One of my favorite things to do as a math specialist is clinical interviews. During a clinical interview, I sit down with a student — one-on-one — and ask questions that help reveal some deep mathematical thinking. I cannot think of a better practice to help me prepare for student learning experiences. Without fail, at the end of the thinking I felt like I knew more about the student, but also more about the mathematics and about teaching.
Learn about “Ali” in Presuming Competence: Using Clinical Interviews to Support Classroom Instruction (Nov. 13, 2018)
Learn about “Eduardo” in What does it mean to be “struggling” in math class? (Eduardo’s Story) (Feb. 5, 2019)
Interviews are one of those practices that I refuse to give up, even during a pandemic when logistics… well, are forced to change.
This year, I am sixth grade classroom teacher. A few times, I tried to arrange one-on-one interviews with students, but several of the students did not return to my zoom channel at the agreed upon time. (I don’t blame them for having a healthy dose of skepticism.) I would love to interview all of my students, but how?
So we tried something new: our first round of Flipgrid video interviews. (These are actually from December, but, well, I’m backlogged with blogging.)
We were studying rates and unit rates. I wanted to know more about how students think about problems about our current work, but also some connected ideas, like dealing with fractional parts and also multiplication and division of larger numbers.
There are a number of different clinical interview protocols I have used in the past. Some of them ask students to complete the tasks mentally. (Marilyn Burns’ Math Reasoning Inventory; New Zealand Numeracy Project’s Global Strategy Stage Assessment, or GloSS; Kathy Richardson’s Assessing Math Concepts series.) Other interviews suggest that students should work with a pencil in hand. (Michael T. Battista’s Cognition-Based Assessment & Teaching series.)
I decided that I wanted to hear students talk about their thinking, so I selected questions from the GloSS. The questions from the GloSS spiral across three domains. First, a question about addition/subtraction is asked, followed by a question involving multiplication/division, and lastly one that asks students to engage with fractions or ratios. As much as I would love to hear all of that student thinking, I know that realistically students would struggle with filming video responses for 20 questions, and, more importantly, I would struggle with watching 20 videos for each of 75 different students. When I conduct the interviews in person, I also decide where to stop and end. There’s an art to it. Posting and requiring questions strips away some of my ability to use my professional judgment.
I posted five questions from the New Zealand Numeracy Project’s GloSS interview: 4 from fractions/ratios, and one from multiplication/division. I adapted a few contexts: changed names, some minor details, and some pronouns (to include a character that uses they/them).
In a secondary school context, assignments often get grades. Students should get full credit for explaining their thinking on a problem, full stop. The goal of the exercise isn’t to get the problem right so much as it is to reveal mathematical thinking.
I posted the link for students, and modeled how to access all 5 interview questions. I showed them some features, like how to write on the screen to annotate their own thinking, and, for the camera shy, how to record without their video. (I was pleasantly surprised with how many students who typically camera off on zoom decided to record their math interviews with their cameras on! Almost everyone showed their face, in fact.)
I set the videos on flipgrid to be ‘moderated,’ so that they don’t post publicly for the class. Only the student and I can see their interview videos, unless the student wants to share.
Students worked on these interviews over the course of two half-periods.
Here are a few samples from students who blocked their faces. (All student names are pseudonyms.) These responses are all addressing Question 2:
Maya picks 6 boxes of raspberries in 18 minutes.
If Maya is picking at a constant rate, how long does it take Maya to pick 2 boxes of raspberries?
“I said that she can pick two boxes in six minutes, because if you divide 6 by 3 you get 2, and if you also do the same to the 18 you’ll get 6.”
Violet is thinking proportionally. She went from a rate of 6 boxes in 18 minutes to 2 boxes in 6 minutes by performing the same operation on both numbers. She chose to divide by a whole number.
“We want to find how long it’s going to take Maya to pick two boxes. It says that Maya can pick six boxes in 18 minutes, and 2 is 1/3 of 6. That means we have to divide 18 by 3, in order to get 1/3 of 18, which is 6. It takes Maya 6 minutes to raspberries.“
Ngoc’s process is similar to Violet’s. He demonstrated a flexible understanding of how 1/3 of a number can be found by dividing that number by 3. (We worked on this a lot during number talks.)
“So for this question I got 6, because first I had to figure out how long it would take her pick up just one box. So I had to do 6 divided by 18 — I mean, sorry — 18 divided by 6 and I got a 3. And I doubled 3 because it says 2, so I had to double it and I got 6.“
Tali calculated a unit rate, and then scaled it back up. She explained why she was performing the operations, and had a beautiful self correction when she realized she was misstating what she did.
“If Maya picks six boxes in 18 minutes, then she will be picking 2 boxes in 6 minutes, because we know that she picks six boxes, so in 18 minutes, we’ll figure out how many boxes she picks in how many minutes. So for 1 box, it will be 3 minutes. Then we know how much 2 boxes is, so we time this by 2, which will be 2, and this one will be 6.”
Grace also found a unit rate. She showed it on a table, and moved vertically down the columns.
Reflecting on the Process
I loved watching my students talk about their thinking! We have class discourse, and students produce written work, but this sort of oral explanation felt different. Most oral communication is synchronous. Here, it was not only asynchronous, but students had the ability to plan a little before recording. I plan to revisit flipgrid interviews again soon.
Students expressed that this was a nice change of pace. “I wouldn’t want to do it every day, but it’s fun for a day or two! I felt very independent,” one student told me.
A colleague mentioned that these short videos would work well in student portfolios, too.
It doesn’t have the same conversational tenor as an in-person clinical interview, nor did it allow me to probe their thinking in the moment, but it served as a reasonable facsimile for my 75 remote students. I can envision using flipgrid interviews even when I return to in-person teaching.