Before this assignment I had never done a student interview, so my first goal was to find a couple resources that would help me. I used NRICH to search for challenging problems to give the students I would be interviewing. One of my favorite problems that I found was called What's it Worth. Even though I did not end up using this problem for my interviews it was one that I seriously considered. Then I found a Student Interview article that gave a lot of great guidance on interviews including questions to ask the students, what to look for, and math problems to use.
I ended up giving all of my students the same interview question. Initially I was going to give them a choice of a couple problems but then I realized that I really wanted to be able to compare the thinking of the students I interviewed. I thought the best way to do this was by giving them the same problem. One of the problems that I found in the Student Interview article aligned with what the students had been doing in class. This is the problem that I ended up choosing:
A restaurant has square tables. Four people can sit at 1 table. Six people can sit at 2 tables. Eight people can sit at 3 tables. How many people can sit at 37 tables?
Before I started my interview I wanted to decide what I wanted to look for while the students were working on their problems. I made a list of things I would be happy to see in the students work.
My List of Awesome Mathematical Modeling:
-Table of Values
-Recognizing a Pattern
I am not going to lie, I was very nervous to do these interviews at first. I was worried that I would not know what to ask the students while they were working on the problem. So again I went back to the Student Interview article and I found an AWESOME list of non-leading questions that I could ask during my interviews.
My List of Awesome Non-Leading Interview Questions:
What do you predict will happen?
Can you solve it in a different way?
How did you figure it out?
Why did you______?
You wrote ______. How did that help you?
I noticed that you stopped what you were doing just now. What were you thinking?
I don't know what you mean by that, will you show me?
Will you draw a picture of that?
You started with _____ and then went to ____. Tell me your thinking.
Can you tell me what ______ means?
Are you right? How do you know?
Is there another way to show me? What is it?
Are there things that you already know that would help you solve this problem?
I was overall very pleased with the way that my interviews went. Two of the three students I interviewed used a table, a picture, and an equation to represent their work. All three of the students identified the pattern (increases by two) in the tables. While only one student had a correct final answer, one other student just made a mental math error that resulted in an incorrect solution.
The most interesting interview was with my second student. This student did not use tables or an equation to model their thinking. They thought about the problem as adding "sets" of tables. During the interview I was confused why they took this approach, because I knew they had done problems similar to this in class. So then once the interview was almost finished and the student had given me their final solution, I asked them to draw what they thought the tables in this problem looked like. More specifically I asked what they thought "8 people can sit at 3 tables" meant. The student then drew 3 separate tables all with 8 people sitting around the table. Suddenly I realized why I was so confused! I had not stated in the problem that the tables were end to end, so this student thought that 3 tables meant 3 separate tables. If I would have asked this question sooner, I would have explained to the student that I meant for the tables to be end to end. Maybe by doing this the student would have solved the problem using a different method. Here is the work of the three students that I interviewed.
I learned a lot from conducting these interviews. I now have a couple resources that have great problems that I can use in my classroom someday, and a list of great questions to ask students while they are working on these problems. The biggest take away I have from this assignment is learning the signs of when a student is struggling and when a student in confident in their work. I noticed that when a student did not feel comfortable with what they were doing they normally slowed down their work, looked to me for validation, or talked quietly to themselves. When one of the students was showing me one of these signs I tried to find a question on my list that could guide the student. Interviews like this could be very valuable to the teacher because by the time the interview is over the teacher will know exactly what their student knows and what they don't. The biggest drawback? Finding time in your plans to do interviews like this.