This one is short but sweet.
See, if you have Stephanie’s (
) gift for clarity of both thought and prose, you can say a lot in a small amount of space. It’s all you need.But what is even more impressive to my mind is the way that she has taken what may on the surface seem like a fairly unimpressive idea and crafted it into a laser focused personal testimony that ostensibly covers her mathematics education but is in truth a genuinely interesting, informative and inspirational take on the damage that school-created assumptions on our worth and abilities can have if we are not careful.
To do all of this in such a compact space is an extremely impressive feat in my eyes. And I’m confident you will feel the same way about it.
Enjoy.
This article is for the strugglers, the stragglers, the lost. If you flailed through algebra or geometry, grinding out grades without grasping underlying principles, it’s for you.
It’s also for me. I’m a risk management consultant. I can program. I majored in information security and wrote a paper on quantum cryptography in grad school.
But at age 14, I had as much chance of understanding algebra as I did of inventing the atomic bomb.
E = M.C. Escher?
Other academic subjects came easy. But an algebra word problem was like an M.C. Escher black hole, with staircases leading nowhere and signs pointing toward dead ends.
My parents hired a tutor. I sat at the dining room table with him, listened and nodded. I knew I was supposed to leave that table enlightened, problem solved for good.
It didn’t happen. I’d glimpse enlightenment, try to grab it with both hands, and feel it slip into ether. I could follow the steps my tutor laid out and arrive at a right answer, but back in the classroom, without his step-by-step guidance, I floundered. Algebra was like a dream never quite remembered. My brain was not ready. I felt stupid.
A Pyramid on a Toothpick
The next year was Geometry, which I did understand. A respite. (Fun fact: students often perform well in either geometry or algebra but struggle with the other subject.) Then Algebra II.
For me, Algebra II class felt like a pyramid built on top of a toothpick. I had no solid foundation. Once again, I sat at the dining room table with tutors, and I could see in their eyes that they knew I was lost. But my parents paid them, so they sat with me.
Then came calculus. I never should have taken AP Calculus. But it was expected. All the other AP students were in the class. My guidance counselor wanted me to look good to colleges. So I enrolled.
(Dys)Functional Haze
To this day I have no idea what happened in that classroom. I remember two things: the teacher’s name and the pretty, swirly “f” he would draw on the board to indicate a function, whatever that was. I got a B- by cramming for each quiz, memorizing specific steps, and then promptly forgetting everything. The smartest thing I did was refuse to take the AP Calculus exam.
In college, I avoided math almost entirely: I took only a required statistics course, and I remember my surprise when it wasn’t as hard as expected. I didn’t think any more about it. I simply moved on.
For the first seven years of my career, I carried around a false belief that became part of my identity: good at writing, bad at math. I’d proven it repeatedly in high school and didn’t see the need to prove it again.
A Funny Thing Happened on the Way to a Life Without Math...
Then I decided to take the GRE and go to grad school. I hired a Princeton Review tutor, but within about 10 minutes of starting their baseline practice test, I realized something was different. This was what had given me so much trouble? I understood almost everything on the test. And it was easy.
I hadn’t looked at math in the intervening 10 years. I hadn’t practiced. But while I wasn’t looking, my brain had changed. My math GRE score wasn’t perfect, but nearly so—about eight light-years beyond where I was in high school.
In my grad-school economics class, I used calculus. Actually used it and understood it. I took grad-level statistics, finance and accounting, and decision making under uncertainty. I got an A+ in the uncertainty class. What had happened?
One Size Fits No One
I don’t think I’m all that unusual. I suspect a lot of people get left behind by traditional educational models, which move at a single inexorable pace, leaving stragglers sprawled on the roadside.
This is a flawed system. Brains do not mature at a constant rate across people, in the exact same way, making the exact same connections. My best advice would be to embrace where you are, and accept that you may be somewhere quite different in several years. Somewhere you never thought you could reach.
Give yourself a break, and then give yourself time and space to be different. We all are.
I have a similar relationship to math. I was 'good at it' only from the perspective of following the school system and executing the rules to provide the answers -- I didn't understand it one bit.
I got all the way through Calculus II in high school on that system, partially helped out by the fact that both my calculus classes allowed me to redo problems I got wrong on homework and exams for half credit. So say you get 50% of the problems wrong, you still had an opportunity to get a 75% if you fixed the problems you did wrong. Since the teacher marked where you went wrong in your problem, he (both years was a he) effectively told you what was wrong, so you just fixed it. I think I normally got around 70-80% of questions correct the first time and then was able to turn those into 85-90% final grades, a solid B+ --> the exact same score I got for writing and composition and history and art classes that I thought I was "good at", because I got the same grade from the opposite direction: instead of making my mistakes and fixing them, I was just lazy about fixing my mistakes.
Anyway I even tested out of having to do any math in college, and left it at that.
Let's talk about logarithms. I remember doing them in Calculus. I remember not understanding why human beings bothered to invent such a weird fucking concept. The book kept insisting "it makes it easier to sum exponents" but it seemed like too much nonsense abstract bullshit to be 'easier.' Until I started color grading.
Color operates on a log scale. A 1-10 change applied to the shadows causes massive change in how they appear. A 1-10 change in highlights does not. Since you have to get 10-100 range to get the same change in highlights as you'd get in shadows, the linear graphs of the color you're manipulating in a color grading program represent a logarithmic increase in values.
And when that was explained to me I understood it IMMEDIATELY. Like immediately immediately. I didn't even go, "Ohhhhhh, so that's why I learned logarithms in high school!" I understood it before I had time to reflect to understand it. And as soon as "log space" was understandable, stuff like financial and economic charts suddenly bloomed into actual information. I could see and understand logs everywhere.
And similar things happened with things like set theory and statistics. It's not that I'm a highly accomplished practitioner, I'm in the opposite position I was in high school: I now understand the underlying concept attempted to be expressed by maths but I don't use the actual functions or processes to execute it. But it's weird how I was literally explained these concepts over and over and over again for several years but then they arbitrarily clicked when I came across them in the wild, so to speak.
People use examples of that to deride "how things are taught" and "the education system" but I don't honestly know if my teachers really could have done a better job for me. I think my brain just had to change.