Jack Driscoll once told me that when he was Editor of the Boston Globe he banned the use of the word “median” because no one on his staff understood the difference between a median and a mean. Alas, the Globe has a great deal of company in regard to its paucity of mathematical thinking.
A recent gaff was made by Bruce Tinsley at The Daily Progress in Charlottesville, VA in his 9 September 2008 rant at teachers. From the bully pulpit of his Mallard Fillmore syndicated comic strip entitled “Mallard’s Back to School Memories #17”, Tinsley’s “fowl”-mouthed surrogate says: “Your tests will be graded on a curve, so it will be really hard to get a bad grade… or a good grade. I got the idea from the way the teachers’ union treat us.” (You can view the original strip here.)
Tinsley must have been hanging out with the likes of Karl Rove instead of going to math class or he would have realized that his analysis couldn’t be further off the mark (but it is misleading—Tinsley is fluent in doublespeak). Grading on a bell curve (or Gaussian distribution) is a method of assigning grades to students based on their relative performance. Such a scheme is designed to distribute the grades, making it more likely that a relatively poor performance will result in a poor grade and a relatively good performance will result in a good grade. If Tinsley didn’t receive the bad grade he deserved, it wasn’t because of the curve.
I assume that the Globe and other papers that carried the strip have no editorial control over the syndicated comic strips that they publish, but a “Page 2 correction” was certainly merited.
There’s something peculiar about how we teach math. If you look at each subject in elementary school—History, English, Social Studies, etc.— you’ll see that each pupil learns hundreds of new words in every term. You learn the names of many countries and organizations, the names of leaders and battles and wars, the names of many authors and books—thousands of new words every year.
However, in the case of school-mathematics, the vocabulary is remarkably small. The children do learn the names of various objects and processes—such as addition, multiplication, fraction, quotient, divisor, rectangle, parallelogram, and cylinder, equation, variable, function, and graph. However, they learn only a few such terms per year—which means that, in mathematics, our children are mentally starved, by having to live in a “linguistic desert.” It really is hard to think about something until one learns enough terms to express the ideas in that subject. Specifically, it isn’t enough just to learn nouns; one also needs adequate adjectives! What’s the word for when you should use addition? It’s when a phenomenon is linear. What’s the word for when you should use multiplication? That’s when something is quadratic or bilinear. How does one describe processes that change suddenly or gradually: one needs terms like discrete and continuous. To talk about similarities, one needs terms like isomorphic and homotopic. Our children all need better ways to talk about, not only Arithmetic and Geometry, but also vocabularies for the ideas one needs to think about statistics, logic, and topology.
The mainstream media has an opportunity to encourage the everyday use of mathematical terms. Rather than banning the use of median, Driscoll should have insisted that his journalists become fluent in the basics of mathematical thinking. The mainstream media should be an oasis the linguistic desert of mathematical thinking.