# Resource Library

#### Statistical Topic

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• ### Poem: WON OVeR

"WON OVeR" is a poem by Lawrence Mark Lesser from The University of Texas at El Paso. The poem was written in 2022 and originally published in the January 2023 Journal of Humanistic Mathematics.  The poem highlights the unexpected occurrence of the constant 1/e in two classic probability problems:  “secretary problem”/”marriage problem” and “hats derangement problem”.  The poem could be used either to motivate students to learn about those particular problems or to cap things off after working through them.

• ### Cartoon: Control Groups

A cartoon to teach the need for a good control group in research studies. Cartoon by John Landers (www.landers.co.uk) in 2003 based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites. The cartoon's caption is similar to one by American cartoonist Peter S Mueller that depicts a control group and an "out of control" group that was produced independently a few years before this one.
• ### Poem: Statistical Anomalies becoming the Norm

A climate change related poem describing the numerous record temperature values being set (expressing that as unusual under a model of no overall warming but the norm in reality).  The poem was written by author with pen name Anubis the Philosomancer in July 2013 and posted on the poetry website hello poetry.com

• ### Poem: Lottery Strategy

This limerick was written April 2021 by Larry Lesser of The University of Texas at El Paso to be used as a vehicle for discussing probabilities and expected values involved in playing a typical pari-mutuel lottery.  The limerick was also published in the June 2021 issue of AmStat News.

• ### Poem: Simpson's Paradox

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 Simpson's Paradox.  The limerick was also published in the June 2021 Amstat News.

• ### Song: Bayes! (You're the One for Me!)

Song celebrates Bayesian inference, includes verbal form of Bayes theorem. The lyrics were written by David Blackwell, University of California at Berkeley. May be sung to the tune of "Who (Stole My Heart Away)?" (Jerome Kern).  The audio was produced by Nicolas Acedo with vocals by Abeni Merriweather, both students in the Commercial Music Program at The University of Texas at El Paso.

• ### Song: Divvy up the Stakes

A song about the Problem of Points, whose discussion in the 17th century led to the foundations of probability theory and expected value.  The lyric was written in 2017 by Lawrence M Lesser from The University of Texas at El Paso and may be sung to the tune of the Sting #1 1983 Grammy-winning hit “Every Breath You Take”.  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.

• ### Song: Means Will Follow You

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

• ### 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.

• ### Cartoon: The Lottery

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.