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Teaching Methods

  • 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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  • The Numbers Guy examines numbers in the news, business and politics. Some numbers are flat-out wrong or biased, while others are valid and help us make informed decisions. Carl Bialik tells the stories behind the stats, in daily updates on this blog and in his column published every other Friday in The Wall Street Journal.
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  • Using cooperative learning methods, this activity helps students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. This lesson also helps students to discover that the standard deviation is a measure of the density of values about the mean of a distribution. As such, students become more aware of how clusters, gaps, and extreme values affect the standard deviation.
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  • This website is a resource of teaching methods and approaches that instructors at all levels of statistics education can use to generate student interest in pursuing more study or a career in the field of statistics.
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  • This case study discussess methods to successfully adapt graduate-level statistics courses for the online environment. Using small-group discussion assignments is not only a great way to create an interactive learning community; it also provides instructors with valuable information about students' reasoning.
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  • This page calculates either estimates of sample size or power for differences in proportions. The program allows for unequal sample size allocation between the two groups.

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  • The following exercise can illustrate the problem of bias in estimators to students in statistics courses. In some advanced courses an alternative estimator may be presented and properties of this estimator may be investigated via Monte Carlo studies.
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  • A specially-designed statistical literacy course is needed for college students in majors that don't require statistics or mathematics. This paper suggests that key topics in conditional probability, multivariate regression and the vulnerability of statistical significance to confounding should be included and presents some new ways to teach these ideas.
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  • This paper presents three graphs that are used in teaching students majoring in business and the humanities. These graphs show the influence of confounding, the meaning of statistical significance, and the influence of confounding on statistical significance.
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  • This paper presents rules for determining whether an index variable in such a table is part or whole depending on whether the associated margin value is an average, a sum or a 100% sum. Tables with missing margin values -- date-indexed tables, half tables and control tables -- are analyzed. Recommendations are made to improve reader understanding of any table involving rates or percentages.
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