ABSTRACT
This chapter considers one methodological aspect of qualitative research—the use of structured, task-based interviews in observing and interpreting mathematical behavior. Several scientific issues and their implications are discussed briefly, including: (a) the reproducibility, comparability, and reliability of observations; (b) the generalizability of research findings; (c) the importance of mathematical content and structures; (d) the role of cognitive theory in designing and interpreting interviews; and, (e) the interplay among task and contextual variables. In evaluating task-based interview methods scientifically, I argue against some claims that have been advanced in the name of epistemological schools of thought ranging from radical positivism and behaviorism to radical constructivism, social constructivism, and postmodernism. Finally, some broadly applicable principles and techniques are proposed for improving the quality of task-based interview research.
