This is related to one of my earlier posts: Partitions and the Quadratic Formula, but written from a broader perspective. Also, with more nostalgia.
One of my most vivid educational experiences dates back to a middle school math competition– Mathcounts. After months of hard work, our team of four students were ecstatic to have qualified to compete at the state level in Austin. In the weeks leading up, our sponsor had one goal in mind: beat St. John’s. This sentiment had been building up throughout the year. St. John’s was the local private school whose team had beaten us at the regional competition.
In preparation for the competition, we worked through lunch for a month to solve math problems in our coach’s classroom. Anyone who walked in would have seen four people huddled around a table talking numbers, but like children mesmerized by magic, we didn’t care what the others thought. Together, we had found something greater.
When we were able to solve a hard problem without guidance, the happiness was contagious. That is, until we realized the multitude of problems ahead of us and that many before us had already solved these problems. Nevertheless, to us each solution was an element in a series of epiphanies. As a team, we explained difficult problems to confused team members. When we were truly stuck, our coach would pull out the solution manual, and we would try to make sense of the official explanations.
As we pushed ourselves through problem set after problem set, we developed a mutual respect for each other. Like four legs of a table, our team was built on the idea that in order for the group to succeed, we needed support from all members. During the team rounds, we split up problems and learned to settle disputes quickly and effectively (though not always accurately). We shared our victories and failures, our laughter and frustration, our stupidest mistakes and grandest insights.
Through solving hundreds of different problems, I gradually learned probability, analytic geometry, and number theory. This was before I had taken Algebra 1. By comparison, my math class seemed dull (though I didn’t tell this to my sponsor, who was also my teacher at the time).
One day of practice in particular stands out. It was the Friday before spring break, and we had finished reviewing a set of problems with nearly 20 minutes left. One of our team members, Alex, decided that the logical thing to do was to go to the chalkboard and write ax^2+bx+c=0 followed by the statement “I’m going to derive the quadratic formula.”
When I was in kindergarten, my brother had made me memorize a sentence starting with “x equals” that included a bunch of a’s, b’s, and c’s. That was about all I knew of the quadratic equation. Deriving this mystical formula was a big deal for me, something complicated and important, though it had no bearing in our preparation for the state competition.
So I watched in awe as he rearranged and factored terms, until we were left with something that looked suspiciously like the quadratic formula.
Wait no. One thing was missing. An “a.”
For some reason, this mistake made us crack up and start repeatedly exclaiming “WHERE’S THE A?”.
The end of lunch bell rang. None of us left the board.
The students from our teacher’s next class began trickling in. They saw the four of us freaking out over a board of algebra searching for some mysterious “a” and silently stared at us.
After balancing our laughing with serious efforts to find our mistake, we found the “a” lost inside a fraction. Alex quickly filled in the chain of mistakes that the ‘a’ had created and we excitedly proclaimed to all within earshot, “WE FOUND THE ‘A’!”
The tardy bell rang, and we were officially late to our next period.
That didn’t stop Alex from exclaiming, “YES! I FINALLY GOT IT! I HAVE TO WRITE THIS DOWN!” Meanwhile, I knew I had to get to my next class. So while he was scribbling down the slanted rows of algebra onto a sheet of notebook paper, I packed my stuff and went to my next class, still feeling the euphoria from deriving a long complicated algebra equation and hoping that my 4th period teacher wouldn’t mind that I was late.
Two weeks later, we had to leave school right after lunch on Friday for the state competition. This was my first time staying away from home overnight with friends. As fun as this sounds for a middle school student, there was still a sense of pressure. This was when we were supposed to beat St. Johns. Something had to result from the loads of math problems and unfinished lunches.
After busting our brains through three intensive rounds of math harder than anything we had practiced, we were a bit demoralized, but still hoped for the best. Fortunately, we ended up placing 7th in the state, beat St. Johns, and all individually ranked in the top 25% of students.
There have been few days where I have felt as happy as I did when I clutched that right-triangle-shaped trophy on stage alongside my team members. But that happiness was mixed. At the same time, I knew that the state competition marked the end of our lunchtime practices, and that the sense of unity we felt as we worked towards a common goal was coming to a close. Two of our team members would be going on to high school, and I knew that the team I had grown accustomed to working with would soon change.
Math is easily the most stigmatized subject in America, even more so amongst girls, but within our 3 girl, 1 guy team, none of that mattered. I was extremely lucky be a part of this amazing experience with such a group of talented people who shared similar interests in middle school, and I’ve carried this motivation with me throughout high school.
We weren’t going through intensive training like the top schools and students did. Our sponsor merely sat back and let us learn from each other. There were no textbooks, no curriculum, no formula memorizing, no technology (even our calculator use was minimal)–we simply had problem sets, their solutions, pencils, and lots and lots of scratch paper. We were doing what we considered to be important in our learning, and we had the freedom to explore the topics that truly piqued our interest.