Departments
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Week of 23 October 1998 |
Vol. II, No. 11 |
Feature Article
Order out of chaos
Field Day for high school students solves mysteries of math in a social setting
By J. Nicole Long
"Students of subjects other than math have many opportunities for field trips," says Robert Devaney, CAS professor of mathematics and director of BU's Learning Resource Network (LERNet). "Art classes visit museums, English classes attend plays, biology classes tour aquariums or arboretums. But math classes have few opportunities for field trips, and that's what I want to provide."
LERNet's most recent undertaking is the seventh annual Mathematics Field Day, held on October 21 in the GSU's Metcalf ballrooms. Because of the large number of students enrolled, the Field Day is held twice -- the second will be on November 3.
Outreach to high school students is the general purpose of LERNet's programs: the Pathways Program for young women interested in science; Johns Hopkins' Institute for Academic Advancement of Youth (IAAY), a program that BU cohosts; a Saturday Academy for students of physics; and the Mathematics Field Day.
During both of this year's Mathematics Field Days, BU hosts 500 students from 53 public and private high schools from Acton to Woburn, including Boston Latin School, Cambridge Rindge and Latin School, and Chelsea High School. Students hear a lecture by Devaney, Fractal Games and Movies, which includes computer projections of fractals. Used especially in computer modeling of irregular patterns and structures in nature, fractals are geometric patterns that are repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. "As you zoom in on them," Devaney says, "you can see the same structure over and over. Ferns, clouds, snowflakes, and coastlines are some examples of fractals."
After the lecture, students divide into smaller groups for presentations by CAS Assistant Professor of Mathematics Eric Kolaczyk, who discusses how statistics played a fundamental role in the recent discovery of a "halo" of energy surrounding the Milky Way galaxy, and CAS Professor of Mathematics Murad Taqqu, clarifying a famous paradox concerning probability. And this year for the first time a non-BU professor is presenting a lecture. Visiting from St. Anselm's College, Greg Buck, professor of mathematics, introduces some relatively new, but elementary mathematics: the mathematics of knotting, braiding, and tangling.
"I try to interact with the students a lot," Taqqu says. "The whole point is to break barriers, and that's a matter of engaging them with things they may not have seen, or things they may only vaguely have heard of. The students tend to respond well because they're on a trip. For them it's like an adventure."
Odds and ends
In his probability lecture, How to Win a Car and Not a
Goat, Taqqu uses a game show format to explain a paradox.
Behind one of three doors is a car; behind the other two are
goats. The participant chooses one door to try to win the
car. Before the host opens the chosen door, he opens one of
the two not picked and reveals a goat. Through the activity,
Taqqu demonstrates that it is advantageous at that point for
the participant to change the choice of doors.
Jacob Borgman, a math teacher at Waring School who has brought his students to Mathematics Field Day for the past three years, says his students have enjoyed the game and taught it to their peers during an all-school meeting when they returned to their high school.
"The kids are proud to be able to go to BU," Borgman says. "And I think it's very important for them to get away from the isolation of staring into their calculators. The Field Day presents math to them in a social context."
After meeting him at a Mathematics Field Day, Borgman began to use Devaney's textbook First Course in Chaotic Dynamical Systems (Perseus Press, 1991), which includes materials for computer labs.
Mathematics Field Day not only exposes students to a university setting and allows them to interact with students from other schools, but also provides a forum for area high school teachers and university professors to get to know one another.
Devaney says he can see the germination of seeds sown by the Mathematics Field Day. "Even more rewarding than the Field Days themselves," he says, "is the number of students who come to BU for the Field Day, and later enroll here as college students. It's been a good way to get interesting and interested students of mathematics here on campus."