Tuesday, February 5, 2013

Building the Logic of Statistical Inference on Day 1: The CATALST iPod Shuffle Activity

How random is the iPod shuffle? Your students can investigate.
What does it mean for a process to be "random"? The CATALST introductory statistics course engages students in this question in the very first activity, written up in the latest issue of Teaching Statistics by U of M's Laura Ziegler and Joan Garfield.

As Rob Gould points out, students have extensive prior experience with data and randomness. They do not enter the introductory statistics classroom as so many blank slates!

This situation presents both challenges and opportunities: we've heard from many students that it seems like some artists play more frequently than others on the Apple iPod's "shuffle" mode, which plays all songs in a supposedly random order.

Apple even ran an ad campaign in 2005 for the iPod Shuffle device with the slogan "Life is random":

But how random is it? Laura and Joan describe how the iPod shuffle activity elicits and refines student's prior conceptions of randomness. Students first examine 25 randomly generated playlists of 20 songs from a library of 80 songs. They discuss what rules they would use to flag a playlist as non-random. For instance, many students think that a playlist that has more than 5 songs by the same artist should be flagged.

We then give them five more playlists and give them an opportunity to refine their rules based on the additional information. Oftentimes, their rules will incorrectly flag one of these additional playlists and students may want to rethink their rules.

Finally, they get a chance to apply their rules to three playlists to make a decision about whether they have enough evidence to decide these playlists aren't random.

The process of the CATALST iPod Shuffle activity

Laura and Joan regard the full-class discussion, however, as quite crucial. Here is where students can hear the variety of different rules and face the logic and perception of what it means to be random. Students make all sorts of decisions that provide opportunities for rich conversations about the nature of chance: some students can provide convincing arguments that their rules are useful even when they incorrectly flag a playlist known to be random, while others are quick to say that their rules "prove" that the 3 final playlists were generated randomly.

This in-class activity is distributed in the Unit 1 Materials (zip) (Unit-01 > Student-Activities > 01-iPod-Shuffle.doc) on the CATALST materials page. The article also describes a follow-up homework assignment where students actually create a computer model of the process in TinkerPlots. This assignment is not publicly distributed, but interested teachers can contact the first author of the paper to find out more.

The publication is timely, because here at the U of M our students are just finishing up this first activity! It's a great way to get students started on the path to statistical thinking, and we always have fun hearing the creative things that students come up with.

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