Using Interviews to Gain Insight Into Students’ Math Thinking

As a math specialist, I’m used to relying on pencil-and-paper assessments to give me information about what math students understand. But I’ve come to realize something: They don’t always offer the full picture.

There is a growing body of research touting the benefits of conducting interviews with students, allowing educators to listen to student ideas and dive deeper into what a student understands about a certain topic.

Listening to how a student solves a problem or explains their strategy not only validates the student’s mathematical identity (“My teacher wants to hear what I have to say”), it also offers opportunities for follow-up questions that can reveal misconceptions that the student may have around a particular concept. This can help the teacher plan and determine next steps for the student.

Interviews do not have to be long and time-consuming. Conducting a five-minute fact fluency interview, as Jennifer Bay-Williams and Gina Kling of Math Fact Fluency suggest, allows you to determine which facts a student can recall automatically and what strategies a student might use, offering a better understanding of the student’s flexibility with numbers. Asking a student to explain how they would solve a computational task, as Marilyn Burns suggests as part of the Listening to Learn tool, might give you insight into how they approach a problem—something that might not be evident in a traditional pencil-and-paper assessment.

Once student interviews become common practice in the classroom, they can also feel less intimidating than formal tests and may allow students who have test anxiety to show more of what they know.

Listening more closely

Recording these interviews, with either audio or video, lets teachers review student thinking and listen again, perhaps allowing them to hear something that was missed in real time. The interviews also offer an opportunity for teachers to reflect on their questioning styles and techniques. It’s important to be intentional about any follow-up questions and to not be too leading when assessing a student’s understanding. Standard questions that can get students talking include “How do you know?” and “How did you decide?”

The following is an exchange I had with a student as I conducted an interview. Each time I asked them to solve a problem, I showed them the problem written horizontally.

Teacher: What is 596 plus 10?

Student: (automatically) 606.

Teacher: How do you know?

Student: Because the 9 is in the 90s place and plus 10 is 4, well plus 4 is 600. Then you minus this, which is 6, so 606.

Teacher: OK, let me just make sure I understand. Can you explain how you did it again?

Student: I took 4 from the 10 and put it there to make 600. Then there was 6 left so I put that back and it was 606.

Teacher: Thank you for explaining that again. I see your strategy now. Let’s try another one. What’s 400 minus 198?

Student: 302.

Teacher: How did you do it?

Student: 400 minus 100 is 300, and then 100 minus 98 is 2, so then 302.

Teacher: OK. I think I understand how you did that. What if I asked you, “What is 400 minus 102?”

Student: 398.

Teacher: How did you do it?

Student: So, I did 400 minus 100, and that’s 300, and then 100 minus 2 is 98.

Teacher: Thank you for explaining your thinking to me today. I learn so much from listening to students!

Using a voice memo tool to record this interview session allowed me to listen back to really hear what the student was saying. I needed to stop myself in the moment from trying to teach, and just allow the student to share their thinking and then make a plan going forward. From this interview, I can tell that the student has developed the “making tens” strategy for addition and can regroup place values efficiently when counting up. For this student, this strategy is not quite as developed with subtraction, and more work building these skills is a next step. It is interesting to note that the student accurately solved problems involving subtraction with regrouping by using the standard algorithm, so this interview revealed a blind spot that a pencil-and-paper task did not illustrate.

Adding opportunities for expression

If the idea of conducting one-on-one interviews seems daunting and time is limited, platforms such as Seesaw and Flipgrid allow students to record themselves completing a task. You can post a problem and ask students to record a video response explaining how they would solve it. You might be surprised about what you find. Students who struggle with writing may not elaborate on their mathematical thinking in journal format, but once the camera comes out, you open a door that allows these students to express themselves. As the videos are reviewed, teachers can provide feedback directly to the students, and then follow up by conducting individual interviews with certain students as needed.

Another benefit of these platforms is that you can share student videos with caregivers. This can strengthen home-to-school connections, offering evidence of how students are thinking about mathematical ideas and providing talking points to continue the math conversations at home. Students can also listen to other students’ strategies and ask questions or provide feedback. This can develop the mathematical community in the classroom, providing opportunities for students to learn from one another and feel heard. All we need to do is ask the questions and listen.