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  • A cartoon to spark a discussion about the normal equations in the matrix approach to linear models.  The cartoon was created by Kylie Lynch, a student at the University of Virginia.  The cartoon won first place in the non-song categories of the 2023 A-mu-sing competition.

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  • A cartoon to teach about the graphical displays of discrete data - especially using bar charts. Cartoon 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.Cartoon was revised in March, 2023 to include a histogram amongst the graphs on the wall.

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  • A song to discuss how a confidence interval made for a population parameter will be biased if the sample is biased (e.g. starting with a random sample of n=100 but then having individuals drop out one at a time based on a non-ignorable reason).  The song was written IN MARCH 2019 by Lawrence Lesser, The University of Texas at El Paso, and Dennis Pearl, Penn State University, using the mid-20th century recursive folk song "99 Bottles of Beer." The idea for the song came from an article by Donald Byrd of University of Indiana in the September 2010 issue of Math Horizons where he suggested using the song for various learning objectives in Mathematics Education.

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  • This limerick was written in April 2021 by Larry Lesser of The University of Texas at El Paso to be used as a vehicle for​ discussing the issues and pitfalls of using .05 as a bright-line threshold for declaring statistical significance, in light of ASA recommendations.  The poe was also published in the June 2021 AmStat News.

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  • A song to aid in the discussion of the meaning and interpretation of p-values and type I errors. The song's lyrics were written in 2017 by Lawrence Lesser from The University of Texas at El Paso and may be sung to the tune of the 1977 Bee Gees Grammy winning hit "Stayin' Alive." The audio recording was produced by Nicolas Acedo with vocals by Erika Araujo, both students in the Commercial Music Program at The University of Texas at El Paso.

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  • A song satirizing the use of fixed significance level hypothesis testing.  The song was written by Dennis K Pearl from Penn State University.  Lyrics may be sung to the tune of the Beatles 1967 hit "When I'm Sixty-Four." (Paul McCartney wrote the song in 1958).  The audio recording was produced by Nicolas Acedo with vocals by Alejandra Nunez Vargas, both students in the Commercial Music Program at The University of Texas at El Paso.

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  • Song about the use of the Mann-Whitney U statistic (also known as the two sample Wilcoxon statistic). May be sung to the tune of "I Will Find You" by Peter Hammill; Fie Records, 1991. The audio was produced by Nicolas Acedo and sung by Jorge Baylon, both students in the University of Texas at El Paso Commercial Music Program.

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  • A song describing how sample means will follow the normal curve regardless of how skewed the population histogram is, provided n is very large.  The lyrics were written by Dennis Pearl and Peter Sprangers, both then at The Ohio State University.  The audio recording was produced by The University of Texas at El Paso student Nicolas Acedo who also performed the vocals

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  • A song to introduce the basic idea of using simulation to calculate a P-value for a randomization test (by simulating lots of group assignments and seeing what proportion of them give more extreme test statistics than observed with the actual group assignments).  The lyrics were written in November 2018 by Larry Lesser from The University of Texas at El Paso and Dennis Pearl from Penn State University. May be sung to the tune of the 1980 number #1 song “Celebration” by Kool and the Gang. Audio of the parody was produced and sung by students in the commercial music program of The University of Teas at El Paso.

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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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