|Ivars Peterson's MathLand|
"She walked around the cow to the other side of the board. She drew a pentagon, a hexagon, and a perfect heptagon."
There it was: a little math lesson in the middle of a new book I was reading to our children.
Kenneth, who is six, interrupted immediately. "What's a heptagon?" he asked. He didn't ask what a cow was doing in the classroom. That was part of the wackiness you would expect at Wayside School.
The book answered his question: A heptagon has seven sides. But it was the next paragraph that really stuck in my mind because it nonchalantly captured one of those little truths of classroom life.
"Miss Zarves was very good at drawing shapes. When most people try to draw heptagons, there is always one side that sticks out funny. But Miss Zarves's heptagon was perfect. Every side was the same length, and every angle the same degree."
Of course, she was drawing a regular heptagon. But that merely enhances the wonder of her singular talent. I can do a reasonable job drawing equilateral triangles, squares, hexagons, and octagons. My freehand heptagons (and even pentagons) nearly always come out wrong.
A few months earlier, we had enjoyed another book that featured math even more prominently. Math Curse by Jon Scieszka and Lane Smith neatly spoofs the types of word problems that educators and textbook writers invent to dress up arithmetic exercises and, supposedly, to demonstrate the relevance of math to everyday life.
Eric, our eight-year-old third grader, laughed loudly through much of the book, and he particularly liked this example:
"The Mississippi River is about 4,000 kilometers long. An M&M is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer.
"Estimate how many M&Ms it would take to measure the length of the Mississippi River. Estimate how many M&Ms you would eat if you had to measure the Mississippi River with M&Ms."
Scieszka and Smith aren't the first ones to take on Mississippi math. More than 100 years ago, in Life on the Mississippi, Mark Twain talked about the river's penchant for shortening its length from time to time when a straight, new channel cut off a deep bend in the river.
Twain noted that in 176 years, the Lower Mississippi had shortened itself by 242 miles, a rate of just over 1.3 miles per year. Thus, he reasoned, a million years ago, the river was at least 1.3 million miles long and "stuck out over the Gulf of Mexico like a fishing rod." By the same token, in 742 years, "the Lower Mississippi will be only a mile and three-quarters long.
"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact," Twain concluded.
Canadian economist and humorist Stephen Leacock also had fun with some of the peculiarities in the use of "concrete problems" in classroom math. In a piece called "A, B, and C -- The Human Element in Mathematics," which was one of a collection of comic stories published in 1910 under the title Literary Lapses, he wrote:
""The student of arithmetic who has mastered the first four rules of his art and successfully striven with money sums and fractions finds himself confronted by an unbroken expanse of questions known as problems. These are short stories of adventure and industry with the end omitted and, though betraying a strong family resemblance, are not without a certain element of romance.
The characters in the plot of the problem are three people called A, B, and C; the form of the question is generally of this sort: 'A, B, and C do a certain piece of work. A can do as much work in one hour as B in two or C in four. Find how long they work at it.'"
Drawing on clues tucked away in the myriad problems featuring A, B, and C, Leacock reconstructed the tragic, misspent lives of these characters. "Now to one who has followed the history of these men through countless pages of problems, watched them in their leisure hours dallying with cordwood, and seen their panting sides heavy in the full frenzy of filling a cistern with a leak in it, they become something more than mere symbols," Leacock mused. "They appear as creatures of flesh and blood, living men with their own passions, ambitions, and aspirations like the rest of us."
From drawing geometric figures to figuring out word problems, the examples I have cited serve as gentle reminders that there is a difference between mathematical exercises disguised as episodes of everyday life and real mathematics applied in the real world. It's a distinction that's not always appreciated in the mathematics classroom.
Sachar, Louis. Wayside School Gets a Little Stranger. New York: Morrow, 1995.
Scieszka, Jon, and Lane Smith. Math Curse. New York: Viking, 1995.
You can visit the Stephen Leacock Museum at http://www.transdata.ca/leacock/leacock.html.
A listing of Mark Twain resources on the World Wide Web can be found at http://web.syr.edu/~fjzwick/twainwww.html.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.
Ivars Peterson is the mathematics and physics writer at Science News. He is the author of The Mathematical Tourist, Islands of Truth, Newton's Clock, and Fatal Defect: Chasing Killer Computer Bugs. He is now working on the first book in his Adventures in Mathland series: The Jungles of Randomness (to be published in 1997 by Wiley).