Solving math problems can be more thought-provoking than the traditional method of repetition and teaching to/for a test. Our May Member Spotlight, Po-Shen Loh, PhD, is the national coach for the USA International Mathematical Olympiad (IMO) team and who has invented a new incentive-aligned ecosystem for massively scaling up math coaching. Po-Shen shares his mathematical journey, expanded thinking, teaching methods, and more.
Mathematics Foundation
Po-Shen has been immersed in mathematics since he was a child. In fact, he shares that his mother taught mathematics in Singapore with more traditional techniques. “I started out doing math when I was very young. [My mom] was a teacher in the 1970s and when I was in elementary school, I learned math that way. I felt like I could do math. I enjoyed it because I was perhaps good at it,” Loh says.
His father taught statistics at the University of Wisconsin and introduced another way of approaching math learning. “When I was around fifth grade [my dad] decided that it would be a good idea to work on questions that were not as traditional, but ones that involved significant thinking because he’s a researcher,” says Loh.
His father would find problems and he (Po-Shen) would spend about a half an hour working on each one, according to Loh. “That’s very different from traditional [mathematics]. [With] traditional mathematics you should be done in like 30 seconds, not 30 minutes. So that got me to enjoy thinking about things for a while, finally getting a breakthrough was a nice feeling,” Loh shares.
Competition Introduction
Po-Shen first crossed paths with competitive mathematics in the sixth grade. He was instantly interested. He found that there were questions that were non-traditional, in which the student would have to use critical thinking to come up with their own idea to solve a math problem. “I hadn’t seen it before and thought it was very fresh. I really enjoy coming up with new ways to do things,” says Loh.
By the end of middle school, Loh spent a vast amount of time working on types of questions he hadn’t done before. However, in high school, he learned about the Mathematic Olympiads.
That’s when I learned about the kinds of ways you think about when you do research mathematics - by doing these math olympiad problems,” Loh explains. “Of course they’re much easier than real research problems, but it introduced me to this idea that the answer to a math problem might be an entire page of writing.
Po-Shen Loh
Thought Process Shift
When he later began working in research, he noticed the similarities with the olympiad problems; you don’t have someone else give you problems, you decide what problems to work on. He credits that major transition to his PhD advisor. “He was the one who taught me how to transition from looking for questions that people give you, to figuring out what questions you want to sink huge amounts of your own time into doing,” says Loh.
My entire style of how I like to do anything is to come up with my own way to do it.
Po-Shen Loh
“I look at actual problems that are facing real people and come up with crazy new ways to solve them. This all comes from the fact that I spent many years when I was young working on things where you don’t know what to do,” explains Loh.
“I give a lot of talks to parents explaining one way to do well in the American Mathematics Competition (AMC) is to practice until you’ve seen every problem type and you can do it cold without having to think. In fact, some parents say that they hope their children won’t have to think when they’re doing the test because they’ve done so much practicing.”
That’s the standard cramming technique, according to Loh, that if this happens you’ve lost the entire point. He was constantly facing new challenges, not repeatedly doing the same problem until he got it right, and this attitude toward solving equations excites him.
“Thinking for a half hour on each problem is something that a lot of parents who advocate for the drilling method, get freaked out or worried about because it doesn’t feel efficient,” Loh explains.
If you spent a half an hour just practicing the thing, then you’d know how to do it by now. But actually a half an hour of thinking is teaching your brain to come up with new ideas.
Po-Shen Loh
AMC Involvement
Members of Po-Shen’s study group informed him of the American High School Mathematics Examination (AHSME).
“That was the old name, at some point the MAA decided to rename the ASHME to AMC. I took it, did well and went onto the next one, the American Invitational Mathematics Exam (AIME), where I did fairly well and they congratulated me and said there’s another test called the United States of America Mathematical Olympiad (USAMO).”
He looked at these problems and noticed that he had never seen anything like it before, but was eager to solve them. He did well and received an invitation to the Math Olympiad Program (MOP). “That’s when I really started to learn how to do a math problem that you have to write up,” Loh shares. Finally, I was surrounded by people who were doing proof style math, where you write explanations and come up with your own ways to explain why something is true.”
Teaching Brilliant Minds
Po-Shen has the opportunity to work with some of the most mathematically skilled young minds in the country. He finds that as a coach, he must think outside of the box when it comes to guiding them.
“When you work with people who are selected as the top six in the country, based on math competitions, they are very good at math. The main challenge with coaching them is to find something that you can teach them,” says Loh.
This is true of everyone who works with the top students in the country, because they come in knowing copious amounts of information, according to Loh. While coaching, he often thinks about how he can add value.
“This is actually something I had a conversation with Michael Pearson (MAA Executive Director), about ten years ago, when he was talking to me about taking this job. I said if you put me on [the team as the coach] we’re going to do worse because I don’t focus on whether the US wins the contest. That’s not my point, my point is to maximize the chance that I will read about these students doing extraordinary things later on as they grow.”
Loh’s main goal as an international coach is to focus on the best interest of the students beyond competitions. He notes that in the curriculum that he gives to his students, there are a lot of topics that have nothing to do with the IMO. Each student is shown what professional researchers care about, which hopefully encourages them, when they grow up, to have something to reach for, according to Loh.
“My goal is to make high school students see that there’s a point to this that is far bigger than trying to get some score,” Loh says. “It’s a different angle, and I’m very happy with the results. The US team ended up winning and that was not because I taught them anything, it’s because they were good and they ran.”
“In 2015 and 2016, those two teams that won number one back to back, was the first time ever in US history that they won back to back number one. Three team members have already made research advancements, and this is what I’m happy about,” Loh shares.
Three former team members from the 2015 and 2016 teams have been featured in Quanta magazine, which is extremely reputable in the math, computer science, and theoretical physics world. Ryan Alweiss and Yang Liu, from the US 2015 IMO team, have been featured, as well as Ashwin Sah, from the 2016 team.
MOP
“What do you do with kids who are super smart,” Loh asks. “Do you bring them 1,000,000 math problems to do? I said, no, I’ll bring them professionals.”
Last year and this year, MOP was held at Carnegie Mellon University along with an international mathematics research conference. “This is very unusual for a national math olympiad program to go and say ‘hi, we are going to bring you things that have absolutely zero to do with math competitions, but by the way, some of the most extraordinary researchers in the world just happen to be 100 meters away,’ let’s go and watch them,” Loh says.
Gender Diversity
When asked about his previous comments on increasing gender diversity, Loh mentions the European Girls Math Olympiad (EGMO) team leaders, Rachel Zhang and Meghal Gupta. “They are doing a fantastic job and what I do is just to support them. They are very passionate about what they're doing,” says Loh. “In my opinion, they are doing the biggest thing right now when it comes to gender diversity in extreme math achievement. I was trying to make sure that we could have the funding available to make sure that we have non-male students who are at the Math Olympiad program.”
This is also a topic Po-Shen cares about because his daughter was on the EGMO team this year. “I will say the important thing to know is I never taught her anything. I was very careful [of this] because if she ever achieved anything, no one can say her dad taught her,” explains Loh.
It’s very important to Loh that his first child knows that she accomplished mathematical success by herself. “I will say, although I didn't teach her anything, we have certain philosophies,” explains Loh. Philosophies centered on teaching students how to think are shared during many of his lectures.
“Although I didn't teach her anything, my style was always networking when I was growing up. I like talking to people and making friends,” says Loh. “When she was young, we brought her to lots of math contests, but we never said that she should try to win. The questions [I ask her] after a math contest are, ‘Did you meet any new people, and do you have ways to keep in touch?’ Ever since she was young, those are the only two questions I have asked.”
Math Accessibility
Po-Shen is also a math professor at Carnegie Mellon University, which provides him with the freedom to teach his philosophies and supports his overall mathematics vision. He’s also able to work on real-world problems.
“The way I inform my decision of what to do is by actually going into sixth-grade classrooms and teaching in Title I schools,” Loh explains. Title I is a federal program that supports low-income students throughout the nation.
Loh teaches sixth and seventh-grade students in math class. He chooses to do this so that he can fully understand the situation before working on the solution. “I was challenged by a Carnegie Mellon University trustee to see if I could make this work in Baltimore. He grew up there and went to a very strong magnet high school,” Loh explains.
The CMU trustee, Larry Jennings, introduced Po-Shen to a middle school principal who allowed him to go into the classrooms, where he began to understand the in-classroom issues further. He has focus group discussions where he speaks to the most motivated students in the classroom to find out what ignites their interest in mathematics.
“My hypothesis is that in every single place, there will be some people who are very motivated, and want to do something to improve their lives, and they don't exactly know how [they can achieve their goals], but they will work hard if they have a path,” says Loh.
When there aren't great paths is often when people give up. It's not a question of if people are willing to work.
Po-Shen Loh
