Donald Barry Publishes Article About Solving Ancient Tablet with Calculus Class

In his article titled, “Mathematics in Search of History,” Donald Barry, Instructor in Mathematics, chronicled his BC Calculus class’ struggle to decode an ancient Turkish clay tablet.

“I described what a group of Phillips Academy students did, how they approached the tablet and what my role was. I was no longer ‘the answer man.’ When they had questions, they had to figure it out,” said Barry.

First published in “The Mathematics Teacher,” a monthly journal by the National Council of Teachers of Mathematics, in 2000, the article was republished in October 2012 in “Real Math,” an online anthology of mathematical application in finance and surveying.

The tablet in Barry’s article was one of numerous ancient clay tablets discovered in a cave in central southern Turkey in the 1990s, near the archaeological site of a known Neolithic village, according to Barry’s article. The origins of the clay tablet are unknown, however.

Because only two-thirds of the tablet had been discovered at the time, Barry created a mathematical problem asking his students to solve the text of the tablet by guessing the numbers in the columns and rows. They then developed an interpretation of the numerical information to determine the text of the missing one-third of the tablet.

“The solution requires that a community of scholars, namely the students, work together to sort out ambiguities and inconsistencies to arrive at an interpretation of the problem with which the community as a whole is reasonably comfortable,” wrote Barry in the article.

Barry has presented the tablet to other BC classes after the Advanced Placement Exam since 1994. The article, however, focuses on one particular BC Calculus Class that he taught in the 1998-99 school year.

“I just recorded what my class did. I observed how they approached the problem, where they went in the right direction and where they went in the wrong direction,” said Barry.

“I was thrilled by the classroom discussions that took place that year,” said Barry in the article. “I hoped to make the case that this use of the history of mathematics is worthwhile.”

Barry said that the experience of problem solving, rather than the conclusion, was what mattered during the exercise.

“They’re reconstructing history using whatever mathematical tools they can bring to bear on that problem. They are reconstructing the mathematical knowledge of some ancient civilization, which means I’m bringing them as close to doing a certain aspect of archeology as I can possibly bring them,” said Barry.

“This feels real. The issues that they’re dealing with are issues that archeologists have faced in trying to understand what an ancient civilization was up to,” he continued.

Barry said that the hardest part of the exercise was that there was no right answer. “The conclusion is a judgment, because there are ambiguities. People have to convince other people that this is how it must be interpreted. There is not a tidy answer at the end,” said Barry.

“I just let them stumble and struggle. There’s no one telling an archeologist that this is the answer. What you have is a community of archaeologists looking at the same information trying to figure out what it is and at the very end there is some, more or less, agreed upon conclusions,” he continued.

Barry lived in Turkey for seven years before coming to Andover in 1980. He taught high school math in English to Turkish students in Tarsus and Istanbul.

“You can’t live in Turkey without being so intrigued by the ancient past because it’s all around you there,” he said. “So I’ve paid a lot more attention to archeology, archeological discoveries the kind of thinking that archaeologists employ, than I would have otherwise. I’m fascinated by it, and I want to share that with my students,” said Barry.

Barry said he plans to give the tablet to his calculus class after the AP Exam this spring. “It gives them a different sort of mathematical experience. It’s a puzzle,” said Barry.

A number of Barry’s articles have been printed in “The Mathematics Teacher.” Barry has also written problems for “The Mathematics Teacher Problem of the Day” calendar.