Tuesday, November 1, 2011

Statistics à la Mode

Meg Dillon—Southern Polytechnic State University

The last time I taught introductory probability and statistics, I turned in my grades and asked my department chair to take me off the course permanently. I’d spent some time working on a committee to update the course and we’d modernized it roughly to my taste, so my chair was puzzled. The best I could offer by way of explanation was, “I just hate it.” Then I went to France and taught their version of the same course.

My stint in France lasted three weeks. Essentially, I was substitute teaching and not looking for more than an excuse to be in the country for a while. My students were second-year engineering students, pretty much like my students at home. And like my students, the French students were a few notches below elite. While the similarities between my home university and my French university were comforting, the contrasts in the probability/statistics courses could not have been more jarring.

Anyone who has taught or learned in a U.S. mathematics department recently knows the typical introductory probability and statistics course. It involves an expensive, gassy textbook with lots of color pictures, word problems involving industrial applications, and charts to help students navigate problems. American students purchase the textbook and far too often, the ancillaries the bookstore peddles alongside the text.

At my home university, the chair has some difficulty finding mathematics faculty willing to teach the course. While I can’t speak for my colleagues, to me the course seems oddly estranged from mathematics. There is a section on probability, and we love that: the probability laws, the counting. It’s possible to trick out that section and get a chewier piece of mathematics into the act, but, by and large, the course is a hodgepodge of recipes, motivated by problems involving IQ testing, rhesus monkeys, salamanders, and the like. Regardless of the text, there is almost invariably a peculiar pair of caveats presented as from on high: Never accept the alternative hypothesis, and never say the probability is 0.95 that the mean lies in a 95% confidence interval for the mean. I dreaded teaching it in France.

The French course, though, was a different kettle of fish. No one expects French students to shell out money for books, so the course was based on notes produced by the instructor of record. The notes were spare and lacked attribution. They started with simple examples involving coins, dice, and lifetimes of electronic gadgets, what one would expect. The definition of sample space appeared on page one. (That was fast.) The definitions of sigma-algebra (Gasp! Are they joking?) and probability space (Is this a grad course?) appeared on page two. The course spooled out from there. Yes, it assumed more calculus than we do but mostly in the more interesting problems, and it treated testing and interval estimates in much the same way we do. No one was joking, and this was not a grad course: it was introductory prob/stats, in an unapologetically mathematical setting.

Statistics is possibly the most important course we teach in mathematics: for life and for cultural literacy, a basic understanding of it is essential. The high schools teach it, yet I’ve heard excellent high school math teachers express fear, if not loathing, of the subject.

An introductory probability and statistics course based on mathematics is missing, not just from the math education curricula, but from American soil altogether, as far as I can tell. While we teach these courses from bloated texts that avoid mathematics, we might seize the opportunity to teach a critical life skill—understanding statistics—through an exposition that glorifies its foundation in mathematics.

A big chunk of statistics courses in the United States are taught by non-mathematicians, outside math and statistics departments. By the looks of things, students can often get by on facility with software and a foggy understanding of principles. We still see many of these students in the introductory course, though. Could we do better there? Could we rope these students in with mathematical ideas, and could this happen anytime soon?

I don’t know, but I’m hoping to go back to teach in France next year.

About the author: Meg Dillon is a professor of mathematics at Southern Polytechnic State University in Marietta, Georgia.

Aftermath essays are intended to be editorials and do not necessarily reflect the views of the MAA.