The Fear of Math
THE PROBLEM
Time and again, I hear from fellow students, "I'm just not a math person." While this statement often comes most vehemently from those who have chosen fields classically defined as very far removed from mathematics (for example, fine arts majors), I also hear it whispered from those that have gone into very number driven fields. Engineers, finance majors, and, oddly enough, some math majors all too often seem to have resigned themselves to a minimal understanding of mathematics, a knowledge defined by a passing mark on a transcript and then forgotten.
"But why?" I ask.
The answer is always identical. A shrug, a few dismissing words, or some version of, "I just don't get it."
A few more prying questions will reveal the same story, again and again. Somewhere between fractions and calculus, a test was failed, a parent was called, and/ or a teacher was displeased. And that was it. The subject was passed with fear or apathy, and the joy from all future math spiraled down the drain. The student learned, in the vast and terrifying world of numbers, that they were not welcome, and that they should pass through as quickly and quietly as possible. For many people, this is the point where they decide, "I do not have a math brain, and I will never be good at math."
If math were not so integral to the American populace, this dismal view could perhaps be ignored, but when the epidemic of math hatred stretches all the way to mathematicians, it becomes more profound. Truly, every field involves at least a little bit of math, and thus every working person must face it. Why then should we be subject to fear every time a fraction comes across our page?
Recently, I've had a side project of making the infamous calculus a less frightening beast for my friends to come across. Perhaps algebra or geometry would be an easier place to start, but taming what many students have been taught to most dread in a matter of minutes seems so much more worthwhile.
For each person that I've taught calculus, I've used a different method, because, after all, we're all different people and have different ways of thinking (a fact forgotten by much of the educational system), but for most the "Ah-ha!" moment seems to come from a visual representation.
AN EXAMPLE
A friend of mine majoring in English with a passion for poetry once partook in the aforementioned, "I hate math," conversation with me. I protested this assertion even more vehemently than usual because:
A) This particular friend struggles with personal empowerment and the acknowledgement of her own intelligence, largely hindered by the social stigma around her major and its validity- something I hope to challenge of everyone.
B) Math is, to me, the purest form of poetry, and anyone who loves the flow of a sonnet should see the equal flow of a particularly well-solved equation.
To alleviate her fear, I drew her a riverbank, and I told her to suppose we knew how big each stone on the bank was (inspired by the origins of the word calculus meaning "pebble").
"Let's say each is 2 units," I said, drawing some large stones around the river. "And there are 6 stones. How big is the riverbank?"
"Well," she replied. "I guess it would be around 12 units."
"But there's a lot of sand between those big stones. What could we do to be more accurate?"
She studied the paper for a moment, clearly afraid to give me a wrong answer, before finally saying, "Use more stones?"
"Exactly. But the big stones won't fit. So let's use smaller stones and more of them."
Then I drew 13 stones, and I labelled them as 1 unit. She instantly gave me the answer: 13 units.
"So now we have a more accurate measurement, and I think you can see the trend: use smaller and smaller stones, and more and more of them to get the best possible approximation for how big the riverbank is."
Now I drew a new riverbank, but instead of stones I put lots of little dots, and I marked the river in feet.
"Let's see how big this riverbank is from the 2 feet to the 3 feet marker. We'll put 3 on top of 2 and draw a squiggly river running between them. Then we'll pretend the tree line follows some weird function - let's just say 4x^3. Throw in this weird symbol [dx], and we have an integral. This just means count all those little stones, all the way to infinitely tiny, and figure out how big the space is."
I proceeded to show her the basics of solving an integral, and I made another example for how derivatives work. The whole conversation took perhaps ten minutes, and by the end her responses came quickly, without the fear of being wrong, and she quipped at the end, "That's way less hard than I imagined."
WHY THIS WAS IMPORTANT
Did my friend magically discover a new passion for math? Did she really understand how to do calculus without my assistance, or even understand what calculus is? No, no, and probably no. However, she no longer grimaced when I brought up my major, and she even posed questions upon seeing me do my work later. We shared a wonderful conversation about the similarities between poetry and math, and a remark about the stones of a certain work of her own building up to a beautiful riverbank was met with a knowing smile. In short, her fear of math was largely alleviated, and all it took was ten minutes and a poor drawing.
Moving forward, my poor drawings will obviously not work on the large scale. My efforts are small, and thus they receive small rewards in return, but they do point to a larger movement that I firmly believe in: a dismantling of the fear of mathematics. I don't have the answers to how this movement will progress, but I see others making large strides in doing so. New programs are being made that cater mathematics to different learners, virtual reality apps are being developed to immerse students in the discipline, and even the time-honored horizontal teaching of arithmetic to algebra and so on to calculus is being challenged. Are any of these THE solution? Also probably not. But if there is one thing I have learned in math, it is that it is okay to be wrong, and the only way to find a solution is try, try, and try again.
CLOSING REMARKS
I am not a mathematics educator, nor am I any authority in math at all. In fact, I am a measly junior in my undergraduate career, struggling to find my place in the vast world of numbers, and I all too often do not practice what I preach (imposter syndrome is real and suffocating.) But this conversation is one that I believe needs to take place between all levels and all disciplines- from the most respected mathematics researcher to the artist who recoils at division- for the fear of failure in a subject that desperately needs more failure to fuel success stifles each and every one of us. Our world is built on numbers, and I hope to see the prolific distrust in this most truthful discipline be replaced by- at the very least- a casual appreciation of its magic.
Thus, I ask the questions:
- What can we do as individuals to help those around us dispel their fear of math?
- What can we do as a society to help dispel the same trepidation?
- What can we do for OURSELVES in this regard?
I may not know the answers, but at least I can finally say this: I am not afraid to try.