On Math
The way we teach math is broken.
We start with calculations in elementary school – how to add, subtract, multiply, divide. Integers, fractions, decimals. Already, the problem is apparent. Math is not designing problems and solutions. Math is calculations. Even children think that calculations are boring. And we are given SIX YEARS of it. Maybe this is when most children lose interest in math. It’s not that it’s hard, though some learn slower than others. But when the quicker students are praised for being ‘good at math,’ we lose the slower students because they are not ‘math people,’ and math is boring anyways so who cares?
We continue with algebra in middle school. But instead of putting the algebra in context (the teachers try sometimes, but do you remember how much we complained about word problems? ) we are given equations to solve. 4x + 1 = 5. Solve for x. This is still calculation. This is still boring. This is two more years. We lose a few more ‘math people’ in the process.
It’s not until high school that you get geometry, trigonometry, statistics, calculus. Math that gets put into context and is applicable. But it’s too late, most students are already of the opinion that math is boring. And suddenly, after 8 years of rote calculation, math requires thinking?! Most students are caught unawares. So of course they think, math is hard. Many former “math people” realize that they are not. And they give up, because they have been conditioned to think that the world consists of “math people” and “not math people,” and that “math” is this innate talent born into you. Which is, of course, bullshit.
I was a “math person.” Then halfway through high school, I looked at my classmates participating in the AMC and various other competitions, studying subjects that flew clear over my head (what was linear algebra anyways?), and decided you know what, maybe I’m not cut out for this math thing after all. I’m not a “math person.” What I didn’t see were the after school classes and additional tutoring those classmates had signed up for.
This mentality persisted for years. I never tried to understand the material in my math classes, because I couldn’t possibly grasp such hard concepts. I was not a math person, after all. I focused on recognizing problems and the processes to solve them, all for the sake of regurgitating it on a test and forgetting everything afterwards. I admired the brilliance of the “math people” around me but accepted that I would never be that smart. I deferred to them for solutions instead of trying to volunteer my own ideas, because they obviously knew better than me.
Then two years into college, I ran into a problem. The subjects I wanted to go into – robotics, machine learning, AI – were all math heavy. Specifically, they were linear algebra heavy. And I still had no clue what linear algebra was because the high school education system separates “normal algebra” from linear algebra when in fact the two are THE SAME THING.
At first I tried passing the linear algebra the same way I did for all my previous math classes – recognize the problem and apply a solution. But this didn’t go so well, as I was literally starting from scratch (how do you multiply matrices again?) and the class demanded less rote calculation and more application of theory. More understanding of the subject.
There was some of hesitation – could I make it as a robotics engineer? But I knew there was nothing else in the world I’d rather do, so last quarter I took a deep breath and enrolled in not one but two graduate-level linear-algebra-heavy courses.
I knew I had to catch up, and fast. So I buckled down and read. Null space? Basis? Eigenvalues. My world became Ax = b and how to solve it. It was hard at first, I was constantly asking for help. But this time I wasn’t just asking for how to solve the question. This time I asked why would you solve it that way, and wouldn’t this work as well? This time I read through the proofs and understood them.
It became easier and easier, until I could not only solve the majority of a pset by myself but also explain it to others. And the more times they, the “math people” I so admired, nodded in agreement when I pointed out an error in their logic, the more confident I grew. By the end of the quarter, I wasn’t even terrified of the finals anymore (though that may just have been the exhaustion).
And I realized that, a “math person” is just someone who realizes that math is a skill that needs to be exercised, just like writing or piano or art or dance. No one has math born into them, that’s just silly. As long as you’re willing to really learn and understand and use math, then you are a math person. I know because I am a math person, and I sure as hell didn’t have math born in me.
Most children probably start out as “math people.” Some drift away in boredom because school imprints the idea that math is rote calculation instead of problem design, which is where the fun and creativity really occurs – given the constraints of the problem, what’s the best way to model and solve it? Others are scared off because they feel that they’re not “math people,” when what they don’t realize is that “math people” are only such because they work hard behind the scenes, not because they have an innate “math-ness” about them.
Instead of teaching children calculation, we need to teach them problem solving, where math is a tool to help. And instead of praising talent, we need to praise hard work. That is the first step to reclaiming math.
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