Seeing the World through One Kindergartner’s Eyes

Sometimes I see Hassan, a kindergartner at my school, at the local mosque where my daughter attends Sunday School. I always wave brightly: “salamu alaykoum! Good to see you, Hassan!” And he will blink a few times, and say nothing.

Then, when we see each other in school, he will whisper to me: “I saw you at the masjid.” (Arabic for ‘mosque.’)

“Yes! I saw you, too!” I smile.

“Yes,” he responds solemnly.

________________________

Today, I interviewed Hassan using Listening to Learn Interview 1: Foundations of Numerical Reasoning. While he is often quiet during our interactions, bringing him into a separate room for a math interview flips a switch in him. He wants to touch everything! He wants to tell me stories! He wants to generate his own mathematical problems! He is a force to be reckoned with, and I do my best to transcribe what he’s saying as quickly as possible.

The last question in the interview is a story problem:

I put 4 apples in a bowl.
When I got home, there were only 2 apples in the bowl.
How many apples were eaten?

“But who ate the four apples!” Hassan cried out.

I paused for a moment, and then leaned in, as if to reveal a dark secret. “I wonder if it was my son, N!” N is entering kindergarten next year, and one of his preschool friends is in Hassan’s Sunday School class.

“He ate the apples!” Hassan’s eyes were wide with surprise.

“Yes! So how many apples did N eat?”

Hassan paused, and then asked: “What did the bowl look like? What color?”

“Hmm… It was a big yellow bowl. It was a big yellow bowl, with four apples. And then N got hungry, and now there are only two.”

“So he ate two!” Hassan said with a flourish of his hands.

I took a moment to finish typing my notes, and then pushed Hassan for an explanation. “So how did you know that he ate two apples?”

“Who, the child?”

“Yes!”

“Because he was hungry!”

Hassan was answering a different question. Not why did my son eat the apples, but how do we know about the quantity. This could have been a confusion Hassan had anyway, although he is also relatively new to speaking English. “But how did you know that it was two apples? And not seven apples?”

Hassan looked at me incredulously. His eyes narrowed. “But who eats seven apples.” Deadpan.

I couldn’t help but let out a light laugh. “Okay, good point. How do you know he didn’t eat just 1?”

“Because it’s two. He ate two and now there are two.”

As I had with previous problems, I offered to let him use some cubes or other materials to act it out, but he declined. He didn’t like the idea of using cubes to represent real things. He liked the idea of using cubes to count cubes. He liked the idea of using cubes to share cubes between the two of us. He didn’t like the idea that the hard, angular cube could represent one of the four apples in the yellow bowl.

________________________

This interview reminded me of how important it is for some students to be able to visualize the problem. It helped him connect to it, and perhaps even solve it. His answer wouldn’t have changed if I had made the bowl silver, or blue, but that it seemed comforting to him to have the context for the story. (And possibly more fun.)

Meanwhile, he did not like using symbolic objects to represent the real apples in this story. I think it’s easy to write this off as that he thinks very literally — and, frequently, he does — but what I’m more interested in is implications for learning. The “Act it Out” Routine in our K-5 curriculum, Investigations (of which variations appear in other curricula, like IM K-5) supports this beautifully. Hassan is very creative, and maybe giving him the space to fill in some of the details will allow him to engage more with contexts like this. And Hassan isn’t the only kid who appreciates details.

Talking with Hassan today also had me thinking about problem posing. (Kristin Gray wrote a blog post recently.) Hassan often extended questions after I asked them. For example, after this story problem:

Two children were on the playground.
Three more children came.
How many children are on the playground now?”

Hassan spontaneously created his own playground problems. “Okay, now there’s seven children, and five children came.”

“How many would that be?” I asked him.

“I don’t know! It’s a very hard number!”

“Well,” I smiled, “you came up with a very tricky problem! I like that!”

“Yeah, I don’t know what does that equal.”

“Do you want to try to figure it out?”

Hassan picked up the small book that I use to show visual prompts during interviews. “Can I flip the page?” An implicit no.

But I could envision a world in which he says yes. He wasn’t problem posing just yet — he was mirroring the story I had shared — but it was the start of something beautiful. Like third grader Owen, he derived some pleasure from continuing on. There’s more thinking to do. Hassan did this when we were also playing the Hiding Game. (There are 5 tiles. I show 3. How many are hiding?)

I was also thinking about how Hassan found it challenging to explain how he knew his answers were correct. They all seemed logical to him, and he did, in fact, answer almost every question I asked accurately. We already push for primary grade students to justify their thinking — we share a lot, we have classroom discussions, we model with some visual tools — but what do we do when they’re stuck? How do we continue to support them with this?

Hassan is one kindergartner, and his thinking is his own. But sometimes, learning from one kindergartner helps me think about learning for more.