Math Class: The Importance of Asking the Next Question
This post is by Kyna Airriess, a 9th grade student at Gary and Jerri Ann Jacobs High Tech High.
In third grade I decided I didn't like math. I wasn't good at it, and I simply wasn't going to pay it any attention. That year everything we did was timed, and we did our timed drills as a class, so I was constantly comparing myself to others and feeling inadequate. I shut down. I felt that if I didn't try in math, I wouldn't have to face that I made mistakes and that I wasn't as quick with my multiplication tables as the rest of the kids in my class. I thought math had nothing to offer me, and it was the last year I was ever excited in math class. Until now.
In eighth grade, something was finally done about it. I asked for help and my mother decided I should do ten minutes of self-paced math practice every day. I became proficient in my times tables and sums. Once I saw myself as someone who was capable of learning math, I accepted it into my heart and perked up in class. Math became a thing of wonder.
I am a few months into my first year of high school. Prior to walking into my math class, I was worried that I might be stepping backward into a structure like the one that shut me down six years ago, but after a day in my new school's math class, I realized this would not be the case. In fact, my math class is very special. We start every class with a warm-up; sometimes it is very simple algebra, sometimes we are given symbols we have never seen before. Our teacher often tells us (as she did on the first day of school), "Find something you know. For Pete's sake, even if it's a four!" She reminds us to focus on what we know and just get started, rather than shutting down when faced with something unfamiliar. The norm that drives us forward is that you are never done with a problem. You always ask the next question.
Take -x+2y=8, for example. This is the sort of warm-up problem we would see during our bivariate statistics unit, and while you can very easily arrive at an answer, we are always challenged to say more. How could you manipulate this equation? What does this mean? What does it look like when you graph this equation? What does that line mean? What solutions make this equation true? Can you find the slope? What's the y-intercept? How do you know?
After everyone writes down all the observations and questions and alternative solutions to the problem they can think of, my teacher chooses two random students to lead the class in a discussion. One student calls on people to share their thinking and the other synthesizes the class's thoughts on the board. It's great to see all the different ways we approach the same problem and to be reminded that all of our brains work differently. Throughout our discussion, the emphasis is on the idea that mistakes make your brain grow. This discourages the shutting down that happens when we get mad at ourselves for getting problems wrong. Instead, we are encouraged to try again and be happy that our brains are growing. If we always get things right and never have to struggle, then we clearly are not being challenged enough and we aren't gaining anything from what we are working on.
It's actually a lot more difficult to think deeply about mathematics and stew in your thoughts than it is to memorize a procedure and carry it out repetitively. It can be very uncomfortable to find full understanding of a problem, but being exposed to that feeling over the past few months has changed my life. I learned how to ask the next question, and found joy in noticing new patterns. I even began noticing them in my everyday life. At the moment, my mother and I are 41 and 14, so our ages are palindromes of one another. What started as a wondering if this would ever be the case again lead me to discover a pattern that goes far deeper than I could've imagined. Not only does it happen with us, it happens every eleven years with anyone who had a child when their age was a multiple of nine. The difference between a number and its palindrome will always be a multiple of nine. (Isn't that cool?)
I brought this wondering to the people in my life--my parents, my friends, and my math teacher--who all gave me fresh ideas and insights into the problem I never would've noticed on my own. I kept working on it and I kept asking the next question, until I finally had a way of generalizing it for an any digit number. I actually proved the theory! And I experienced what it's like to be a mathematician, and to do math in the world beyond school. I noticed a pattern, explored it using the tools of mathematics, and collaborated with other interested people to learn something new.
My math class is powerful because it explicitly attends to a common misconception: that you either have a math brain or you don't. I think this is what derailed me all those years ago and led me to believe that I couldn't get better at math. In my math class today, my math teacher believes that anyone can do math at high levels, and your math brain depends on your willingness to exercise it. Your brain grows the more you use it. Now more than ever I believe I am living proof that this is true, and that anyone who wants to do math can find joy in it.