Math's Magic: Believing Is Seeing
By Margaret Zheng
This is the first of a series of three articles exploring the teaching and learning of mathematics in Council Rock. The second will appear in June’s issue of The Indianite, and the third will appear in the first issue next school year.
Belief is powerful. It affects even the way you begin reading this article and your decision to continue reading. If you believe for any reason that this is not worth reading, suspend that belief and blow it away. It will prevent you from learning what a fellow human has to say, and whenever that happens, you may miss out on something magical. So read on.
For a while I believed that there was something amiss about how we learn and teach mathematics, my love and others’ loathing, in school - something wrong in "the system," which I saw as a huge educational machine that renders most of us silent moving parts. Because I believed this, I became angry, and sometimes I directed my anger at teachers, hurting cherished mentor-friends (I apologize to them sincerely). I don't know if the belief was correct, but it shackled me to a prickly seat of unproductive rage. Belief is powerful. It makes you see limits and obstacles, or opportunities. I relaxed hold of my blinding belief, and I opened myself to a sharper sight.
Perhaps it is not inherent sin of an incorrigible system that keeps many of us uncomfortable with mathematics. Perhaps it is our beliefs about math and school that limit our mathematical imagination and potential. Both students and teachers whom I surveyed stated that one’s attitude towards or perception of mathematics influences one’s learning, with one math teacher noting, “If you think something is difficult before you even try, it usually is.”
When asked why some people are not yet good at math, many students answered that those people are not motivated to learn, believing the material not interesting or not relevant, or that they thought themselves unable to solve difficult problems. A freshman disliking math claimed she was “not a math girl.” Few students believed math to be creative or to involve interpretation; when asked if the variety of mathematical proofs implied creativity, a junior answered, “I just don’t associate [math] with being creative.” Some cited perceived rigidity of the subject or the class as the cause of their personal disinterest.
Yet I believe math, or maths as I like to call it – for, like “sciences,” maths are more than one -- is magic. Have you ever heard a child say that you could see magic if you would only believe? Whether or not you believe math is more mechanical or more creative is up to you, but if you would believe in a creative aspect of math, you might allow yourself to be in awe of ingenious and inventive manipulations of symbols and abstract objects into desired or unexpected results. You might see the magic. And further, like that imaginative child, if you would believe in your power to perform math’s magic, you could see yourself accomplishing what you once thought only a “math person” could do.
Math’s magic is not in speedy calculations, but in deeper conceptual understanding, in pushing the boundaries of your current abilities. And decades of psychological research have shown that when you believe your intelligence grows with hard work, you empower yourself to actually become smarter. Believing in yourself is seeing opportunity and eventually success. I write both to students and to teachers of any subject who might not yet like or find success in math, for according to some math teachers at North, learning math as an adult is valuable for recreation and mental fitness. Math teacher Ms. Cardamone observes, “[M]any adults may even come to appreciate the field more than they did when they were students in high school.”
There is another belief I have discovered among teachers and students that may harm our growth as a school community. It was what fixed me into toxic frustration: the belief that the educational system is an incorrigible machine in which we must be submissive levers and gears. It would be disingenuous to deny that a public school is under much pressure to comply with standards and to prepare for mandatory, high-stakes testing and so may have limited time to experiment with new teaching and learning methods. But considering that schools in many mathematically high-performing countries such as Finland and Japan spend considerably less time in teaching and more time in professional development than American schools (link), I wonder if we have more opportunity to imagine educational possibilities and to collaboratively improve than we have been accustomed to believe.
I speak to both teachers and students; I call upon them as one. I imagine that the Professional Learning Communities, which have the potential to help CR classrooms more effectively synthesize educational tradition and innovation, could involve teachers and students, the latter of whom educational consultant and science teacher Paul Anderson contended in his essay "Be Disruptive" to be professional when they are seriously motivated to learn, which all students can become. I intuit that our students have ideas about how to best learn math and that our teachers are motivated to learn to teach the best they can so long as things do not get chaotic. Do not worry about chaos yet; I only ask you to believe in the possibility of change.
To the end of making real that which is now the ideal, you might be curious to explore the online resource Youcubed.org, run by Stanford educational psychologist Jo Boaler, and some of you might then see opportunities to apply some of the psychology explored or the mathematical activities mentioned to your classroom. Others of you may be interested in the Students page on the website, which may show you math as you have never imagined. We may not need to uproot all current practice or incorporate every educational exoticism -- some of what our teachers already do may be highly effective -- we just need to believe that education can be more than what we see every day.
There is magic in belief, magic virtually omnipotent. It affects even the way you react to this article and your decision to proactively respond. If after considering my ideas, you choose not to believe that we as individuals and a school can and should grow mathematically, well, it is your choice, but you may miss out on something magical. So learn on.
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