Triadic interaction in clinical task-based interviews with mathematics teachers

A clinical task-based interview can be seen as a situation where the interviewer– interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to increase procedural replicability of the interview and accuracy of drawn conclusions about the interviewee’s thinking process. Excerpts from interviews with 25 inservice mathematics teachers working on a task to make up a problem whose solution requires division of two fractions are discussed. The excerpts illustrate the relationship between methodological decisions taken by the interviewer during the interview and the applicability of the interview output to the research questions. A divergent analysis of the interviews with these teachers, which spanned over two years and were conducted by four interviewers, is used to offer a framework for analyzing data collected in clinical task-based interviews.