As an elementary math coach, I spend all my time thinking about elementary math. I had a partner for this task and, in this partnership, I was the less confident and less competent member. I was, if you will, the "low" kid.*

After a few moments to think on our own, my partner, who I'll call Joel, stood up enthusiastically, moved toward the number line on the wall, and began to place post-its on the number line. I stayed in my seat a few more moments than he did. (What kind of body language do students use to give us the message that they are unsure or unconfident about a task?)

The facilitator, Kyara, asked me to stand up and move closer to my partner and the number line. She prompted me to try to place a post-it on the number line.

I had ideas about where to place some of the expressions, but because Joel was so enthusiastic and jumped right in, I hung back and let him do the beginning work on his own, even though I really wanted to think about the math. (When do students hang back because of an overly enthusiastic classmate? How can we moderate this dynamic?)

Joel and I started to talk about where the expressions might go. Kyara pushed us to be explicit about the assumptions we were making as we placed expressions. "Under what conditions would that work?" she asked a few times, and we elaborated what x would have to equal in order for our placement to be true.

We played around with what would happen if x were a negative number. Joel placed x near the middle of the number line, with x^3 off to the left and x^2 off to the right. "Why did you do that?" Kyara asked. Joel began to explain, easily and quickly. I could

*hear*his explanation, but that didn't mean I really understood it. Kyara asked me to restate it in my own words. This was the perfect facilitation move, giving me the chance to say for myself how I understood it.

"Let's see, if x = -2, for example, then x^2 would be -2 x -2, which equals 4," I said. "And x^3 would be 4 x -2, which equals -8."

(When do we make sure students have the chance to say for themselves what they understand, to explain and re-state and give another example so they understand more deeply?)

As teachers, we sometimes say, "Some of my students really need to use manipulatives," or "My low kids need more time to think through the math," or "Even though they know more efficient strategies, sometimes they keep using the old, inefficient strategies."

When I was in the position of thinking through a task that was somewhat challenging for me, I needed time to think, time to talk through my thoughts, and time to try out sometimes inefficient strategies to be sure about my and my partner's reasoning.

It's not that "some" students or "low" students need those things. Everyone needs to think, to talk about their ideas, and to have space to try things out even if they aren't doing it in the most efficient way. That's how learning happens.

I'm excited to spend time this June doing some hard math with teachers. We all need to be reminded of what it is like to work through a hard problem, to be a little stuck, to have a partner who goes faster than we do, to need extra time, to need to talk in order to solidify our learning. We all need regular reminders of how learning happens.

*I do not use the phrase "low kids," and I cringe when I hear it. I used it in this blog post to emphasize my experience of being the "lower" kid in a partnership and what I learned from that experience.