Let’s say that three students—we’ll call them Donald, Hillary and Michael—are running for class president. Fifteen percent of the class like Michael, 40 percent root for Hillary, and the rest cheer for Donald. In this simple scenario, the outcome is clear: Donald would win.
Now let’s add a few variables: Donald’s camp would never vote for Hillary, and would rather have Michael; the similar is true for Hillary’s camp, which would prefer Michael over Donald any day. Michael’s supporter would rather have Donald than Hillary.
Assuming people vote rationally, who should win?
This is a beginner problem from a set of weekly math teasers crafted by Po-Shen Loh, Associate Professor of Mathematics at Carnegie Mellon University and founder of Pittsburgh, PA-based startup, Expii. Each of the five math teasers get progressively tougher; Loh admits even he finds the final question in each set quite difficult
These puzzles can be found on Expii Solve, a weekly set of free online math problems that aims to show the beauty of math and help students develop a greater appreciation for the subject. Rather than emphasizing rote memorization and drill-and-kill exercises, these problems focus on logic and critical thinking to “show the amazing beauty of math,” he tells EdSurge.
The purpose of Expii Solve is to get kids—and adults—to approach math as an art. “When people look at art, they say, ‘neat!’ It makes you feel some kind of emotion,” says Loh. “But if you try to teach art by telling exactly how to hold the brush, measure the hues of each color and mix in exact proportions, and then assess students not by painting a picture but how well they can do these steps, everyone will say, ‘I hate art.’”
A wiry man with a flair for gesticulation, Loh speaks of the subject with the passion and eccentricity of a mad artist. He is a polymath who sees, well, math in everything, from politics and the Super Bowl to Gondor (the fictional castle in “The Lord of the Rings”), and draws upon his eclectic hobbies to come up with math problems.
He’s also the coach of the U.S. International Math Olympiad team, which in 2015 won the competition for first time in 21 years. To solve the math problems in this tournament, a 17-year-old student told The Washington Post, “you don’t need to have a college degree to understand. However, you do have to be creative.”
That’s the kind of mentality and approach that he believes is missing in math. The current instructional approach puts undue emphasis on finding the right formula and plugging in variables. That’s often the reason why students hit a wall at some point in math. (For me, it was calculus.) “If you learned math through memorizing and quickly plugging into a formula, that’s not the point,” says Loh. “The real point of math is thinking through which formula to invent, how to twist it and use it in a different way.”
The difficulty levels for the weekly math puzzles range from middle-school math to high school AP calculus. Even the first “easy” problem in each set can appear tricky; in the case of the aforementioned election problem, the solution required nothing more than simple addition and a dash of logic (as Loh patiently explained to me). “What makes these problems hard,” he adds, is that “you have to combine logic and a different way of thinking.”
“The beauty of these puzzles is that they don’t fall into any textbook chapter,” he adds. “The idea is that there is a lot of beautiful math that doesn’t fit into any linear curriculum.” According to him, the first puzzle in each weekly set should be appropriate for most middle-school math classrooms. It’s up to the teachers to check out the problems and see whether they find it appropriate for the students.
While the math problems don’t align neatly with any specific grade levels, Loh says advanced students are more likely to find them more enjoyable.
Expii Solve is just the first feature of a bigger tool, Expii. Describing it as a “mashup between Google Form and Tumblr,” Loh says Expii is a free platform that allows anyone to create and explain interactive problems, and surfaces the best explanations through a crowdsourcing platform. The platform is still a work in progress, but expect it to be polished by March, when Loh will pitch Expii to a panel of educators, investors and fellow entrepreneurs at SXSWedu’s Launch competition for edtech startups.
By then, Loh will also need to answer another math problem: monetization. A possible revenue source may be through online tutoring. “As people are interacting with the free content, we will be offering opportunities to interact with humans to assist them,” he hints. So far Expii has raised $1.31 million in seed funding from Great Oaks Venture Capital, Rothenberg Ventures, Tim Abbott and Adam D’Angelo.