Framing a Classroom Intervention Study in a Middle-School Algebra Environment

Abstract

It has become a tradition in the field of mathematics education that before a researcher outlines the research design for a study, he or she should outline a theoretical framework for the investigation which is about to be conducted. Then, after research questions are stated, and the design of the study is described, the investigation takes place. The data gathering, data analyses, and interpretation are guided by the theoretical framework and conclusions are couched in terms of, and seen in the light of, the theoretical framework. There are many mathematics education researchers who regard this theory-based process as sacrosanct, as absolutely essential for high-quality research. In the first part of this chapter it is argued that the traditional “theoretical-framework” process just described is flawed, that it can result in important aspects of data being overlooked, and that it can lead to incorrect, or inappropriate, conclusions being made. It is argued that the first thing that needs to be done in a mathematics education research investigation is to identify, in clearly stated terms, the problems for which solutions are to be sought. Having done that, historical frameworks—which have only occasionally been taken seriously by mathematics education researchers—should be provided. Then, having identified the problems and having provided a historical framework, a design-research approach ought to be adopted whereby a theory, or parts of a theory, or a combination of parts of different theories, are selected as most pertinent to the problems which are to be solved. This chapter identifies three main problems: (a) “Why do so many middle-school students experience difficulty in learning algebra?” (b) “What theoretical positions might be likely to throw light on how that problem might be best solved?” (c) “In the light of answers offered for (a) and (b), what are the specific research questions for which answers will be sought in subsequent chapters of this book?”