## Illicitly Counted Coins

The past month I’ve had the joy of teaching a real, proper class again, after a hiatus of a few years. The hiatus has given me the chance to notice some things that I would do because that was the way I had done them, and made it easier to spot things that I could do differently.

To get a collection of data about which we could calculate statistics, I had everyone in the class flip a coin twenty times. Besides giving everyone something to do besides figure out which of my strange mutterings should be written down in case they turn out to be on the test, the result would give me a bunch of numbers, centered around ten, once they reported the number of heads which turned up. Counting the number of heads out of a set of coin flips is one of the traditional exercises to generate probability-and-statistics numbers.

Good examples are some of the most precious and needed things for teaching mathematics. It’s never enough to learn a formula; one needs to learn how to look at a problem, think of what one wants to know as a result of its posing, identify what one needs to get those results, and pick out which bits of information in the problem and which formulas allow the result to be found. It’s all the better if an example resembles something normal people would find to raise a plausible question. Here, we may not be all that interested in how many times a coin comes up heads or tails, but we can imagine being interested in how often something happens given a number of chances for it to happen, and how much that count of happenings can vary if we watch several different runs.