Math Modeling Event Tests Students' Skills

WILMORE, Ky. — With empty pizza boxes stacked neatly on a chair and an extensive assortment of snacks to banish any potentially distracting hunger pangs, four teams of Asbury math students clustered around laptops and whiteboards early this week to wrap up one of the Math Department’s most anticipated yearly events.

Asbury students Cali Thomas '14, Kara Wiltrout '12 and Carl Durcholz '14 wrote an academic paper to describe their solution to this year's Math Modeling Competition problem.
Asbury students Cali Thomas '14, Kara Wiltrout '12 and Carl Durcholz '14 wrote an academic paper to describe their solution to this year's Math Modeling Competition problem.

The annual COMAP Math Modeling Contest is a weekend-long exercise in creative thinking and project management through the real-world application of mathematical concepts. Each team chooses a scenario with a problem that can be addressed with math and then spends about four days developing a solution, testing their model and writing a paper to describe their process. More than 2,000 teams from around the world compete each year.

Junior George Lytle joined the fun for the third time this year, joining teammates Aaron Hill and Kaity Bradley in selecting a problem that involved a suspected conspiracy in a large office complex.

“This weekend went more smoothly than any other modeling weekend,” Lytle said. “We settled on a problem Thursday night and spent Friday afternoon reading up on graph theory. By the end of the night, we had developed our own model and replaced it with a more sophisticated one, which is rare for math modeling. The rest of the weekend was spent verifying the properties of our model, running the simulation, and writing the paper.

“We were well stocked with food,” he continued, “and as for funny moments, we keep a running quote board throughout the weekend to record the hilarity.”

Though math modeling weekends feature enough food, socializing and deadline-driven adrenaline to draw multiple teams each year, the educational benefits extend beyond even the new math skills students learn in the process of addressing their chosen problems.

“In the classroom, much of what we do are routine problems with answers in the back of the book,” Lytle said. “Math modeling allows us to try our hand at real-world math as a profession, which is often very messy with no specifically correct answer.”

One of the math problems students could chose involved estimating the weight of a tree's leaves. Both real leaves and models were fuel for thought.
One of the math problems students could chose involved estimating the weight of a tree's leaves. Both real leaves and models were fuel for thought.

Senior Laura Hochstetler found the skills developed during math modeling competitions — using the strengths of different team members effectively, writing clearly under pressure, articulating insights and even simply managing relationships well through fatigue and frustration — to be applicable in many situations.

“Math modeling is about ‘stepping out of your comfort zone’ in the very best, freshest sense of that cheesy phrase,” she said. “If you look through the collection of things I’ve learned through math modeling, those are all skills I wouldn’t learn in a traditional class but certainly need in life. No matter where life takes me, I’ll count math modeling among the most valuable elements of my education at Asbury.”

Each team submitted an academic paper by 6 p.m. Monday evening to be scored by judges associated with the Consortium for Mathematics and its Applications, a nonprofit organization that works to improve mathematics education. Results are expected later this spring.

 

What do you think?

Are you up for a challenge? Here is one of the problems this year's math modelers could choose:

Camping along the Big Long River

Visitors to the Big Long River (225 miles) can enjoy scenic views and exciting white water rapids. The river is inaccessible to hikers, so the only way to enjoy it is to take a river trip that requires several days of camping. River trips all start at First Launch and exit the river at Final Exit, 225 miles downstream. Passengers take either oar- powered rubber rafts, which travel on average 4 mph or motorized boats, which travel on average 8 mph. The trips range from 6 to 18 nights of camping on the river, start to finish. The government agency responsible for managing this river wants every trip to enjoy a wilderness experience, with minimal contact with other groups of boats on the river. Currently, X trips travel down the Big Long River each year during a six-month period (the rest of the year it is too cold for river trips). There are Y camp sites on the Big Long River, distributed fairly uniformly throughout the river corridor.

Given the rise in popularity of river rafting, the park managers have been asked to allow more trips to travel down the river. They want to determine how they might schedule an optimal mix of trips, of varying duration (measured in nights on the river) and propulsion (motor or oar) that will utilize the campsites in the best way possible.

In other words, how many more boat trips could be added to the Big Long River’s rafting season? The river managers have hired you to advise them on ways in which to develop the best schedule and on ways in which to determine the carrying capacity of the river, remembering that no two sets of campers can occupy the same site at the same time. In addition to your one-page summary sheet, prepare a one-page memo to the managers of the river describing your key findings.

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