Updated: Nov 8
Hi everybody! This week's article is actually one that I wrote for my school's newspaper, The Blue & Gold. I know I'm preaching to the choir here because if you're a member of my site, you probably already love (or are learning to love) math, but I still wanted to provide you with my perspective about the school system and how it communicates math.
It's good to remind all of us that if someone we know is struggling in math class, it doesn't mean they're not a "math person", and it doesn't mean they don't "understand math." It only means that the way the school system teaches it doesn't work for them. Math is often the most misunderstood subject, and as math people, we sometimes have to put ourselves on the defensive when we explain why we do what we do. As my members, I'd love for you to be my ambassadors. Go out there and show everybody that there's more to math than what's taught in school, explain to them why you love it, and most of all, use it as your stepping stone to whatever you want to accomplish in life! Point them to my site and show them what math truly is. So without further ado, here's my article!
Stop Teaching Our Students to Fear Math
by Catherine Cossaboom
Last week, I listened to a podcast on NPR’s TED Radio Hour called “Don’t Fear Math,” a program intended to raise awareness about what math can do for all of us and to address what we’re doing wrong as a society and how we can counteract that. The speakers made very valid and bold claims, arguing that as we move further and further into the digital age, it’s important that we learn how to become mathematically literate. Some guests addressed the gender gap in STEM and others talked about education reform, but all understood that we’re approaching the subject the wrong way.
The show was well done, but its title got me to thinking. Doesn’t “Don’t Fear Math” imply that fear of math is predicated, rejustifying that stigma? If most of the press out there — even the press intended to change society’s perspective — assumes that its listeners and readers come from a place of fear and apprehension, doesn’t that distance them from math before the dialogue even starts?
It’s been over a year since I wrote my last opinion piece on math, and I thought it was time I readdress it. Last time, I tried to give readers an angle on how the mathematical world feels about their subject, and how different it is from what schools condition us to think math is. This time, I thought I’d focus on how we can change this, showing a mindset that gets us moving forward and the educational system that supports it.
I’ll start with an idea all the speakers in this podcast share. You don’t have to have a “math brain” to understand math. Math is all around us, and sure, it comes easier to some of us than others, but it’s something we all can pick up. After all, as Masha Gershman, a Russian speaker on the podcast put it, Americans are embarrassed if they admit they can’t read, but we are somehow totally okay admitting that we can’t do basic math. Becoming literate in the traditional sense and becoming literate mathematically are actually so similar, and it’s a shame that one is regarded differently than the other.
But that’s not our fault at all. That’s the way we’ve been conditioned. We’re taught math in such a way that we’re given problems that can be solved within 30 seconds and if we can’t solve them, we convince ourselves that we simply don’t have the aptitude for it. That’s not math. Math is about struggling, about playing and about cleverly approaching problems from the creative limitations of our toolbox. It’s about thinking for ourselves and reaching the extents of what we think we can do and pushing past even that.
If our students want to pursue a career in STEM or even just gain an appreciation for a subject that makes up the foundation of our culture, we need to give them a chance to understand how a real mathematician or scientist thinks — inspired by all the ideas around them.
Our schools, instead, tell us that we need to memorize methods. As mathematician Dan Finkel explains it, we give answers before questions instead of questions before answers. We give students the steps to long-divide or cross-multiply instead of asking them to think critically. They’re expected to rinse and repeat the same algorithms and if they find a new way of looking at it, they’re told discouragingly to return to the same Common Core standards.
All the while, we deprive our students of an important creative thinking process, and we shield them from the aspects of math those of us lucky enough to have discovered find beautiful and even awe-inspiring.
For me, it was a couple books leading into an obsession with Numberphile videos, full-length math explorations and my place on the state math team, and for Finkel, it was a summer camp. I find myself asking why we don’t show that in school. Why don’t we expose our students to the creative process behind Euclid’s proof of the infinitude of primes or to the open-ended unknowns of the 3n+1 (Collatz) conjecture? Both are as simple to explain as synthetic division but all the more powerful in revealing how real scientists, computer programmers and mathematicians think when approaching practical problems across the globe — a layer of insight most people don’t reach until college.
There’s an analogy I think explains this perfectly. Imagine if we lived in a world where all throughout school, you had to take “music” classes where you had to write down notes and rests on staffs and learned “principles” of music theory through exercises, and finally, when you broke free of music classes upon graduating, you sighed with relief in escaping it. Imagine nobody ever allowed you to actually listen to or play music. That’s the way we’re teaching math.
It’s bizarre to me that a subject that is so creative, that has taken everyone from the Greeks to the Germans to modern-day geniuses to the very brink of intellectual frontiers, and that has established practically all the innovations we rely on today from the first Roman aqueducts to our first trip in space, can be dumbed down to the point of mind-numbing exercises and rituals, especially throughout elementary and middle school.
And not only is this system far from creative, but teachers often reward only correct answers and ignore valid mathematical reasoning if it reached an incorrect answer by accident, giving students a fear that stems from a potential stumble as they slog through the wasteland that makes up their daily worksheets. This is a system that has its origins in the Industrial Revolution and factory system era, and we’re somehow still attached to it.
But how do we fix this? How do you balance grading with allowing students to play with mathematical concepts? Finkel has a five-step process, so forgive me as I borrow heavily from his ideas with three of these steps.
First, start with a question, and don’t rush to an answer. Imagine if you were given the chance to doubt, to refuse, to wonder in your math classes. Imagine if you weren’t told, “Here’s to how to multiply,” but instead given the opportunity to explore what repeated addition means. The common core gives students no room to do that and squashes their ability to think about themselves as the “math people” we all can be.
Second, build on that and give students time. The world of problem-solving is a world of perseverance. The American school system gives no time to struggle but instead rushes each child to an answer. That does not prepare them for the real world, and once again fosters our fear.
Third, stop making it about the answer. The obsession should be over the reasoning, not over the answer. What happens in school is teachers keep rejecting students if their answers are wrong. Math can be multilayered and complex, and so much of it can be right, so why discourage students? Why can’t we let our students participate, encouraging them to venture to try, even if they shout out something wrong?
How many of you would I surprise by saying math is a place where we can break rules? We’re conditioned to believe we can’t take one wrong turn, but yet mathematicians go out on a limb all the time. Negative numbers were once never a thought in any one’s mind. Square roots and the irrational numbers that come out with them also completely shattered the foundations of their society when they were discovered. And every single day, mathematicians battle their own barriers and discover their own possibilities, creating chains of reasoning nobody thought possible. We can even divide by zero if we want to. Just ask my GHP teacher, Bill Shilitto. (Visit www.1dividedby0.com!)
Young children can do even more than you think they can, and our school system is depriving them of a challenge. The Russian School of Math has had immense success exposing students to complex ideas that are essentially algebra in disguise at a young age, and it makes it such that they don’t have to make such a huge mental leap when they reach algebra. Recognize that.
And please, stop talking about fear. Tell people they can. For girls especially, a study shows that around the age of 15, many manage to convince themselves they can’t pursue math, one of the reasons we have such a large gender gap in STEM. It’s hard enough to stay committed in general, but even harder when society is pounding anxiety down your throat. So do yourself a favor and become more open-minded.
So, next time you start to think “maybe I’m just not a math person,” ask yourself if it’s you or if it’s the system that brought you up. Bit by bit, we can begin to reverse the stigma, encourage ourselves, recognize the source of our shortcomings, and slowly but surely reform the way we approach math education.
A couple notes before I leave:
The other opinion piece I mention here is one of my favorite articles I ever wrote for The Blue and Gold. It's called "Math: The Poetry of Ideas" and it's also the first article I published here, so feel free to go read it after this!
All in all, I want to remind all of you to never ever let anybody discourage you from pursuing anything you love! If it's math, I'm right behind you. If it's something else, the same goes for that.
If you do continue to pursue math throughout your life, at some point you will stumble. At some point, you'll encounter a problem or a topic so difficult your brain initially won't be able to comprehend what's going on. That's okay. That's natural. Just keep pushing, and I know you'll get through it!
I can tell you that I've worked hard for everything I've achieved, and sometimes, I thought I'd never get through one of these mental blocks, but the moment I got through it, the most amazing, incredible topics were on the other side of that wall. It's all part of the process.
And, since you've got this site, go ahead and post on the forum if you've reached a point like that, and I'll do my best to help you through it!
Thank you to all my members and everybody who's supported GLeaM's mission, and I really hope you spread the word to anybody else who'd enjoy my content. I'd really like to make more of an impact, and you're where it starts! Have a great week everybody!