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  • 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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  • A cartoon to teach ideas of elementary probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University) in 2008. Free to use in the classroom and on course web sites.

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  • A cartoon to teach ideas of conditional probability. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University) in 2008. Free to use in the classroom and on course web sites.

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  • A cartoon that can be used in teaching about the efficiency of using simulation in statistics. Cartoon 2006 by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.

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  • A quote from popular fiction that might be used in a discussion of conditional probability. The meaning of the phrase "ninety-eight percent more likely" is also good fodder for class discussion as students might confuse its interpretation between a 1% chance becoming 99% or becoming 1.98%. The quote is by American author Jennifer E. Smith (1980 - ) from her book "The Statistical Probability of Love at First Sight."

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  • A haiku poem that uses a fortuitous numerical fact about a birthday probability that can launch discussion of the "68-95-99.7 rule" and how 99.73% of values are within 3 standard deviations of the mean for a normal distribution. Here 364/365 ≈ 0.9973 (365/366 is the same out to four decimals so this also applies to leap years).  Students can also recognize that birthdays do not follow a normal distribution, but approximately a uniform distribution (so that the approximate chance that two people have different birthdays is about .9973) . The poem was written by Lawrence Lesser from The University of Texas at El Paso in February, 2021.

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  • A limerick to teach the inclusion-exclusion rule for finding the probability of the union of two events.  The poem was written by Marion D. Cohen from Drexel University and published in the January 2021 issue (vol 11 number 1) of the Journal of Humanistic Mathematics.

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  • A limerick to teach the addition rule for finding the probability of the union of disjoint (mutually exclusive) events.  The limerick was written by Marion D. Cohen from Drexel University and published in the  January 2021 (vol. 11, issue 1) Journal of Humanistic Mathematics.

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  • Regression to the Mean is a 2009 poem by Andrew Porter of Wirral, England. The poem can be used in teaching about regression to the mean and the regression fallacy. Free for use in non-profit educational settings. A video featuring the poem being read aloud is at https://www.youtube.com/watch?v=D66I36fksZA

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  • A cartoon with a neat double pun that can be a nice vehicle to discuss how the expectations of non-linear functions of a random variable is not the same as the function of the expectations. The cartoon was used in the February 2019 CAUSE cartoon caption contest and the winning caption was written by Joseph Gerda from College of the Canyons. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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