Educator, Mathematician Po-Shen Loh Speaks With the Eagle


Photo courtesy of Carnegie Mellon Swartz Center for Entrepreneurship | Po-Shen Loh speaks at CMU event

Sam Bisno, Editor-in-Chief

Po-Shen Loh wears many different hats, each of them in some way related to math. A graduate of the California Institute of Technology, Cambridge, and Princeton, his official job description lists him as a teacher of discrete mathematics and external combinatorics at Carnegie Mellon. When he’s not inside the classroom, he’s occupying himself by coaching the United States International Math Olympiad (IMO) team, which he led to back-to-back competition victories in 2015 and ‘16. Oh, and he’s the founder of Expii, an educational website that aims to make math and science learning both fun and more easily comprehensible. We had an opportunity to chat with Mr. Loh, one of the foremost experts in his field, about Expii, his career, and his beliefs about the subject he’s dedicated his life to.

We started by asking Mr. Loh what made him want to become a mathematician, to which he replied that there were three main aspects of the gig that he most enjoys: “doing things that are supposed to be impossible”, “analytical thinking”, and, of course, “making people laugh.” That’s right, folks, you heard it from one of the country’s most distinguished math geniuses: comedy is key.

Next, we touched on Mr. Loh’s involvement with the IMO. As it turns out, he competed in the tournament when he was in high school, around two decades ago. Surprisingly, he wasn’t always such a stud: “I say that [my participation] was maybe a stroke of chance. It’s not that I was particularly great, I just happened to really enjoy math and I had a really good year after that.” Modestly, Mr. Loh revealed that he won a silver medal at the event, and that this ignited an interest in math education.

Before we moved on, I couldn’t resist picking the brain of such an illustrious figure regarding a question I’ve had for years now: whether it’s truly possible for someone to be “good” at math — in other words, that math is an innate skill — or whether we all begin on a level playing field, and it’s simply a matter of practice. According to Mr. Loh, the answer is definitively the latter, but his justification is perhaps more fascinating than the response itself. Without hesitation, he had pulled something up on his phone. “I’m going to give you five seconds to memorize this picture,” he said, a slight grin begging at his face. “This picture has a bunch of random lines on it. I’ll give you five seconds to memorize it, and afterwards the challenge will be to redraw as much of the picture as you can.”

The image? The word “hello” in six different languages – English, Arabic, Hebrew, Hindi, Mandarin, and Russian. “Which part did you get? The English, right? It probably took you like half of a second. Any others? No. This is what I’m trying to say. Is someone born with the ability to read in English? I don’t think so. A three year-old in China would get the Chinese, but probably not the English. To you, those squiggly lines are just that — squiggly lines. To others, they’re letters. Since you understand the letters ‘H’, ‘E’, ‘L’, ‘L’, and ‘O’, you can use that information to know that they spell the word ‘hello’, whereas with the other languages, even now that you know that they all say ‘hello’, you don’t understand the conceptual pattern of how the squiggly lines fit together, and so you don’t actually understand the language. It’s the same deal with math. If you understand the concepts – why each formula works — it’s so much easier to learn. With memorization, though, it’s information overload.”

“Sometimes memorization works. There are only so many formulas, and it might be the easiest way to do well on a test. But then as you start to get into high school, there’s too many, and that’s when people start to get like, ‘What the heck is going on?’. It’s just too much. But if you take a step back and you start to understand why each of those things fits together, then you can actually learn math much easier. What I’m trying to say is that the difference between ‘math’ people and ‘not math’ people is about who is getting all of the concepts of how everything links together, the same way some people can read Arabic and some people only see squiggles. So I think everyone can get it.”

When asked to offer a few words of advice to any students who feel as though they are of the “not math” camp, Mr. Loh employed yet another striking analogy: “A lot of times, it’s just fear that’s holding you back. If you tell me to a walk for a mile on a sidewalk, I can do it, no problem. But if you raise the sidewalk a mile in the air and put cliffs on either side, I won’t make it. I won’t make it because I’m just going to be completely thrown off by the possibility of falling. If you’re afraid of math like this, one of the best things to do is to talk to someone. Talk to a peer that can help you understand the part that you’re not understanding and build a foundation from there. But if you believe you can’t, you won’t be able to.”

This train of thought proved a convenient transition to the main course of the conversation: Expii. First, what exactly is it? In its creator’s words, “a social enterprise which seeks to bring more to and transform the landscape of math and science learning in the U.S. and the world ….. A way for anyone to be able to learn in a setting that’s very similar to a one-on-one tutor.” Essentially, the website acts as a supplement to traditional classroom instruction, helping students struggling with certain topics bolster their skills in an interactive and accessible way, as opposed to the traditional “sift through Google.”

The project came about shortly after Mr. Loh became the head of the US IMO team. Previously, he explained, he had been focused almost exclusively on expanding CMU’s math program, but after taking on the responsibility of a national leadership role, he began to ponder education and its methods in general. From there, he decided to explore new ways to integrate technology into already established curriculums, and he didn’t look back, attracting colleagues along the way until the Expii office became what it is today — a bustling community of some of the brightest minds in the industry, “uniting the diverse skills and ways of thinking necessary to solve something this big.” Of course, a tech-based workspace wouldn’t be complete without all of the requisite gadgets, and this one doesn’t disappoint — a fancy doorbell, a green screen, and plenty of overly tall monitors displaying plenty of overly confusing numbers.

So, the specifics. First off, Expii features a built-in algorithm that automatically adjusts the difficulty and topic of practice exercises based on a student’s prior performance. But these aren’t your same old, boring, meaningless word problems. On the contrary, thoughtful writing makes using the software not only an edifying endeavor, but an engaging and downright funny one.

I re-visited Mr. Loh and his team at a later date to put these claims to the test, and I can attest to this effect firsthand. Here’s an excerpt from one of the lessons I encountered during my brief session:

“The Pythagorean Theorem was discovered by Pythagoras around 500 BC when Pythagoras was running late and saw his bus pulling away. Struck by the sudden understanding of geometry and the universe, he realized he could cut through an alley (doing sick parkour along the way) and arrive before the bus.”

This introduction alone immediately paints a stark contrast to most other published materials on the same concept (in this case, the Pythagorean Theorem). Regardless of individual opinion on this style, it is indisputably a change of pace. But it doesn’t stop there. Remember that green screen? Well, Expii has been experimenting with other forms of media, namely film. Here’s the video that accompanies the above passage:

Overall, the hands-on, flexible, conversationalist, and student-first nature of the website allows it to offer a more relaxed, stress-free experience relative to some of its fellow learning services without diluting any of the educational value. Expii knows its audience, and it makes an active effort to convey useful information without boring them to death or overwhelming them with needlessly complex or technical language.

Before our meeting came to a close (Mr. Loh, busy as he is, was rushing to his next engagement), the man in question was kind enough to divulge a few final tidbits of wisdom. As far as math is concerned, he maintains that the subject transcends mere figures, graphs, equations, and so on: “One of the most important aspects of our humanity is our mind and the fact that we think. I’d like to create a more thoughtful world, and a mathematical way of reasoning is a way in which everyone in the world can be equipped with a way of looking at the world and understanding what’s fair, what’s not fair, what they should do, and why they should do it, instead of having to listen to what somebody else told them and trust based on having heard enough people say something and therefore believing it.”

He also hopes to separate math from its associated stereotypes, thus making it more ubiquitous. “Picture of a brilliant mathematician who is maybe in his twenties or thirties notice I’ve already said the word ‘his’. And if you picture this person, you are probably picturing Sheldon from Big Bang Theory. This is not what mathematicians necessarily are. Everyone could be a mathematician. It doesn’t have to be a guy, and the person doesn’t need to be completely socially awkward. I think that needs to change …. Go and tell movie producers to change the way that they’re casting or writing scripts. Sometimes the only way to do it is to do it yourself. In fact, one of the goals we have here is to also work towards production of media – of different things that portray the different lights.”

As for Expii itself, Mr. Loh says that his ultimate aspiration is to reach one billion people. Current analytics suggest that the company has broken through into the hundreds of thousands, so, in his own words, “There’s a ways to go.”

Lastly, a recommendation for any students looking towards CMU as a possibility in their future: “From a young age, it’s healthy to start picking up an insatiable for knowledge and for pushing the limits. This doesn’t mean just getting good grades. This means thinking about what the next big thing that can be done is, saying ‘I’ve achieved X, but what does X+1 look like?’. And if you don’t achieve X+1, then trying again. Don’t just go for perfection by someone else’s standards, but define your own standard. Do that, and schools like CMU will take note whether it’s for math, drama, whatever.”

With that, our time together had elapsed. The Eagle would like to extend its gratitude to Mr. Loh for taking the time to sit down and talk, and would also like to encourage interested readers to explore Expii.