Student Interview: Multiplication and Division

  1. For this interview, the student should be 5th or 6th grade.
  2. Interview the student. Set a friendly tone. Give student time to think deeply about the problems. Provide paper for students to illustrate the problem or manipulatives to represent the problem. Ask follow-up questions that reveal the underlying thought processes. Record all student responses and comments. You may want to tape record the interview.
  3. Write up the results using the template below.

Possible Multiplication and Division Interview Questions:

  1. Describe to me what this problem means: 7 x 4
  1. How would you solve this problem? (Make sure you show the equation horizontally and have the student solve it. The student can rewrite it vertically. )

34 x 15

  1. Describe to me what this problem means: 36 ÷ 9
  1. How would you solve this problem? (Make sure you show the equation horizontally)

1575 ÷ 25

  1. Try this problem without writing it down on paper. Tell me out loud how you did it.

30 x 12

  1. There are 609 students at a school. Candy canes are sold in packages of 6 for $.29. How much would it cost to buy each one a candy cane?

Multiplication and Division Student Interview Write-up

Introduction

Interviewer:

Student Interviewed: Pseudonym, age, grade and any other pertinent information about the student, andInformation about the interview setting.

Responses and Analysis

For each question asked explain

  • What you said and what the student said and did.
  • Your understanding of the child’s responses.
  • The implications of the student’s responses for future instruction.
  • How the child’s responses support what you have been learning about mathematics instruction.

Also include any student work/drawings.

Note: Avoid evaluative statements such as “she was really smart” or “she seemed slow.” Discuss what the student did instead. For example “When I asked her what 8 + 9 was, she solved it by saying ‘8 and 8 is 16, and 1 more is 17.’ “ Be thorough in describing the student responses and what it showed about the underlying cognitive processes.

Student Interview Rubric

General information about student and interview setting / Thorough / Mostly complete / Partly complete / Missing
4 / 3 / 2 / 0
Questions and responses / thoroughly described including both interviewee and interviewee responses / Mostly described / Partly described / Missing
5 / 4 / 2 / 0
Understanding and analysis of child’s cognitive processes / Clear description and analysis of child’s cognitive processes / Some description and analysis / Limited description and analysis / Missing
6 / 4 / 2 / 0
Implications for future mathematics instruction / Clear and thorough description of what should come next as far as instruction / Some description of implications / Limited description of implication / Missing
6 / 4 / 3 / 0
Writing conventions / All writing conventions followed (spelling, punctuation, sentence structure, paragraphs, organization, APA) / Most writing conventions followed / Some writing conventions followed / Few writing conventions followed
5 / 4 / 2 / 0
Student work / All work included / Some work included / Missing
4 / 2 / 0
Total / /30

Interview Tips:

Include possible questions that you will ask to follow up on the student’s response.Consistently use probes such as “Why?”, “How did you figure that out?”, “Whyis that important?” “Why did you do that?”, “How do you know?”, “How come?”Experiment with cultivating an open and neutral tone of voice that makes you soundinterested, not challenging.

If the student says something like “I just guessed.” or “I just knew.” ask, “Whydoes that answer make sense to you?” A further probe might be to ask if anotheranswer, which is clearly wrong but not to outrageous, would make a sensible “guess.”Experiment with avoiding validating the student’s responses by saying, “That’sright,” or “Good!” If you are feeling pulled to say something of this kind, try, “That’sinteresting.” If the child looks to you or asks directly for confirmation that his or hersolution is correct, maintain a neutral demeanor and ask, “Does it make sense to you?Why?” Being neutral does not mean to be mean or cold--you can seem supportive andinterested without conveying what you think about the correctness or “goodness” ofhis or her thinking.

Do not preface or interpret questions with comments like “This is a tough one.”or “Here’s one about rectangles.” If you feel the need to make transitions betweenquestions, try “Let’s move one to something else now.”If a student says, “We haven’t learned that yet, “ ask, “Can you figure out a way

to do it yourself?”Sometimes it may be useful to ask, “How would you explain your solution tothis problem to the rest of the students in your class?” or “What if someone said______(something different from what the student said but plausible)--what wouldyou say to him or her?”

Encourage writing and drawing. Try to make very careful notes as the child is workingthat describe what he or she is doing.