Using Statistics Effectively in Mathematics Education Research

Funded by the National Science Foundation, workshops were held over a three-year period, each with about twenty participants nearly equally divided between mathematics educators and statisticians. In these exchanges the mathematics educators presented honest assessments of the status of mathematics education research (both its strengths and its weaknesses), and the statisticians provided insights into modern statistical methods that could be more widely used in such research. The discussions led to an outline of guidelines for evaluating and reporting mathematics education research, which were molded into the current report. The purpose of the reporting guidelines is to foster the development of a stronger foundation of research in mathematics education, one that will be scientific, cumulative, interconnected, and intertwined with teaching practice. The guidelines are built around a model involving five key components of a high-quality research program: generating ideas, framing those ideas in a research setting, examining the research questions in small studies, generalizing the results in larger and more refined studies, and extending the results over time and location. Any single research project may have only one or two of these components, but such projects should link to others so that a viable research program that will be interconnected and cumulative can be identified and used to effect improvements in both teaching practice and future research. The guidelines provide details that are essential for these linkages to occur. Three appendices provide background material dealing with (a) a model for research in mathematics education in light of a medical model for clinical trials; (b) technical issues of measurement, unit of randomization, experiments vs. observations, and gain scores as they relate to scientifically based research; and (c) critical areas for cooperation between statistics and mathematics education research, including qualitative vs. quantitative research, educating graduate students and keeping mathematics education faculty current in education research, statistics practices and methodologies, and building partnerships and collaboratives.

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Richard L. Scheaffer and William B. Smith
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