They say you can’t know what you don’t know. There are things we learn in certain seasons that wouldn’t have landed at an earlier time. I recently had one of these epiphanies. It’s the thing that has made the single most profound impact on my own teaching practice. There are rarely magic bullets in life or math education, but sometimes you learn something that ends up having a significant effect on how you live your life or go about your work. You can think of it as a keystone habit or core practice. It’s a habit that propels other new habits and leads to profound change over time.

Here it is. Are you ready?

Take time to understand how a student is thinking about a problem.

Simple, right? Before you try to propel students forward by suggesting a strategy, giving a hint, or reviewing a concept, listen to the student’s thought process. You are the learner here. The student is teaching you something about how they think. Peg Smith and Mary Kay Stein refer to this when they describe the monitoring phase of a task, the stage where you are asking assessing questions. These kinds of questions serve the single purpose of revealing what students know and getting them to articulate their reasoning. As teachers, I think we feel much more comfortable with advancing questions, which push students to make their thinking more rigorous and connect to the learning goals of the day. These are important too, of course, but I think we skip way too quickly over the process where we genuinely want to understand a student’s thought process.

### Doesn’t every teacher already do this?

This idea doesn’t seem revolutionary, but I can think back to Geometry lessons I’ve taught in my first few years of teaching where I was trying to get students to solve for a missing side in a right triangle using trig ratios and I could not for the life of me figure out why it was so difficult for them. I kept reviewing the process with them, getting them to label the adjacent side, opposite side, and hypotenuse and asking scaffolded questions like “What sides do you have?” “What trig ratio relates those sides?” and so on. Had I allowed more time for students to explain their thinking to me and articulate what they do understand, I could have made more clear connections between their current thinking and where they were headed.

When we teach without having students share their thinking, we treat students as blank slates that simply receive information, instead of as sense makers that come to us with their own understanding, prior knowledge, and experiences. By not drawing on what students already know and understand, I was actually losing a lot of time, because I would try to re-explain the whole lesson to struggling students instead of focusing on the key elements they were missing. I remember a time when I gave a beautiful 10 minute soliloquy about how the derivative gives us information about the original function, and after patiently listening to me ramble the student said, “Yeah, I get all that, what I don’t understand is [insert incredibly small technical detail I could have explained in less than 10 seconds].”

### Using assessing questions to promote equity

We don’t just elicit students’ ideas so we can evaluate them and put a mark in our mental or physical gradebook. We invite students to share their thinking to honor their voice and help them see themselves and be perceived by others as people that can know and do mathematics.

Assessing questions are used to draw out students’ thinking about a problem and prompt them to explain their reasoning. The key posture of the teacher is one of curiosity, coupled with a belief and expectation that students come to us with ideas and experiences that we can leverage to build new knowledge. This is critical to the work of equitable teaching.

I once did an exercise with other teachers where three people in the group acted as students working on a task and the fourth person played the role of the teacher. The catch was that the only interaction the teacher could have with the students is to ask assessing questions. Now this was an exercise, of course; in our classrooms we do want to mix assessing and advancing questions. But exercises help us practice skills in isolation before we have to incorporate them into more complex coordinated behaviors. We have to practice staying in a state of curiosity for a little while longer than we’re comfortable with. The goal of this exercise was to not only learn how to come up with assessing questions and use them in the moment, but to notice our strong inclination to use advancing questions instead of unpacking what students are already thinking about. Our students are not blank slates. When students say they “have no idea,” that’s simply not true, and it’s our job to help them see that.

### My go-to assessing question

There are some assessing questions that are specific to the particular approach you noticed the group use. But there are also generic questions that you can use on any day, with any lesson, whether the group is struggling to get started or already has some ideas on the table. The question I pull out every day is a simple “What are you thinking so far?” I have never had a group respond with “nothing” even if their paper is blank. This question is best asked once students have had at least 5 minutes to look at and begin the task. If you ask assessing questions at the beginning, there will be mostly blank stares because they just finished reading the question. If that happens, you should leave and tell them you’ll be back later to hear their ideas. Don’t stick around to help them parse out a solution path, because they need the opportunity to brainstorm some ideas that may or may not be worthwhile instead of feeling the urge to use the approach they think you’re looking for (students have a 6th sense about these kinds of things). As much as we tell them that we appreciate their rough-draft thinking and are just here for the ride, students act differently when the teacher is in proximity. It’s true. Other assessing questions are “Can you tell me what you’re thinking about?”, “What have you noticed so far?”, “What have you figured out so far?”, “Can you explain your approach to me?” or simply “Tell me more.”

Taking time to listen to and understand students’ thinking has not only made my classroom more student-centered but it has also genuinely increased my joy in teaching. Now when I start the school year I tell students that I’m excited to have them in class and learn about their thinking. And I mean it.

I love this, I call these diagnoses questions. I use many analogies for teaching and in these “help incidences “, I use the analogy as doctor is to patient, so too a teacher is to a student. None of us would let a doctor work on/with us without them diagnosing us, in a similar matter we would want our own teachers to diagnose us. If you ever want to collaborate,I have a 2 part workshop on these practices. I love your ideas and it’s create to find more spirit teaching family out there.

Thanks for this post! I have scribed for students with disabilities during state exams. Sitting there and simply having to write everything they tell you (without being able to offer any suggestions) is worth more than a lifetime of professional development hours.

During remote learning last year, I used Zoom exams at the end of each Calculus unit. Students had 15-minute time slots and had to answer and explain three MC questions. I found I learned much more about their understanding during these sessions than I did from exit tickets or problem sets. I was lucky to have a small class, but I will work on ways of implementing this idea on a larger scale.