Math Interviews: Uncovering Students’ Math Stories

In recent years, there has been a growing awareness within the math education community about the benefits of individual math interviews. And, there is an even broader awareness of the importance of building mathematical strength, confidence, and joy during early childhood. We know that having a one-on-one conversation with a student about mathematics can yield much more information than traditional forms of assessment. And, it’s rare to find a child who doesn’t enjoy the attention they get from uninterrupted quality time with their teacher. We do individual reading assessments, why not for math? 

 

Assessment in Development

During the past two years, the team at Math Transformations has been developing an asset-based assessment that uses math interviews to uncover students’ math stories. The goals of UncoverMath, our math interview instrument, are to find out what students CAN do as they share their numeric reasoning, support teachers to notice and leverage student strengths, and report the findings through a strength-based lens. We are grateful for the grant funding from the Heising-Simons, and Silver Giving Foundations that have supported this development. 

Teachers and administrators at Baker Elementary, Horton Elementary, and the Global Vision Charter Academy have been gracious and enthusiastic, sharing their classrooms, students, and expertise, as we work together to pilot math interviews that…

• Focus on what students CAN do 
• Immediately serve to guide math instruction
• Tap into students’ interests and backgrounds
• Incorporate students’ language needs and preferences
• Support teachers in noticing numeric reasoning strengths and identifying how to build on them
• Connect to the Standards and district reporting
• Use student mistakes as learning opportunities that can yield valuable information
• Evaluate students’ ways of thinking, accuracy, and ability to communicate

UncoverMath is our TK-2nd grade online math interview application, which teachers use to guide in-person one-on-one interviews, capture their strength-based observations, generate reports, and guide next instructional steps. The Uncover Math app includes reports for teachers, administrators, and families that sum up what the assessment reveals about student learning and will provide recommendations to the teacher for next steps in instruction.

 

A Sample Interview

I recently interviewed Jorge, a second grader at Baker Elementary. In this post, I’ll share two of the questions I asked him from one of the interviews. The following questions, responses, and reflections will provide you with a glimpse of how UncoverMath works. The examples will also show how UncoverMath can reveal students’ strengths, especially those who might think outside the box, or for second language learners whose math abilities may not be apparent. 

To establish rapport and create an informal, safe environment I began the interview by asking Jorge about his lunch and chatting about school. I told him I was interested in his math thinking. Then I asked my first question, guided by easy-to-follow instructions from the UncoverMath website. I kept track of his ways of thinking and accuracy using the website’s different options. 

 

How Many Groups of Ten?

For this math question, I poured a pile of Color Tiles onto the tabletop. “There are twenty-six tiles in this pile,” I said. “Can you please write the number 26 on the small white board?” 

After Jorge wrote down the number, I asked him the following question to test his knowledge of place value. “If I put these 26 tiles into groups of ten, how many groups would there be? And will there be any leftovers?” 

Jorge immediately said, “One!” 

“Will there be any tiles leftover?” I probed. Jorge thought for a moment, and then said, “Fifteen?” 

At first, Jorge’s answers really stumped me. Based on his responses, it seemed that he wasn’t making the connection between the digits in the number 26 and the tiles. Did he not understand that the 2 in 26 means 2 groups of ten and the 6 means six extra? But when you think about it, there really is one group of ten in 26 and 16 leftovers (Jorge’s ‘15’ was just one off). It’s just another way of looking at it. Had Jorge been taking a paper pencil test, he would most likely have gotten this question wrong. But during a one-on-one interview, teachers have the opportunity to reflect on the students’ responses in real time. 

In hindsight, I wish I would have asked Jorge about the digits in 26. I might have asked him what the 2 means and what the 6 means in the number. I might also have asked him about the one ten and 15 extras. “If you have 15 extras, can you make another ten?” This would have given me even more information about his understanding of tens and ones. I’m finding that the more I practice interviewing the more I learn and the better I get at it. 

Jorge’s responses to this question are examples of the surprises that often happen when teachers interview their students one-on-one and when the focus is on listening and looking for what students CAN do. 

 

How Many Goldfish Crackers Do You See?

One of my favorite questions in this interview is the goldfish cracker problem. We noticed that when students are given contexts that are familiar or interesting, they perk up and engage. “What’s your favorite snack? What’s your favorite animal? Can you count these buttons? Let’s play this game! Let’s figure out this puzzle!” All these contextualized challenges make for a joyful assessment experience for students.

For the goldfish cracker problem, I showed Jorge the following picture and asked, “How many goldfish crackers do you see?”

Photo Credit @bedtimemath

Jorge quietly stared at the goldfish for several seconds before answering, “Fifty-one” (there are 55). 

“Can you show me how you figured it out?” I asked. 

“I was counting in my head,” Jorge responded. 

“Can you show me how you counted?”  

“I counted by ones,” he said. 

“Can you show me?” I prodded. 

Jorge started this time counting by tens till he got to forty, then he seemed to second guess himself and went back to counting by ones. It was interesting listening to him count aloud by ones because he consistently left out all the sevens. For example, he would count 21, 22, 23, 24, 25, 26, and then skip to 28. He did this for every decade which caused him to end up with a total of 59 goldfish crackers. 

When he was finished counting, I said “I noticed that you were counting by tens at one point, did you notice that?” He nodded. 

“Can you try counting by tens again?” 

This time Jorge successfully counted by tens and then added on the extra five crackers to get to 55. 

“So, there are fifty-five goldfish crackers,” I confirmed. “How many more crackers do you need to get to one hundred?” 

Jorge got the answer of forty-five immediately, explaining that, “You need five more to get sixty and then forty more to get to a hundred.”

Once again, I was impressed by the information yielded from the interview.  And I wondered what impressions I would have had about Jorge’s math ability had I not probed a little to move past the soft spots in his thinking. Asking questions like, “How did you figure it out?” and “Can you show me?” opened a world of thinking, adding to my picture of Jorge’s math story. Jorge’s teacher shared that people tend to underestimate him due to his English language proficiency level and because he tends to be shy and quiet in class. But in this individual interview, Jorge’s strengths are apparent. 

 

Jorge’s Math Story

Uncovering a student’s math story is kind of like digging for buried treasure, especially if you’re looking for what a student CAN do. 

From the two questions in this post, together with the other items in the interview, I learned a lot about Jorge’s math thinking. I learned that Jorge is good at figuring in his head. Although he’s an English language learner, Jorge has strong communication skills in English. He can clearly explain his reasoning, regardless of some bumpy grammar and syntax. He effectively uses landmark numbers like 5 and 10 to reach answers. He can count by 10’s (and 11’s!) and uses this skill when figuring answers.

Jorge uses the relationship between addition and subtraction to solve problems. And he decomposes and recombines numbers without having to calculate when making sense of true and false number sentences. Jorge is a confident mathematician who is persistent and willing to change course and change his mind amid problem solving. I gleaned all of this in a 10–12-minute interview. 

 

We Do Individual Interviews for Reading, Why Not for Math?

Teachers, for good reason, worry about the time it takes to do individual interviews, and the effort it requires to make sure the rest of the class is engaged in meaningful, independent work. But the time and effort are worth it. We do individual interviews for reading because they yield important information about a student’s proficiency, and they serve to inform next steps in instruction. The same can happen for mathematics. 

Our asset-based math interviews are under construction, so stay tuned as we put the finishing touches on UncoverMath!

Finally, we want to thank and show our appreciation to those in the math education community, including Marilyn Burns, for their leadership and work around the importance of individual math interviews and their effectiveness. Many thanks!