3: Method

This chapter is concerned with research methods in mathematics education and, more broadly, with research methods in education writ large. As explained below, space constraints do not allow for the detailed consideration of individual methods, or even classes of methods. Hence I have chosen to address broad metatheoretical issues in much of the chapter, which is divided into three main parts. Part 1 provides an overview of the process of conducting and reflecting on empirical research. It examines the major phases of empirical research and some of the issues researchers must confront as they conduct their studies. A main thesis underlying the discussion in Part 1 is that there is a close relationship between theory and method. I describe the process of conducting empirical research and elaborate on how researchers’ theoretical assumptions, whether tacit or explicit, shape what they choose to examine, what they see and represent in the data, and the conclusions they draw from them. Part 2 presents a framework for evaluating the quality of research. In it I argue that research must be judged by at least the following three criteria: trustworthiness, generality, and importance. A range of examples is given to elaborate on the issues discussed in Parts 1 and 2. In Part 3 I try to bring together the general arguments from the first two parts of the chapter by focusing methodologically on a topic of current interest and long-term importance. As this Handbook is being produced, there is great pressure on educational researchers and curriculum developers in the U.S. to employ randomized controlled trials as the primary if not sole means of evaluating educational interventions. In an attempt to move forward methodologically, I propose and discuss an educational analog of medical “clinical trials”: the structured development and evaluation of instructional interventions. Part 3 offers a description of how the development and refinement of educational interventions might be conducted in meaningful ways, beginning with exploratory empirical/theoretical studies that reside squarely in “Pasteur’s quadrant” (Stokes, 1997) and concluding with appropriately designed large-scale studies.