HIGHER MATH, DEMYSTIFIED

June 03, 1993|By Ellie Baublitz | Ellie Baublitz,Contributing Writer

What do fractals, topology, cryptanalysis, graphing calculators and estimation in ecology have in common?

Many of Carroll County's brightest seventh-graders -- high achievers from the public schools' Extended Enrichment Program -- were understandably in the dark one morning last week.

By that afternoon, though, the 100 students not only knew what the terms meant, but had some hands-on experience with the subjects.

Learning the new terminology was part of a Mathematics Conference put together as a culminating math activity for the seventh-grade EEP students from the county's middle schools.

"We've found that kids have an interest in math in middle school, but by the time they get to high school, they lose that interest, especially in geometry," said Don Bell, EEP teacher and an organizer of the workshop.

"We thought if we could put together a professional program, like we do for adults, we could keep them interested in math through high school or even college."

The five above-mentioned items are mathematical topics, all but cryptanalysis being relatively new disciplines in the field.

As recently as 25 years ago, most of these topics hadn't been heard of by the average person, even though the subject may have been discovered hundreds of years ago.

Topology, a branch of geometry, was pioneered by a Swiss, Leonhard Euler, who lived from 1707 to 1783. He founded the network theory, dealing with shapes that you can trace without having to lift your pencil or retrace any lines.

It doesn't sound like something relating to everyday problems, but what if you live on an island connected to the mainland by seven bridges, and you want to have a parade whose route goes over each bridge only once?

In trying to figure out the answer, Euler came up with the theory that an object that had zero or two "odd points" (a corner with an odd number of lines coming into it) is traceable; objects with three or more odd points are not. There is no such thing as a shape with only one odd point.

During the workshop with Beth Brown, an EEP teacher, one group of students figured out how to have the parade: Take away two of the bridges.

But that's not all topology is. It's also how the mathematical qualities of objects change when the objects are stretched, crushed or pulled, like drawings on a balloon when it is blown up.

"I didn't know topology was out there. You never think about it, and it's so simple," said Lindsay Iadevaia, of West Middle School.

Or take fractals, the repeated patterns in all things natural.

Jeff Yantis, a computer scientist, showed students examples of natural and synthetic things that have distinct patterns. The patterns may not be as visible in real life, but put them on a computer and the pattern becomes clear.

Start, for example, with the whole item, such as a fern branch, whose individual fronds have the same pattern as the whole, only in miniature.

"I took fractal geometry, and I like how everything repeats itself over and over," said Megan Chenoweth, from West Middle School. "It shows you how man-made things are simpler than things in nature. But everything makes sense when you think about it -- it's supposed to be that way."

Even the adults were fascinated with some workshops. William Piercey, EEP supervisor, confessed to sitting through the fractals workshop twice.

"I'm really into that," he said. "It's the chaos theory, that there's an orderliness to chaos."

Cracking codes, or cryptanalysis, was another enjoyable topic for the students, who were given two codes to break by Sylvia Impett of the National Security Agency.

The students, who were able to pick topics of interest to them, attended four of eight workshops during the day.

The program was conducted May 26 at Western Maryland College, which volunteered space in Lewis Science Hall.

The conference was supported by donations from the Maryland Mathematics Coalition and the Maryland Science Week dTC Commission. Students attended free of charge.

Other speakers were from the Maryland Science Center, Hashawha Environmental Appreciation Center and the State Department of Education.

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