When students as young as the second grade show an advanced avidity for mathematics, many are given the opportunity to participate in international mathematics competitions.
The first opportunity is the Continental Math League, designed for elementary-age students. Although not the intentional goal of these competitions, they instill a particular philosophy early-on regarding the nature of understanding and learning mathematics.
These competitions progress in their rigor up to the infamous Putnam competition for undergraduates in North America.
I was given the opportunity to participate in a number of these intermediate competitions, including the Virginia Math League, the American Mathematical Competition and the American Invitational Mathematics Examination. A majority of these are run by the Mathematical Association of America, the leading organization for the field’s integration in education.
The types of problems found in these competitions fall under the branch of recreational mathematics. The problems are designed to incorporate concepts of common knowledge but require that these concepts be utilized in unusual and creative ways.
For example, a problem may appear to be in the field of number theory yet require the use of the pythagorean theorem, usually found only in geometry.
For some mathematicians, this kind of critical thinking is exciting, and the “aha moment” achieved when the solution finally comes to light is truly a glorious and satisfying moment.
Yet, it is an all too common experience for a student to be stumped on one of these types of problems. When they read the solution, they become frustrated at how simple the answer seems. Again, these problems take very basic concepts but use them in unusual ways.
In another perspective, there may exist a pressure on the students that detaches the enthusiasm from mathematics. Instead of the competition being about learning new things or having fun, it may become exclusively about winning or making a particular achievement (such as a particular score or a particular rank).
When I was in the twelfth grade, I was preparing for the American Mathematical Competition, the entry-level competition that eventually leads to the International Olympiad. The night before the competition, I had woken up at three in the morning to prepare. I sat in front of the computer in an attempt to understand a problem, and three hours later, I began to cry out of frustration.
I was simply unable to solve this problem.
My teachers at school were counting on me to lead my high school, the Commonwealth Governor’s School, to the next level for the first time in its history. And I felt as if I had an obligation to win for them. My failure to do so was quite upsetting.
Thankfully, this kind of pressure does not exist to the same degree in college.
Even when engaging in online communities, high school groups are incredibly competitive regarding sharing resources on how to perform better, whereas the college groups I engage in are more than happy to help each other.
Perhaps this is coincidental, but my performance in the Putnam competition far surpasses my performance in any high school competition, despite my excessive preparation in high school and lack of preparation in college.
One cannot learn creative thinking. It is not a skill that a student can read a book on. Rather, the skills required for these competitions are gained over time, and the pressure to perform well is futile and unnecessary.
The Mathematical Association of America designed these competitions to instill a love for mathematics in students. Although, these programs can clearly be used in ways that are detrimental to such enthusiasm. Thus, it is critical that students understand the true purpose of these competitions and remember to have fun participating in them.
By: Nathan “June” Richardson