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Elementary Probability

  • A song for use in helping students to apply Bayes Theorem and examine marginal and conditional proportions in a table to see how, for rare conditions, most positive test results may be false positives.  Lyrics and music by Tom Toce copyright 2015.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

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  • How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.

    By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science.  This course includes 62 interactive quizzes and more than 400 probabilty-based problems with solutions.  Access to this course requires users to sign up for a free account.

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  • This site offers separate webpages about statistical topics relevant to those studying psychology such as research design, representing data with graphs, hypothesis testing, and many more elementary statistics concepts.  Homework problems are provided for each section.

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  • Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.

    STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.

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  • A pun to aid in discussing Stirling's approximation.  The joke was written by Larry Lesser from The University of Texas at El Paso in January 2018.

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  • A song to be used in discussing the value of random selection in sampling and random assignment in experimentation. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 2014 hit “All About that Bass,” by Meghan Trainor. Also, an accompanying video may be found at https://www.youtube.com/watch?v=br-5FtoYfkc

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  • A song to be used in discussing the idea that the probability of at least one can be calculated at 1 minus the probability of none (i.e. the result of one of DeMorgan’s Laws) The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of Sheryl Crow’s 1994 hit song “All I Wanna Do.” Also, an accompanying video may be found at
    https://www.youtube.com/watch?v=S0IzpxRRUME

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  • A song that may be used in discussing the concept of independence as P(A) = P(A|B). The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the folk Ballad Oh My Darlin’, Clementine assumed to have been written by Percy Montrose in 1884. Also, an accompanying video may be found at https://www.youtube.com/watch?v=7Li7VBGOc5Q

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  • A short story that can be used in an out-of-class assignment in association with the study of probability rules, Bayes Theorem and expectations as they relate to games of chance. The story was written by Canadian Mathematician Robert Dawson from Saint Mary's University in Halifax, Nova Scotia and appeared in the Journal of Humanistic Mathematics (volume 7, issue 1, January 2017).
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  • A poem to develop an understanding of permutations. A question like "Why is the word importunate used in a poem about a permutation?" will help the conversation. The poem was written by Larry Lesser from The University of Texas at El Paso in 2017.
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