So it happens. A student finally feels comfortable and safe enough in your classroom to share his thinking. However, when he does, it's a strategy laced with misconceptions. You're unsure of your next teacher move. If that student feels embarrassed after interacting with you, he may feel "math injured" and refuse to participate in the future. On the other hand, you want to make it clear that there's something you don't understand about his thinking.
You're in a predicament. You feel forced to respond because the other students clearly know something is incorrect in his logic. But you're sensitive to feelings and classroom culture. In these moments, the response by a teacher is critical for maintaining a sense of safety in the classroom.
Well, I faced that exact situation recently. Luckily, I had the chance to meet with Ruth Parker, co-author of Making Number Talks Matter, the text that's at the heart of an online book study I'm co-leading with Laureate Kristin Gray as part of my Getting Better Together series. I shared with Ruth a video that I recorded of myself (see below) leading a subtraction number talk in which a student demonstrates deep misconceptions. We watched as the student shared his solution to the problem 10 1/2 - 3/4 (the 2:18 to 3:42 mark in the video).
Though the student got to the right solution, when I asked the question "why is ½ + ¼ = ¾?" he was unable to respond. So I asked him to come back later in the number talk if he wanted to explain his thinking.
As the student returned to the conversation (6:45 to 8:50), he shared several misconceptions. He began with ½ + ¼ is 2/6 (a common misconception) but followed with an additional misconception I was unprepared for: he determined that 2/6 should be reduced to 2/3. Finally, he proceeded to say that 2/3 is equivalent to 3/4.
These misconceptions unveiled numerous, deep misunderstandings. As the teacher, I didn't know where to start. I worried that the number of questions I would need to ask to help him identify why his strategy was inaccurate would overwhelm him.
As Ruth and I reflected, she gave me the critique and advice I desperately needed. She told me there was little I could do in that moment to help the student brush up against his own misunderstandings. What I could do was let the student know that I needed time to think about his strategy and get back to him at a later time. Honoring a student's participation in the Number Talk is absolutely critical.
Ruth reminded me that my job in the midst of a Number Talk is not to "fix" the student's thinking. So it was essential that I let the student off the hook. This is not to say that I won't meet with that student privately and use this formative data to guide that discussion. I will, and have.
In the weeks since I met with Ruth, I've been getting back to students privately. When unable to do so, I've been using this data to drive future lessons to help overcome the misconceptions I witnessed. In addition, I've been carefully guarding how many questions a student is asked by peers. When an interesting strategy is shared, there are often four to six student questions. While one or two may be appropriate to clarify thinking, too many questions can cause a student to shut down and create a feeling of being picked on.
I'm tremendously thankful for my meeting with Ruth. Teaching a subject matter that has high stakes testing attached, I feel such pressure to perform. Call it perfectionism, a type A personality, or overachieving. Whatever the label, for me, the result is stress. I needed to be reminded that sometimes it's ok to let students sit with their misunderstandings until the time is right to address them. It's OK to get back to students later. In fact, by doing so, you maintain an environment where kids feel safe and comfortable and willing to share their thinking, which is what allows them to reveal their misconceptions to begin with.
By addressing them privately, they avoid being embarrassed in front of their peers. Most importantly, they're able to maintain a level of calm, which makes deep thinking and learning possible.