The last week in April has been designated Mathematics Awareness Week by the august authorities who declare such things.
And prescriptions for the betterment of U.S. math education have been offered by everyone from Secretary of Education Lamar Alexander down to Mr. Logarithm at PS 101.Although their recommendations - combined with some elements of President Bush's new education plan and significant increases in federal expenditures - could indeed raise math awareness, I think exploding some crippling and widely held misconceptions about math would be almost as therapeutic.
- MATH IS COMPUTATION. Mathematics has as much to do with computation as writing has to do with typing.
Imagine that throughout the course of one's education all one ever did in English class was diagram sentences. It wouldn't be surprising if one didn't acquire a terribly keen appreciation of literature.
Most students (and most adults) can't interpret graphs, don't understand statistical notions, are unable to model situations mathematically, seldom estimate or compare magnitudes, are immune to mathematical beauty and, most distressing of all in a democracy, hardly ever develop a critical, skeptical attitude toward numerical, spatial and quantitative data or conclusions.
- MATH IS A RIGIDLY HIERARCHICAL SUBJECT. A common belief is that first comes arithmetic, then algebra, then calculus, differential equations, etc.
There is a cumulative aspect to parts of math, to be sure, but it is less important than many realize.
Often, when I explain sophisticated ideas in probability or calculus to people who might have difficulty adding two fractions, self-styled innumerates seem amazed at their new insights, much like the Moliere character who was surprised to discover he'd been speaking prose all his life.
- MATH AND NARRATIVE ARE DISPARATE ACTIVITIES. Storytelling is as effective an educational tool in math as it is in other domains. It puts the subject into context and illustrates its limitations.
For example, in teaching correlation, a traditional topic in statistics courses, I've given students data demonstrating conclusively that children with bigger feet spell better. (You may have noticed this yourselves.)
Should we therefore use foot stretchers to increase spelling scores?
No, because the correlation is not causal: Children with bigger feet spell better because they're older.
Note that there isn't any number crunching in this little story. And there are innumerable other vignettes from areas such as sports, lotteries, medical fraud and sex-discrimination cases that communicate mathematical ideas in a non-technical and topical manner.
If the connection between math and ordinary language and thought is established early, then the tables, formulas and algorithms that come later are justified: They're a shorthand means to get to solutions.
- MATH IS ONLY FOR THE FEW. "I'm a people person, not a numbers person."
Almost everybody can develop an understanding of numbers and probabilities, of relationships and logic, of graphs and rates of change and of the role these notions play in everyday life.
- MATH IS NUMBING. Finally, there is a romantic belief that a concern with numbers numbs one to the big questions, to the grandeur of waterfalls and sunsets.
Too many people cling to the usually unarticulated belief that one must choose between life and love on the one hand, and numbers and details on the other. Such sentiments are as prevalent as they are unfounded - and help bring about the dismal test scores we hear so much about.
(John Allen Paulos, professor of mathematics at Temple University, is the author of "Beyond Numeracy: Ruminations of a Numbers Man.")