The team that won in the 10-day Hong Kong competition was trained by head coach Loh, an associate professor of mathematics at Carnegie Mellon University in Pennsylvania. The United States won in 1994 but then had a drought until 2015, when it surprised pretty much everyone by taking the gold medal. Winning in consecutive years is astonishing but telling, Loh said.
“I think that we see excellence springing up all around the country because of the growth and adoption of free online resources, which can combine nicely with the creative and open culture of our education system,” he said in an email. “It is now becoming possible for any student who wants to excel at math to do so, no matter where they come from, or what their local resources look like. This is accessible to the mainstream, and isn’t just for people with existing ability.”
The six members of the team — all males — are Ankan Bhattacharya (International Academy East, Troy, Mich.); Michael Kural (Greenwich High School, Riverside, Conn.); Allen Liu (Penfield Senior High School, Penfield, N.Y.); Junyao Peng (Princeton International School of Mathematics and Science, Princeton, N.J.); Ashwin Sah (Jesuit High School, Portland, Ore.); and Yuan Yao (Phillips Exeter Academy, Exeter, N.H.).
They were selected through a series of competitions around the country organized by the Math Association of America. Scores at the competition are earned by individual team members who are given six math problems to solve.
Why no females on the team?
“My feeling is that the low number of girls at the very top in the high school math competitions is a consequence of effects which start in middle school, and I’ve been interested in addressing the issue at its root,” Loh said. “At the same time, a very interesting feature of these high school Math Olympiads is that the challenges do not involve calculation.
“This is very different from the types of mathematical challenges that students have been used to from school — the same challenges which have already created a gender gap at calculation-based advanced math.”
Here is what some of the Olympiad problems look like:
It is worth noting that although Americans overall perform, at best, average on international tests such as PISA, which are taken by 15-year-olds, kids who attend schools with low poverty rates often do as well as students from any other country.
As for the winning 2015 and 2016 International Math Olympiad teams, Loh said that they were very different (except that both were all male.) The pioneering 2015 team consisted of four students in their final year of high school, plus one student in 11th grade who had won a gold medal at a math Olympiad before, plus one more student in 11th grade. The 2016 team consisted of four 11th-graders, none of whom had any Olympiad experience, together with the two students from last year’s team. All six won gold medals this year.
“This is a remarkable turn of events, because a team composition like this year’s would normally be thought of as a “rebuilding” year, not a winning year for a country whose wins came 21 years apart,” Loh said.
How did this happen?
He said that the Olympiad featured an unusually large number of math problems which “fused multiple subjects in nonstandard ways.”
“For example, one of the questions combined elements of geometry, number theory and algebra, and required highly creative insight in order to solve. Formal training was of course useful, but not sufficient on its own. On that particular question, this U.S.A. team achieved the highest combined score over all countries, building up a lead which ultimately contributed to its No. 1 finish. The American system encourages creative, out-of-the-box thinking, and invites young people to challenge norms. That is not to say that the American system is perfect. The ideal might come from a fusion of elements from systems which stress creativity and systems which stress core skills.”
Loh said he wouldn’t claim that the United States is “equal to other countries at math” but that the results provide an interesting lesson in the advantages a “creativity-focused system” can provide. Loh, in his training of the team, uses “analogous out-of-the-box principles.”
Loh has used the techniques he employed to train the team — along with dozens of other leading high school mathematicians — in the summer at Carnegie Mellon to develop a free program for anybody who is interested, whether or not they are math whizzes. He is launching a weekly math challenge called Expii Solve, which is intended to help people at all levels learn math concepts from examples rooted in the real world. Hosted on Expii, a crowdsourced database of explanations to math and science concepts, he is concocting math adventures each week for five different levels of expertise — and it’s all free on a smartphone.
Here’s some information about Expii Solve, with questions answered by Loh:
Can you give us a little background about yourself and why you started Expii Solve?Besides being an associate professor of mathematics at Carnegie Mellon University, I serve as the national coach of the USA International Math Olympiad team, which won this summer for the first time in 21 years. As a coach and professor, I’m constantly being asked by people how to get better at math. I started Expii Solve because it not only solves the problem of helping people get better at math — it really teaches people what math is.What do you mean by that?If you ask the average person what math is, they’ll probably answer that it’s doing addition and multiplication, or making graphs, or something along those lines. That’s not really what math is. Math is the art of thinking in a systematic and organized way. It applies creative problem-solving techniques in a quantitative way using a sound system of logic. Math is all around us, and the general public doesn’t realize how applicable it is to their everyday life. My goal with Expii Solve is to not only help people understand more about math, but to get them excited by it.So how does it work?With Expii Solve, every week we release five different prompts. Each prompt is a different level of difficulty and revolves around a different topic and skill. You start out at the first level, and get to learn a surprising new skill that’s presented in a real-world application. For example, we just launched a weekly Expii Solve. The first level is about the lottery, which was just looming on everyone’s radar. We created a fictional lottery called the Power Ten, and we explain how it works, and the mathematical concepts behind it — namely statistics and probability. At the end, we have a question that combines mathematics with some out-of-the-box thinking. The punchline is at the end, we highlight an article with a real world application — something very similar to the very problem you were solving was actually done by a group of MIT students, who realized they could game the lottery to virtually win money every time.The first level should be understandable by the average high school student, but the answer will often still surprise many who are more familiar with math. If you like that one, you can try the next, which takes it up to the next level. Sometimes there will be continuity between them, sometimes there won’t, but the idea is to always use a topic that highlights some interesting math which might not be commonly known.Our goal is that every week, you can pop this open on your phone and learn something new and interesting–perhaps while waiting for the bus, or between places. We want to make sure that everyone can access it, so it’s completely free for anyone in the world to use. The design was also very important to us, so it’s visually pleasing along with being mentally engaging. The team working on it isn’t only comprised of mathematicians — we have people from all sorts of backgrounds, like creative writing, design, software engineering and science.Why is it called Expii Solve?Instead of just being a weekly quiz, the goal of Expii Solve isn’t only to test you, or even to teach a single concept. The goal of Expii Solve is to explore, which is why it’s hosted on our site, Expii.com. I think that one drawback of pure testing is that it doesn’t encourage further exploration, which is really what we’re trying to facilitate. Expii.com is a much larger project that I started that crowdsources math and science topics.Think of it almost like Wikipedia, except there’s not just a single page for a topic that every perspective has to conform to. For any given topic, there can be unlimited submissions with all sorts of different ways to explain the topic — and they all support interactivity, with instant-feedback Q&A, videos, etc. The idea is that there is no single best way to explain a math or science concept. Every person who has a good explanation might have a different angle or perspective they approach it from. With Expii.com, we don’t discriminate, and instead crowdsource human creativity. Anybody can submit an explanation, and/or questions to test your comprehension of the concept.Expii.com is like having thousands of tutors in your pocket who don’t only teach you the concept their own way -they also make sure you understand it by asking questions, like any good tutor would. Our goal is engagement, so you can vote on someone’s explanation, and the best-voted (most engaging) explanations go to the top of the list for a topic. The core idea is that accuracy isn’t enough. Accuracy alone doesn’t engage people. Creativity engages people.So how does Expii Solve fit into that?Expii Solve can be the first step to an exploration. You can go down a rabbit hole of learning on our site, where you keep clicking and learning about new topics that interest you. The vision is to have a time every week for math appreciation. We provide a guided starting point with our feature, and you can then go on from there!
Loh also is working with colleagues on a new program called the Spirit of Ramanujan Math Talent Initiative, aimed at finding undiscovered mathematicians around the world and giving them an opportunity to advance in the field.
The project, which remains open until Sept. 15 and which you can learn about here, is led by Ken Ono, a professor of math at Emory University. Partners include the Templeton World Charity Foundation in conjunction with IFC Films and Pressman Film, producers of the motion picture “The Man Who Knew Infinity.”
That film is about Srinivasa Ramanujan, a gifted mathematician who in 1913, as a poor college dropout who had taught himself math, contacted British mathematician G.H. Hardy. (Dev Patel plays Ramanujan and Jeremy Irons plays Hardy in the film.) Ramanujan’s math theories were so extraordinary that Hardy invited him to Cambridge to study and collaborate. He died at 32 but left behind material that is used as the basis for math research today.