math talk, problem solving, and playfulness of in-person teaching was retained.

* Teachers at the Atrium use the online platform Zoom for their lessons. One feature of Zoom is that teachers can create “breakout rooms” and assign smaller numbers of learners to specific groups. Teachers can visit these rooms and then bring the class back together in the “main room.” Another Zoom feature is a chat box where participants can send text messages to individuals or the whole group. In this session, Bob discourages the use of the chat feature, noting how sending individual messages is “like whispering to a friend during a conversation” and messaging everyone is akin to “calling out during a class discussion.”