How Math Taught Me to Take Risks

by Raymundo Gonzalez Leal | Dec 10, 2016

Traditional education can feel like a ladder. You are told which way is “up” and that all you have to do is keep climbing: never pause, or look to the side. Climb the ladder and you’ll do well in life; memorize information, then regurgitate it on exams. Remember the steps for a math exercise, and use them when you see another exercise just like it. Each and every time. This will lead to good grades, and good grades eventually translate to good job opportunities.

Don’t they?

The reality is that these opportunities are often influenced more by factors unrelated to one’s ability to climb the educational ladder. Don’t get me wrong: doing well in school can move students closer to better opportunities for professional development. But being born with certain advantageous circumstances (for example, into a stable socioeconomic status) might give access to the elevator instead, allowing one to speed past the ladder that many less fortunate people are struggling to climb. In that world, simply getting good grades does little to help underprivileged students catch up. Becoming a critical thinker and practical problem solver are far better objectives for one’s higher education.

I happen to be good at memorization, following rules, and taking exams. So, to be honest, I never questioned the ladder until I discovered something better — first at Kumon, a math institution in which students work at their own pace to master a skill level, then while training for the Mexican Mathematics Olympiad, and now at Minerva. At Kumon, I wasn’t lectured at. I was presented with examples, asking questions when things were not clear, and then receiving problems to solve. Once I had solved them, my work was graded and returned to me. I could see which problems I got wrong and in which parts, but I was not told what I should have done instead; this was left for me to figure out. I would then do those problems over, hand them in, and repeat the process until I got them right. Through this process I developed patience and persistence, as well as a much deeper understanding of the material. For the first time, I was required to actually think, to solve problems for myself — and that was more satisfying than doing math the way I had been taught in school.

Then, when I joined the Math Olympiad team in my last year of middle school, the idea of climbing a prescribed ladder was challenged even further. On my first day, a problem was written on the board, and after considering it for a while, I concluded that I didn’t know how to solve it.

“If you knew, it wouldn’t deserve to be called a problem, and you would learn nothing from it,” said the trainer, Héctor Flores. Héctor is the kind of educator that never tires of giving this kind of sage advice, year after year. Notice, I say “trainer,” not “teacher.” The faculty at the Math Olympiad believe that most of the time, they shouldn’t try to “teach” you, but rather act as coaches for your independent learning. True understanding of a theorem doesn’t come from listening to a teacher talk. Understanding results when your mind makes the right connections. When you are given a solution, you know how to solve that specific problem. When you work to find a solution, you acquire insight, which allows you to solve problems that might at first seem completely unrelated.

Math Olympiads taught me that real problems don’t have an easy or obvious answer. Real problems are those where you have to figure out how to reach the end goal on your own, and then do it. It was in this program that I suddenly realized how none of my previous math classes at school had challenged me to work to solve problems at all!

The Math Olympiad defied the ladder. Héctor uses a different analogy, saying that math is a vast land, and schools normally take you through the most transited roads. However, things only get interesting when you get off those roads, by exploring and finding your own paths to reach solutions. After all, how can you expect to solve what no one else has solved before, just by following the steps others have already taken? For me, math became something where creativity was essential, where thinking in different ways could lead to the best solution. I found that discovering the path to solving an “impossible” puzzle is extremely gratifying — especially when you arrive at ideas that most others didn’t see.

When I learned about Minerva, the undergraduate program I now attend, I saw an opportunity to completely leave the proverbial ladder. I had a substantial scholarship at one of the best (arguably the best) universities in Mexico. I was, admittedly, a hardcore ladder climber. I’d gotten into the best middle school in my town, where I had to be the best to get a scholarship for a high school in the city. In that high school, again, I had to have the best grades to get a scholarship to university. Naturally, when I considered leaving traditional education, I was afraid. I had invested so much effort in that direction: the ladder I had been climbing for years. I was afraid of disappointing family, friends, teachers, and everyone else who had helped me along the way. But I realized the ladder would always be there, even if my attempts to find something better failed, but opportunities like Minerva might not. I did with my education, what I had learned to do with math at the Math Olympiad: I departed from the most transited road.

The Minerva model is designed to prevent us from getting high grades in a class just by memorizing information and spitting it back out; we really need to think and engage. We have learned about biases and their effect both on ourselves and others, and we constantly try to challenge them, or use them to communicate with different audiences and predict how people will react. We learn to analyze economies and societies as complex systems, and we consider the best ways to convey information to others in a given context. We are encouraged to use what we learn creatively. For example, when discussing policy in a social science class, we are recognized for appropriately applying the game theory learned in a math class. At Minerva, I exercise the kind of thinking I developed at the Math Olympiad, but for things that go far beyond math!

I am also finding the benefits of this non-traditional path as I begin my professional career. I currently have an internship at Audible, where I am tasked with designing, running, and evaluating experiments. Here, I’ve found that my employers aren’t concerned about grades, or the fact that I am a sophomore not a senior. What matters to them is what I can do, the problems I can solve, and the ideas I bring to the table. An education that helps you develop key skills like critical thinking and effective communication is a much better route to opportunities than the traditional education ladder.

In Ray Bradbury’s novel, Fahrenheit 451, schools prevent children from thinking by bombarding them with useless information to keep their minds inundated. Though Bradbury’s scenario is extreme, it illustrates a valid concern that the systems supposed to educate us are not focused on helping us develop the most useful skills. I am sure there are other places to find the kind of challenge and growth opportunity I first experienced at the Math Olympiad, but in my opinion, these opportunities should be inherent in all educational systems. After all, life is not a ladder. It is something much more complex and fascinating, and the skills necessary to face the world’s problems go far beyond memorizing information in service of good grades.