ABSTRACT
During the closing years of the 20th century, a number of books and articles were published describing the status of research in mathematics education and discussing possible ways to increase its usefulness (Romberg, 1992; Sierpinska & Kilpatrick, 1998; Steen, 1999). Most of these publications focused on summaries of past research, or, insofar as they shifted attention toward the future, they stated the authors’ views about problems or theoretical perspectives that (they believed) should be treated as priorities for future research. Should teachers’ decision-making issues be treated as higher priorities than the decision-making issues that confront policymakers or others who influence what goes on in classroom instruction? Should issues of equity be given priority over issues of content quality or innovative uses of advanced technologies? Should theoretical perspectives be favored (for funding, publication, or presentations at professional meetings) if they are grounded in brain research, or artificial intelligence models, or constructivist philosophies? Should quantitative research procedures be emphasized more than qualitative procedures (or vice versa)? My own prejudices about such issues are not central concerns of this paper. Instead, I’ll address the following question: “What kind of research designs have proven to be especially useful in mathematics education, and what principles exist for improving (and assessing) their usefulness, power, shareability, and cumulativeness?”
