Teaching Statistics: A Bag of Tricks by Andrew Gelman and Deborah Nolan
Reviewed by Nathan Stein, Departmental Teaching Fellow for Statistics
Teaching Statistics is an excellent resource to help instructors create more interactive introductory statistics classrooms. The book is organized in three parts, with the first devoted to activities for an intro course, covering descriptive statistics, linear regression, sampling, probability, inference, and statistics in the media. The second part focuses on the nuts and bolts of incorporating demonstrations while keeping the class on track, including a sample syllabus. The final part suggests activities for more advanced courses. As you might expect from a book called Teaching Statistics, the activities themselves are specific to concepts from statistics, but Gelman and Nolan also offer a lot of broadly useful advice on creating engaging, interactive classrooms. I can’t resist mentioning some of the most compelling examples in the book, with the hope that thinking about why these examples work so well will inspire teachers in other fields.
Gelman and Nolan’s most successful exercises inspire a sense of play or end with a surprising twist. On the playful side is an activity that uses an inflatable globe to teach students the concept of random sampling. The instructor tosses an inflatable globe into the audience. Students are told to hit it with one finger when ball comes to them, and to shout “Water!” if their finger hits water and “Land!” if land. The instructor tallies the results on the blackboard. At the end of the game, the class uses the counts of water and land to construct a confidence interval to estimate the proportion of the earth covered in water. Wouldn’t you rather learn about random sampling to estimate a population proportion this way than talking about yet another opinion poll? If you need extra convincing that students will enjoy this, check out the YouTube video of a similar (though unplanned) moment in Stat 110:
The other key trick for engaging students is to give your activities a surprising punchline. A great example of this is a “magic trick” to demonstrate that most people don’t have a good intuition for what real randomness looks like. Students are divided into two groups. One group is told to flip a coin 100 times and write down the sequence of heads and tails (as a sequence of 1s and 0s). The other group is told to invent a sequence of 1s and 0s that should look as much as possible like a sequence of fair coin flips, but without using any randomization device. The instructor leaves the room while the students generate their sequences and write them on the blackboard, without identifying which sequence was the real random sequence and which was the fake one. Once they are finished, the students invite the teacher back into the classroom. The teacher then looks at the blackboard and, if everything goes as expected, immediately points to the true random sequence. It looks like magic, but it’s convincing—and memorable—proof that almost everyone believes that randomness looks more regular and less clumpy than it actually does. The fake sequence is likely to switch from heads to tails far more often, while the true random sequence has more long repeated runs of heads or tails.
These activities sound like a lot of fun, but they also require careful preparation. Gelman and Nolan suggest making a list of necessary materials and writing a five-part outline for each activity (concept, mechanics, punchline, context, and follow-up). Staying focused on the goal of the activity can help teachers avoid common mistakes like losing the punchline. Gelman and Nolan caution that being sloppy about how exactly the activity is set up and what exactly the students are expected to do can make a demo miss the mark entirely and fail to illustrate the intended concept.
One of my favorite lines in the book is Gelman and Nolan’s offhand reminder that “students must learn to be both skeptical and constructive.” This is a good thing for teachers in all fields to keep in mind. Statisticians love to indulge their skeptical side, pointing out flaws in published studies or areas where the statistical analyses could be made more sophisticated or robust, and these observations can make for powerful “aha” moments in the classroom. But in the end, we don’t want students to believe that every scientific study is fatally flawed. We want them to learn how to make better use of published results by placing them in context: To what population does this result generalize? How could the conclusion be strengthened? Is it even possible or ethical to carry out a study that could yield a substantially stronger conclusion? Activities that challenge and engage and surprise students can inspire more of the critical thinking that we hope to see.