Student Mathematics Concept Interview: An Assessment Strategy

In order to plan effective mathematics instruction, you will need to know how to assess your students' knowledge and understanding of particular mathematics concepts. One way to assess students' thinking is in an interview setting. Student interviews are an authentic assessment strategy.

This assignment will give you some experience in conducting an interview to assess a student's understanding of a particular mathematical concept. If you are observing a mathematics classroom during your initial field experience, you may want to select a “rich” problem out of their text or “jump” ahead to a topic in their mathematics curriculum that have not yet been covered in class – the latter are often referred to as “novel” problems because they are new to the student and solving them requires the student to make connections to concepts previously learned in class. Pick a problem that requires the student to think mathematically, conceptually, and draw on their prior knowledge and experience in order to solve. Consider this problem a “baseline.” If your baseline problem proves too difficult or too easy for the student, have alternative problems (one easier, one more difficult) available to use instead.

Conducting the Interview

1. If possible, audiotape the interview. Recording allows you to concentrate on the student's actions during the interview and enables you to play back the interview when writing the report.

2. Conduct the interview in a quiet place away from distractions.

3. Read the entire problem to the student. If the student does not understand the problem, read the entire problem again before providing any pieces of information.

4. Have paper and pencils available if the student wants to use them. Do not force the student to use these materials. In some instances I have interviewed a student and found that they cannot work without calculator. Sometimes a student may be so dependent on a calculator that he/she become upset if one if not available to use. I usually keep a calculator in my bag, out of view of the student. If they ask if they can use one, or indicate that they are unable to solve the problem without it, I will allow its use.

5. Take notes about the student's actions (e.g., use of calculator, counting on fingers, drumming or tapping, etc.) during all phases of the problem solving (i.e., anything that will not be captured on the audiotape but provides clues for your interpretation of the student's solutions).

6. Encourage the student to articulate his/her thinking. The interview can be interactive, but it is not an occasion for instruction. The goal is for the student to show you what he/she can do with the tasks you present. If a student is interested in learning how to solve a particular problem, I will assist them with that at the conclusion of the interview.

7. Ask questions that will further your understanding of the student's work. For example, you might say:

• Would you tell me what you were thinking as you solved the problem?
• Would you tell me about the diagram you drew?
• How did you figure that out?
• Why is that important?
• How did you reach that conclusion?
• How would you explain your solution to the rest of the students in your class?

8. If the student says something like “I just guessed,” or “I just knew it,” ask, “Why does that answer make sense to you?” and follow up with, “I'm very interested in the ways you think about the problems.” I often encounter students who tell me they knew that their answer was right because they “felt it inside.” Experiment with cultivating an open and neutral tone of voice that makes you sound interested, not challenging or threatening.

9. If the student cannot solve your baseline problem, reassure them that is “ok” and move on to the “easier” problem you prepared. If the child solves the baseline problem easily, pose the “more difficult” one.

10. If the student asks you for confirmation that his/her solution is correct, initially maintain a neutral demeanor and ask, “Does it make sense to you? Why?” Being neutral does not mean that you are mean or cold— you can seem supportive and interested without conveying what you think about the correctness of his/her thinking. My personal belief is that every occasion, even an interview, is an opportunity for learning so I will confirm the student's solution at the conclusion or the interview or offer assistance in finding the correct solution.

11. If the student has struggled throughout the interview, you might want to close with a problem that you are fairly confident that the student can solve.

Things to think about as a future teacher of mathematics:

• Were there unspoken assumptions that guided your actions?
• Based upon the information you gathered during your interview, did you learn anything that will assist you in making decisions for future instruction?
• What might you do differently the next time you interview a student?
• What did you learn about yourself as a teacher who is learning about students' understandings of mathematics?