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Deanna Pecaski McLennan

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Dane Camp, John Carter,, and David Masunaga

Song parodies are a fun way to engage others with mathematical topics. The challenge, of course, is finding a song and lyrics that fit just right. While teaching together in Honolulu, we stumbled across a popular song that turned out to be a math parody in disguise! You will notice that we have not changed the words, just how the words were displayed. You might want to try singing this yourself or sing along with the YouTube version: https://youtu.be/d1mqNdZ0obA. What do you notice? What do you wonder?

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Jennifer Noll and J. Michael Shaughnessy

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data sources included survey data collected in 6 research classes and 4 comparison classes both before and after the teaching episode, and semistructured task-based interviews conducted with students from the research classes. Student responses and reasoning on sampling tasks led to the development of a conceptual lattice that characterizes types of student reasoning about sampling distributions. The lattice may serve as a useful conceptual tool for researchers and as a potential instructional tool for teachers of statistics. Results suggest that teachers need to focus explicitly on multiple aspects of distributions, especially variability, to enhance students' reasoning about sampling distributions.