Submitted by Aaron Arkin.
Ever since I can remember I’ve had difficulty with math. Well, almost forever. When I was ten I scored high in a city-wide aptitude test (which I assume had at least some math questions). And I should acknowledge here that I was able to memorize my times tables. So for a time I thought I was doing OK. But the 8th grade changed everything and after that it was all downhill. The pivotal event I remember most vividly went something like this (performed in front of a chalkboard):
Alright class, today I’m going to introduce you to a new kind of math. It’s called . . . algebra! Now I know you’re familiar with addition/subtraction/multiplication and division. And we’ve studied decimals and fractions. But algebra is different: you can use it to solve mathematical problems when there is an unknown. For example, if I say two times something (an unknown) equals four, you would say that the something, the unknown, is two based on what you know about multiplication from your times tables. Well here is the fun part: instead of saying two times something equals four, we replace the something with an x. So if 2 times x=4 (2x=4), then x=2. See, we’re already doing algebra!
Fair enough. So far so good. Then we went on to the next example: if 2+x=16, then x=14. Hey, this is great, I’m getting it. Then . . . the third example:
What just happened? I looked around the classroom. Was I the only one confused? Everyone was dutifully writing in their notebooks: nobody looked upset. Had I blacked-out or been in a fugue state only to wake up after several weeks or months of algebraic lessons? Was it more sinister: had I been kidnapped and taken to another planet? (OK, kids aren’t particularly bound by reality when trying to come to terms with scary situations.)
Somehow I got through (or was passed through) elementary school algebra. In high school I avoided intermediate algebra and thought I had escaped for good only to be advised in college that in order to graduate I had to make it up (the course, that is).
I took the dreaded course in summer school and the experience was a revelation. The instructor was a humorless but focused Eastern European with an ability to clearly and concisely present the material. His logic was laser-like when it came to explaining the reason why something did or did not make mathematical sense. And I actually understood everything he was teaching! Because if you didn’t understand something, he went back and explained it another way until you did. I got an A: an A!
Heartened by this experience and wanting to broaden my education, I decided to challenge myself and take an elective math course for non-math majors. I settled on: Introduction to Mathematical Thinking (analysis, on an elementary level, of the nature of mathematical reasoning; elements of set theory; some simple postulational systems). What could go wrong?
Our Professor was in love with mathematics. Enthusiastically, he flitted in front of the room chalk in hand dropping equations like a crop-duster spreading pesticide. I remember one episode in particular when as he was racing in front of the equation-saturated chalkboard, he suddenly stopped, turned, faced us, pointed his finger at a set of equations (I think it included a square root sign) and exclaimed: “So, the only possible answer is this!”
I remember looking at the chalkboard and thinking, why this? Why not some other candidate: like the algebraic equations in the upper left-hand corner? They looked like an upstanding set of numbers, symbols and letters: probably came from a good family. I should stand up and challenge this. But when I looked around and saw the other students dutifully writing in their notebooks (why does this still happen?), I kept still.
I sweated the final: can still feel my anxiety the day of the examination. I studied hard and even enlisted my more mathematically-inclined friends to help me prepare but I flubbed the exam and received a D. To this day the only things I remember about the course (outside of the peripatetic professor) are the 3 circles in Set Theory with their common overlapping area (I think it was green).
As an adult I have read many books designed to explain mathematics: mathematics in physics, fractiles, numeric properties, mathematical modeling, etc. They all promise a view into the wonders, elegance and utility of the discipline. Sadly, I glimpse only slightly the delights and insights that mathematicians seem to enjoy. But then I think, doesn’t written language also have rules that are complex and demand precision and rigorous application? Good writing has elegance and subtleties and requires practice and extensive knowledge in order to make meaningful use of it: to use language to good effect, to show things in a new light, even as a way to model the world in new and imaginative ways. How is that not unlike the discipline of mathematics?
My regret in all of this is that (1) unfortunately, language skills don’t automatically translate into mathematical skills, and (2) frequently mathematics is taught poorly: an observation often made by others.
Had I to do it all over again, I would glom onto my intermediate algebra instructor at all my mathematical experiences; then too, I might be transported into that special world he so much appreciated.