From: Public Affairs
The basic object of mancala games is pretty straightforward: Continue moving stones or seeds from pit to pit until you get them in the ruma and win, or until you run out of moves and lose.
Creating mathematical equations to explain the possible moves and outcomes for the games, also known as sowing games, is proving to be anything but clear-cut for four students participating in this summer's mathematics Research Experience for Undergraduates program at James Madison University.
"Deriving things for the first time is much harder than working through a more complicated problem in a textbook," said Benjamin Warren, a senior at Ramapo College of New Jersey who is majoring in mathematics.
Warren and the other students in the program were selected from more than 100 applicants from around the country, said Dr. Laura Taalman, professor of mathematics at JMU. The program is funded by the National Science Foundation and each student receives a $4,000 stipend to conduct the research. They began their research on June 6 and by the time they finish on July 29, they will have a good start on a research paper that could be submitted to a scholarly journal.
"They've already written 10 typed pages of serious math results," Taalman said.
This is the third summer Dr. Anthony Tongen, associate professor of mathematics at JMU, has mentored student researchers exploring ways to explain mancala games with mathematical equations. "There's some neat things about this," he said, noting that a French mathematician wrote a paper about the games in the 1950s. Some of that research along with previous research at JMU has helped this summer's students adapt the game in ways to aid their research. "The math is actually very complicated," Tongen said. "Some of the proofs they're going through are very difficult."
Of the four students, only Jeff Anway, a junior at Longwood College who is majoring in math and computer science, had any math research experience before the REU program, but it paled in comparison to what he is doing this summer. The high-school research consisted of 50 minutes once a week, he said.
"It's their job," Taalman said. "They basically work all day long. They're in here nine to five plugging away, working and we stop by throughout the day and force them to tell us things or give them even more problems to work on or see where they are. And they probably go home at night and they still can't get it out of their brains and then they wake up in the morning and they do it all over again."
Fanya Wyrick-Flax, a junior math major at Bard College in New York, sees it as a win-win situation. "It's a summer job where we learn while we're getting paid. Up until this summer, I've only done music and you have to pay a lot of money to do music programs in the summer. So this is nice," said Wyrick-Flax, who also is a flutist at the Bard College Conservatory of Music.
"It's been a lot of fun," said David Creech, a senior at Central Michigan University who is majoring in math, statistics and geographic information sciences. "I didn't really know what I was getting into. I was thinking more that we would be going along (multiplayer) mancala lines, but as I did more research into game theory and what we are actually addressing, we don't have the tools yet. So through Tchukaillon (a single-player game), we're developing the tools to help analyze mancala."
When played using basic strategy, the player who goes first in the two-player game usually wins, said Wyrick-Flax. "We don't know why and haven't been able to explain that mathematically because there are so many rules and so many variations."
In addition to getting their feet wet in the world of research, Tongen said the REU experience is giving the students a taste of what graduate school would be like. "Do you like banging your head against the wall? That's what they're finding out."
"As much pain as possible," quipped Taalman. "Really, It's about putting them through the wringer so they know if that's what they want to do for four years, five years, six years, plus."
By Eric Gorton, JMU Public Affairs
Published June 29, 2011