Studying student work is important. It can tell us so much about what students know. It’s our jumping off point for future lessons. It gives us a window into the minds of our kids, especially the quiet ones from whom we don’t hear much in class. I personally enjoy studying student work in the peace and mental quiet of my own home, in my classroom at 4 pm, or in any place that is not a room filled with children shouting, “Can I go to the bathroom? I’m done. What are we supposed to do now? He hit me. Is it almost time for lunch?”

And yet, I’ve noticed that when teachers get together and study student work, it can sometimes be hard for us to see what kids know and can do. We often see what they **don’t** know. Why is this?

Recently I was at a conference where I was working with a group of teachers to study some student work and consider what our next teaching steps might be if these were our students. To give some context, we had never met the students whose work we were examining, nor did we have access to their teacher. We just had the work. We put it between the four of us. We put on our serious teacher faces. We studied.

I’m always wary of the person who speaks first in one of these situations. I’m wary to be that person and I’m wary of that person. But someone’s gotta do it. So that person (it wasn’t me this time) did it: “Well, we can see that he really doesn’t understand the meaning of the equals sign,” she said. I considered this. It was true that the student seemed to be confused about the equals sign, I thought to myself. The next teacher chimed in: “It’s hard to get a sense of anything from this chicken scratch.” Uh oh. Handwriting commentary gets under my skin. I waited a little longer. Next teacher: “He subtracted where he should have added. He doesn’t understand negative numbers.”

None of these comments are out of the ordinary for teachers studying student work, and I don’t think any of them are “bad.” But they made me wonder why it’s often our default to approach students from a deficit perspective. Until I recognized this in my own teaching (which took a while), I was guilty as well. Maybe we default to this because it justifies our existence and importance as teachers — if there’s a problem, we have some work to do! If they don’t know something, we can fix it! We can be the Givers of the Knowledge.

The problem with this perspective, for me, is that a) I don’t want to see my students as knowers of nothing or heads stuffed with “misconceptions”* awaiting correction, because I don’t think it is true and I don’t think it honors kids very well; and b) I don’t want my students to see me as knower of everything and provider of correction, because I don’t think it’s true and I don’t think it honors teaching very well. If I believed my job was just about correcting mistakes and telling kids how to do stuff, I might never have been interested in teaching in the first place.

Since I want to be a teacher who helps kids see their own power to make sense of math (and the world), I have to be a teacher who sees kids as having power and knowing things. If I want to be that teacher, I have to approach students and their work by thinking, “What does this student know?”

Even with this approach, though, it’s not always easy to understand student thinking. If you like reading research, this article by Jacobs, Lamb and Phillips nicely highlights how difficult it is for teachers to get good at studying student thinking and noticing what’s important. They write, “Expertise in attending to children’s strategies is neither something adults routinely know how to do nor is it expertise that teachers generally develop solely from many years of teaching.” They also say that the skill of attending to children’s strategies is regularly overlooked by professional developers. In their study, Jacobs, Lamb and Phillips found that it wasn’t just processing capacity (e.g. all the kids in the room yelling your name as you’re trying to look at a kid’s work) that created challenges for teachers in noticing the right things in student work; it was that teachers actually need more instruction in noticing what is mathematically significant and need help developing “skill in finding those mathematically significant indicators in children’s messy, and often incomplete, strategy explanations.”

How can we get better at noticing what kids know mathematically? Approaching students with the disposition that they have important mathematical ideas, that they are making sense of something, and that their ideas are meaningful to them, is a necessary, but not sufficient, first step. It’s a goal I’m taking with me into my classroom this year (and every year) as I get ready to teach my 2nd graders. I offer it up if you’re looking for a goal for yourself this year as a math teacher that doesn’t involve a lot of making copies, putting manipulatives in baggies, or even writing awesome tasks that will get your kids excited about math. It’s more of an internal math teacher goal, but I like it.

* I can’t stop thinking about Rochelle Gutierrez’s talk at NCTM this April: “Mathematics Teaching as Subversive Activity: Common Core, Social Justice, Creative Insubordination” She had a lot to say about the weight of the words we use when we talk about students, and one of her pet peeves is the word “misconceptions.” She said (paraphrasing from my notes here), “We often tell teachers ‘anticipate your students’ misconceptions.’ Students don’t have misconceptions! They have conceptions. They have conceptions until those conceptions bump up against something that causes them to no longer work.” I loved this reframing. I still say misconceptions, but this idea tickles my brain every time I do. Passing that on to you.

Powerful thoughts before the start of a new school year. Thanks, Kim – I’ve always known you to be kind and positive. I look forward to following you. Have a great year!

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What an inspiring and thoughtful post. I am thrilled to follow your blog this year! Also- any way you can get a transcript of that speech? It sounds awesome!

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Amazing observations beautifully described. What you just passed on to me was a lovely intertwining of your ‘brain tickling’ and what students are doing when they are ‘bumping up against’ and ‘making sense’ of an novel idea. We tend to focus on what we see as the result of that bumpy process as ‘having misconceptions’ and call it such, as opposed to affirming, for the student and others, that what is essentially happening is that the brain is being tickled by new ways of thinking about something, and isn’t that a much more encouraging way to think about it?

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