Resource Library

A piece of mathematical wordplay-based art displayed in the 2024 Bridges Exhibition of Mathematical Art, Craft, and Design (see https://gallery.bridgesmathart.org/exhibitions/bridges-2024-exhibition-o...). The lowest level of understanding the arithmetic mean (Pre-K-12 GAISE II, p. 18) is a “fair share value” -- each person’s portion if a resource were shared equally. This is also a “levelling value” corresponding to the height x of the A’s extended crossbar, and x is the mean of the 4 letters’ heights if they were .5x, .5x, 2x, x. A higher level of understanding the mean is as a “balance point,” where A’s apex is the fulcrum placed where unit weights at M and E balance two weights stacked at N: the mean of the 4 weights’ x-coordinates is the x-coordinate of the fulcrum.

This lyric, written by Larry Lesser (The University of Texas at El Paso) and Michael Posner (Villanova University) and recorded/sung by Lesser in 2019, won fourth place in the 2019 A-mu-sing contest. The song may be sung to the tune of "She Blinded Me With Science" by Thomas Dolby and is designed to introduce some key terms and concepts in data science.

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.

This lyric was written and recorded/sung by Larry Lesser from The University of Texas at El Paso in 2017 to the tune of the Miley Cyrus hit “Wrecking Ball.”  The song won honorable mention in the 2019 A-mu-sing contest and is designed to be a vehicle to discuss common instances of expected value as a benchmark for making real-world decisions in one’s life. In particular, students should be aware that most people sometimes choose to buy something (an insurance policy, a warranty, a lottery ticket, etc.) whose expected value is negative, but that is still outweighed by other considerations.  The second verse refers to an episode of “Deal or No Deal” (Season 4, Episode 7) that NBC aired on October 22, 2008.

A poem reflecting on the idea of standardization in statistics by Dane C Joseph from George Fox University in Oregon that earned an honorable mention in the 2025 A-mu-sing Contest. In his submission for the contest Dr. Joseph indicated:
"I wrote this poem to highlight the essential importance of standardization to some of the most basic scientific and social endeavors. Far from a perfect solution to many of the sociopolitical, educational, and technological issues we face, standardization is still immensely powerful when aptly done and is arguably indispensable to our daily lives—from making policy and admissions decisions to calibrating instruments and building machines. My hope is that learners will acquire a sense of the tension between the usefulness and appropriateness of standardization, appreciate how very simple tools like Z-scores can help us to responsibly rank various objects, as well as openly critique why they can also lead to problems when the objects to be ranked and compared are human attributes. Among other things, instructors should encourage students to explore the meaning of the contrasting big 'M' little 'm' moniker, and allusions to central tendency (e.g., C grades)."

This poem, with an accompanying video reading of the poem by Michael A. Posner from Villanova University, took first place in the poetry category of the 2025 A-mu-sing Contest. The poem is designed to teach about word (or term) frequencies in text mining which involves thoughtful construction in defining the actual measurements to use.  Instructors might have students go over this poem and then discuss how to define what words or stems of words should be included or excluded in a different textual application.

A statistically-themed crossword puzzle written by Indy Wink, a high school student at Germantown Friends School in Pennsylvania. The puzzle won an honorable mention in the 2025 A-mu-sing Contest (note that an instructor must be logged into CAUSEweb.org to view the solutions to the puzzle).  An instructor might ask students to try out the puzzle for fun and then challenge students to write their own clues for statistical words and develop their own statistics puzzle using one of the free online crossword puzzle makers.

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.

A poem reflecting on Type I errors and the use of the null hypothesis in testing by Micah Wascher, a high school student at North Carolina School of Science and Mathematics.  The poem won an honorable mention in the 2025 A-mu-sing Contest. 

Lyrics by John Bailer from Miami University about the value of successful statistical modeling that won an honorable mention in the 2025 A-mu-sing Contest. The song is a parody of the 1972 hit song by Johnny Nash "I Can see Clearly Now" and the vocals on the audio were performed by Kent Peterson from Oxford Presbyterian Church in Miami Ohio.  In using the song for teaching, John suggests that each verse could be connected to a question or two.  Here are examples:

Verse 1:  How does an effective visualization reveal pattern? What types of patterns might emerge? How might such patterns be captured in a model?

Verse 2: What are ways variables are 'engineered' as part of an analysis?

Verse 3: How does the introduction of a confounder in a model potentially impact the estimated coefficients of other variables in a model?

Verse 4: AUC* is one way the predictive quality of a model is described. What are other features of a useful model?

* AUC stands for Area Under the Curve for the Receiver Operator Characteristic

Bridge:  Residuals following a normal distribution are expected for some types of models. What other distributions might be expected? What else might be learned from the residuals?

Verse 5: Why are we more confident with interpolations than extrapolations?