This cartoon caption illustrates the idea that the normal approximation works better for larger samples. The cartoon was used in the April 2024 CAUSE cartoon caption contest and the winning caption was written by Grant Zou a student at the University of Virginia. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.
The Probability Song video is part of a series of musical summary reviews of different statistical and data science topics by Professor Rafael de Andrade Moral from Maynooth University in Ireland, including a set of three that won the grand prize in the 2021 A-mu-sing Contest.
The lyrics reviewing probability-oriented learning objectives were written and the video was produced and performed by Dr. Moral, while the music may be sung to the tune of Billie Eilish's 2019 hit “Bad Guy.”
This lyric written, performed, and recorded in 2018 by Larry Lesser (The University of Texas at El Paso) won honorable mention in the 2019 A-mu-sing contest. The song helps launch learning about permutations by showing how many ways n distinct objects can be ordered for the first non-trivial case (n = 3), modelling the systematic strategy of listing orderings in alphabetical order to make sure none are missed. (Before using the song, students can be asked for their prediction – many will say 3 or 9 instead of 6. After using the song, students can be asked to find the answer for n = 4, which is just small enough to generate by hand.) The song also introduces vocabulary (“order”, “permuted”, “sort”) commonly used in this context.
An honorable mention winner in the 2025 A-mu-sing Contest, “Bell Curve Areas” was written in 2024 by Lawrence Mark Lesser of The University of Texas at El Paso to give students a rough but aesthetically concise mnemonic (it “rings a bell”) for accessing approximate fractions of area under a bell curve between successive whole-number z-scores. (Students can use an applet or table to assess and discuss how good the approximation is, comparing the poem’s numbers of .3333, .1250, and .0200 to .3413, .1359, and .0214, for the normal distribution respectively.) More important than the convenience of a first-order assessment of answer reasonableness, this poem could be used to inform class discussions about confidence intervals because students often initially have the misconception that confidence is spread evenly throughout a confidence interval and the poem helps them realize there's more confidence closer to the estimate (since they'd know that 1/3 is much bigger than 1/8 which is much bigger than two percent. Finally, the final line of the poem recalls the common rule of thumb that a z-score greater than 3 is an outlier, as well as offering a vehicle to discuss hypothesis testing.
This poem (slightly revised from its publication in the January 2013 Journal of Humanistic Mathematics) was written by Larry Lesser from The University of Texas at El Paso. It is a vehicle to discuss equiprobability bias – the misconception that all outcomes must always be equally likely.
A cartoon that provides a good way to introduce the Law of Large Numbers using the negative expectation for games of chance at a casino. The cartoon was used in the March 2022 CAUSE cartoon caption contest and the winning caption was written by Rich Einsporn from the University of Akron. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.
A cartoon that can be used to discuss the appropriateness of the normal errors assumption in a variety of settings. The cartoon was used in the May 2021 CAUSE cartoon caption contest and the winning caption was written by Dashiell Young-Saver from the Knowledge Is Power Program Public Schools. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.
A joke for discussing the calculus prerequisite for an upper division probability course. The joke was written by Dennis Pearl and Larry Lesser in October 2022.
A song for teaching about the multiplication rule. Using the popular topic among young adults of relationships, the multiplication principle is memorably illustrated by having Paul Simon's #1 hit song (which states only a half-dozen ways to leave your lover, not 50) revisited to show 50 literal paths for ending a relationship: (5 reasons for the decision) X (5 methods to relay the decision) X (2 options for handling acquired stuff). The lyrics were written by Larry Lesser from The University of Texas at El Paso to the tune of Simon’s same-titled 1975 song. The audio recording features vocals by Abeni Merryweather and production by Abeni Merryweather from UTEP's commercial music program. The song tied for second place in the 2023 A-mu-sing contest.
The structure of the problem in the song is similar to Exercise 3 in the progressive curriculum sequence outlined in the Spring 2024 Journal of Mathematics Education at Teachers College article “A Problem-based Curriculum to Develop the Multiplication Principle for Counting”: https://journals.library.columbia.edu/index.php/jmetc/article/view/11949/6300
"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.