Educators add 2 and 2 together, develop more applied math courses


One bright college student, she joked, reasoned that since there was a 50 percent chance of rain on Saturday and a 50 percent chance on Sunday, there was a 100 percent chance of rain over the weekend.

Gloria Dion, a math teacher at Pennsylvania State University at Ogontz drew some chuckles when she told the story. The student was all wet of course,and not because it rained.

College liberal arts majors increasingly seem to have problems with mathematics, said many of about 3,500 researchers and teachers gathered in Baltimore this week for the Joint Mathematics Meeting, sponsored by three national math groups.

"It's always scary when you go to the store, and something is two for a dollar and the person selling the thing doesn't know how much one would cost," said John Emert, who works at Ball State University in Indiana.

To combat this situation at the college level, there has been a boom in new courses for non-science majors that don't simply review algebra or calculus courses taught in high school. Instead, these courses offer real-life applications for standard mathematical concepts and give students a taste of the more exotic branches of the field.

These include fractal geometry, where complexity grows out of the repetition of simple patterns, and chaos theory -- the study of how some "dynamic systems," like long-term weather patterns, develop in unpredictable ways.

Quadratic equations? Statistical theory? Presented abstractly, teachers find they have little meaning for most non-science majors.

But students perk up, teachers say, when the discussion turns to the probability that a drug test for athletes will yield a false positive, or the likelihood someone will contract AIDS from unprotected sex.

Some math teachers are asking their students to write newspaper stories based on analysis of statistical data. Others are having them play war games, or predict the incidence of condom failures or think deeply about the children's game "Chutes and Ladders."

"The idea is, let's start teaching them mathematical ideas that areless than 100 years old," said Kay I. Meeks, who teaches at Ball State University. She and Mr. Emert organized the meeting's two-day session on liberal arts math courses.

Alan L. Levine at Franklin and Marshall College in Lancaster, Pa., was faced with teaching a math course to 17 freshmen, some from inner city neighborhoods. All these students were judged "at risk" of flunking or dropping out of school.

So he introduced them to Lanchester Combat Models, formulas that can be used to pit imaginary armies against one another in "battle." The side that wipes out its opponent's forces is the winner.

"A couple of the students came from downtown Los Angeles, and they viewed it as a battle between gangs," Mr. Levine told a room filled with fellow college math teachers. It was the single most popular part of his course. "I think it appealed to their sense of violence."

Steven Gadbois of Rhodes College in Memphis, Tenn., teaches a course that includes an analysis of "Chutes and Ladders," where players use a single die to race 100 squares to the end -- taking short cuts when they land on squares with "ladders" that lead higher, and falling back when they land on "chutes" that carry them to lower squares.

Mr. Gadbois found that on average it took 38.8 moves to complete the game, with seven the fewest number of moves possible. Surprisingly, he found that giving players a modest head start actually handicaps them. That's because players starting from the second square miss a ladder on square one.

"Remember that when you play with your children," Mr. Gadbois advised.

To get her Math 101 students interested in the course, Anne S. Growney of Bloomsburg University in Pennsylvania applies math to current events, sports and gambling issues.

One problem she uses: "Due to the recession, Jennifer's salary was cut by 10 percent. Her employer promises that when prosperity returns, she will get a 10 percent raise. Will Jennifer's salary be the same, or more, or less than it was before?"

(The correct answer is less. The 10 percent raise will be calculated on a smaller base.)

Students also seem fascinated by the real-life implications of the notion of degrees of separation, she said. There is a widely accepted -- though unprovable -- conjecture that everyone on Earth is connected to everyone else through a network of friends of friends that is never more than six deep.

First, she said, most students refused to believe it. "Then they begin to experiment with it," she said. One student realized his father knew the school superintendent, who knew a congressman, who knew more famous folks.

"Eventually he found out he was connected to Saddam Hussein," she said. "What a horrible thought!"

Mathematics teachers, and some students, are concerned that popular courses could turn into "math lite." "There is a danger you'll pull too far ahead to the applications and never get back to the meat of it," Mr. Emert said.

But William Jaco, executive director of the American Mathematical Society, is more concerned that people will increasingly regard mathematics as simple arithmetic -- boring computation that should be left to calculators.

"The perception of what math is, is exactly wrong," he said. "It is critical thinking, analysis and problem solving."

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