NISKAYUNA — The student becomes the teacher.

Alison Miller, 22, of Niskayuna, returned home last week after spending two weeks as a coach for eight American girls representing the U.S. team at the China Girls Math Olympiad held in Zhongshan, China. About 180 students participated in the competition and the U.S. team brought home two gold, one silver and five bronze medals.

Four years ago, Miller herself competed in the International Math Olympiad held in Athens, Greece. She became the first American woman to win a gold medal at IMO and only the second woman to qualify for the U.S. team.

The organizers were looking for people to help coach the U.S. team at the Olympiad. Miller, who served as one of three coaches, said it is a different role.

“You have a lot more responsibility because you’re there to look after the kids and make sure everything is going all right. There’s less pressure in that nobody is making you compete anymore,” she said.

Miller traveled to Nebraska for three weeks in late June and early July for a training camp. She said she went over problems from previous Olympiads and they also did some timed tests. They also talked about general strategies for solving math problems.

The coaching is not new for Miller. She also coached the Iroquois Middle School MATHCOUNTS team and mentored students at Rosendale and Craig Elementary Schools in Niskayuna as well as the Martin Luther King Magnet School in Schenectady.

Miller said it was definitely a culture shock being in China. She and the students stayed at a Chinese boarding school.

“I did not speak any Chinese but some of the girls knew some Chinese because they were from a Chinese-speaking family, so that helped somewhat,” she said.

The group travels as a team, but it is an individual competition. During the two-day event, each student had four hours to solve difficult math problems. Although that sounds like a lot of time, Miller said, it really isn’t. Students have to spend a lot of time thinking about the right way to solve the problem.

“Often, you have to find some sort of trick that makes things work out nicely. It’s not expected that people will solve most of the problems. I think the average student on our team solved a little less than a half of the problems and did very well,” she said.

The problems cover algebra, geometry, logic and reasoning.

One example is a problem that requires people to determine how many different ways they can fill in a grid with letters. Students are also required to show their work. They cannot just write down the number.

“You have to prove that your answer is the correct answer. You have to explain everything and carefully. If you don’t, you won’t get full credit although we do give partial credit on this competition for good ideas,” Miller said.

The coaches are there to provide more support and assist if an issue arose during the grading process. She said the Chinese organizers’ English skills were not always the best.

“If we thought they had misunderstood something of our student’s solution, then we would argue with them and try to convince them,” she said.

It was not all about math during their time in Asia. Before the competition, the group spent a few days in Hong Kong where they went hiking on a peak and had fun at an amusement park. Following the competition, the group visited Shanghai where they did some souvenir shopping, took a riverboat cruise and even got to take in an Olympic semifinal soccer game between Nigeria and Belgium.

“It was pretty cool to be actually seeing the Olympics in this huge stadium,” she said.

Miller was homeschooled from December 1994 until she went to college in September 2004. Both of her parents are mathematicians. She initially wanted to be a writer but then got more deeply involved in math. She said she is fascinated by the theory of numbers.

“There’s a lot of hidden connections and things we don’t understand all that well,” she said.

She graduated magna cum laude from Harvard University in June with a major in mathematics and a secondary concentration in medieval studies. In a month, Miller will be pursuing graduate studies in mathematics at the Cambridge University in London. She received the Churchill Fellowship, which covers all her expenses, including tuition, room and board.

In September 2009, she will be attending Princeton University, where she has received a National Science Foundation Fellowship.

“I definitely want to keep doing math research and keep on teaching mathematics,” she said. “We’ll just see where things take me.”