Using Diagnostic Interviews to Understand Students’ Math Thinking

From the Marshall Memo #448

In this Teaching Children Mathematics article, Thomas Hodges, Terry Rose, and April Hicks recommend periodically doing a few individual student interviews in which teachers ask a series of diagnostic questions to understand students’ misconceptions and inform instruction. Here is their suggested protocol:

• Select an assessment task or a short sequence of tasks that highlight students’ conceptual and procedural fluency with the selected topic.
• Ask questions that elicit students’ understanding of the topic, following up as needed –  for example: Can you explain what you were thinking? What did you do first? How did you decide to do that? Tell me why…
• Document students’ explanations and understanding of the assessment task, including brief descriptions and sketches of the manipulatives, pictures, symbols, and language used.
• Collect any written work done by the student as additional evidence.
• Try to avoid the following: Teaching, remedying, or correcting students’ errors; restating students’ responses in another way (“So, what you’re trying to say is…”); and giving value to students’ responses (“Great job!”). 

“Interviews as RtI Tools” by Thomas Hodges, Terry Rose, and April Hicks in Teaching Children Mathematics, August 2012 (Vol. 19, #1, p. 30-36), 

http://www.nctm.org/publications/article.aspx?id=33737