Chapter 2: Toward a Definition for Research

Abstract

"[Note: This abstract applies to all articles within this issue."] The chapters in this monograph describe qualitative research methods used to investigate students' and teachers' interactions with school mathematics. Each contributing author uses data from his or her own research to illustrate a particular technique or aspect of research design. The different chapters present a wide range of methods, representing a variety of goals and perspectives. Rather than a comprehensive reference manual, this monograph illustrates the diversity of methods available for qualitative research in mathematics education. The monograph begins with a discussion of key elements that contribute to the dynamic and evolving domain of mathematics education research. Background information is then provided that relates to the philosophical and epistemological assumptions underlying all qualitative research. In the chapters that follow, actual studies present the contexts for discussions of research design and techniques. Issues of research design include the importance of making explicit the underlying theoretical assumptions; the selection of an appropriate methodology; the interpretative, intersubjective nature of analysis; and the establishment of reliability and validity. Specific data collection techniques include clinical interviews, stimulated recall interviews, open-ended survey questions, and field notes and video or audio taping to record classroom events. Methods of analysis include participant validation, the categorization of data through constant comparison and software indexing and retrieval, phenomemographic analysis, and the identification of empirical examples of theoretical constructs. The monograph ends with a discussion of general issues, including the role of theory and the establishment of criteria for judging the goodness of qualitative research.