In a post last January, I wrote about how the “mental load” teachers carry can impact their ability to *listen* to their students.

…but listening is critical. It’s especially critical when working with students from traditionally marginalized population, like new EL* students.

*I think EL is the most current acronym for English Learners.

Third grade students Noam and Ari arrived from Israel last summer — separately. They are both from Hebrew-speaking families. They are both new to using the English language. They are both clearly frustrated with their limited abilities to express themselves in this new language. These similarities do not, however, make them friends. In fact, they seem to harbor some disdain for one another.

Out the window went the brilliant plan everyone had devised independently: pair them up throughout day to build confidence and communicate freely. Noam and Ari were not on board.

The first time I went to visit Room 306, their third grade classroom, I took note of both boys during the teacher’s launch: they looked terrified. Noam sat with his body facing the back of the room, tugging at a loose string on his shirt. Ari’s eyes darted nervously from anchor chart to anchor chart, to desk to desk, never once connecting with the patient gaze of the classroom teacher.

They looked terrified.

Caitlin, their classroom teacher, pulled me aside while the students worked independently and in small groups. “Do you see Noam and Ari? They’re new, and while they act pretty similar, I think they’re very different,” she mused. “I don’t know much about them, but, I mean, just look at how they are in math.”

Noam was chugging through some multi digit subtraction with the blasé attitude of someone trying to act cool at fashion week in Paris. No big deal.

Ari’s page was blank.

Caitlin sighed. “Noam seems to have some computation down, but they both leave a lot of assignments blank. I don’t really know what to think.”

I didn’t know what to think, either. That meant it was time to listen.

A few days later, I returned to Room 306 to model the “choral counting” routine. Students cheerfully counted along, and then dove deep as we hunted for patterns in the record of our count. Noam and Ari sat in silence. After the count, I got out some base 10 blocks to see if they could follow along. Neither of them seemed interested in this manipulative. Although I often view visuals as a point of access, I wondered about their experience with manipulatives in the past. Did their previous classrooms use them? Were these familiar, or was this one more new thing?

I returned to Room 306 the very next day. Caitlin, the classroom teacher, was leading students in a warm up. She closed with asking students to puzzle about how many weeks are in 27 days. Most of the students had done similar things in their 2nd grade classrooms, so they quickly signaled that they were ready to talk, even though Caitlin insisted on a full minute of think time for all.

Penelope shared first. She came up to the board to show her thinking. Her recording style was a bit unusual, and had some internal inconsistencies, but she spoke eloquently about her repeated subtraction strategy.

27 days minus 7 days (1 week) is 20 days (recorded below the 27).

Then take away another 7 days to make 13 days, and that’s 2 weeks passed.

Then take away another week, which is 7 days, and you have 6 days.

You can’t take away any more weeks, so it’s 3 weeks and 6 days.

The end.

I wondered what Noam and Ari thought of this. I was thrilled to see Penelope experimenting with her own recording style, but I knew that this may not have been easy for Noam and Ari to follow. Or maybe it was? Was I underestimating them? I had so many questions, and I knew that there were infinitely more that I hadn’t thought to ask.

Students were then tasked with discovering ways to break down given numbers into place value parts: 100s, 10s and 1s.

I watched Ari as he worked with 152. A paraprofessional in the classroom had helped him set up his paper, and write the first two solutions. That’s all he had on his paper.

It looked like he had tried to prove that 152 had 152 ones by drawing tiny dots… albeit not 152 of them. It looked like he had tried skip counting by 10s, and then 2. “Show me,” I asked him. He looked confused, so I pointed to the 10s.

“10… 10… 10… what’s this?” I asked.

Ari added the 150 in parentheses. I added a smiley face on the side, for encouragement.

He seemed stuck on others, so I wrote a 1 in the 100s column. “Show me this,” I said, handing him some base 10 blocks. Even if he had never used the in a previous classroom, he had now seen them several times in this classroom. He got out a 1 block, and I pointed to the “100s” at the top of the column. He gave me a 100 block with a shrug, then filled out the rest. I wondered if he knew what he was doing, or if he was just looking for different ways to write the digits 1-5-2 in that order.

He then wrote 14 tens and 106 ones. It looked like neither of my hypothesis were correct. When I asked him to “show me,” he shrugged again. He needed an access point. It wasn’t just about him getting correct answers, but about Ari being able to show me something he understood — we needed to build off something.

Meanwhile, Noam was working on 122. He accurately wrote 122 ones, and then 12 tens and 2 ones, and 10 tens and 22 ones. I watched as he looked at this pattern. 12 tens, 10 tens… he wrote 8 tens. Then he looked at the ones place: 2 ones, 22 ones… so he wrote 222 ones.

So he recognized that patterns are helpful, but I didn’t know what we understood about place value. I decided to bring both boys over to the classroom computer to explore “Number Pieces,” a virtual manipulative (app + web-based) from the Math Learning Center. In the basic version of the app, the 100s are red, the tens are green, and the ones are yellow. One advantage of the app over the actual manipulatives is that they can regroup and ungroup instantaneously. One click, and that red hundred becomes 10 green tens. Another click, and one of the tens becomes 10 yellow ones. Circle 12 ones, and they become a group of 10 and 2 ones. It’s so fast.

Watch this screencast of our exploration.

I built Noam’s number, 122, out of the blocks. Then we practices ungrouping the pieces: the hundred became 10 tens. Then two tens became 20 ones. We followed Noam’s pattern: 12 tens, 10 tens, 8 tens… what was happening?

Noam looked inspired. He went off to record his thinking following this pattern.

Noam seemed pleased with himself. But what he did next surprised me:

Noam looked up at me expectantly. “Yes?” He asked, seeking approval.

Well… yes! It turns out that Noam felt could extend the pattern using negative numbers, without any sense of cognitive dissonance. A student who was fixed on using the manipulative might become confused by the idea of -2 tens, but for Noam the base 10 visual seemed to make a connection, not limit him to the system. He had invented a new world.

Ari continued his work, too, although he focused on systematic decrease of 1 ten.

Ari seemed to be more comfortable working with one group of ten at a time. He used the virtual manipulative to solve most of those, relying heavily on the tool to arrive at a solution.

Both boys had very different understanding of our number system: place value, integers, and patterns. A single experience with a visual was able to help me listen to what the boys knew. Because they did not feel comfortable with the language — they spoke very few words throughout this experience — they founds ways to converse with me using numbers and patterns. The boys did not want me to be a passive observer, they wanted to interact with me nonverbally. The boys looked for facial cues, and sometimes handed me a pen or pencil to write back to them. I tried to speak simply while I wrote, to give them some exposure to some English orally, but we focused on the numbers. We focused on our common language, and, in that moment, it was my job to learn from them even more than it was their job to learn from me.

Just because no words were spoken doesn’t mean I wasn’t listening.

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