Grokking Calculus

I think I’m innately pretty decent at Math. I’m no whiz, by any means, and I’m definitely not the greatest at mental calculations (though I think I’ve gotten better over the past few years), but I’m probably a B student without trying (I can, and do, stretch that to an A when I dare to exert a modicum of effort). Heck, I’ve even learned to like Math, to some degree, mostly thanks to Physics courses. So why do I have so much trouble just doing it?

Honestly, I feel like the system failed me in Mathematics. I was set up for failure and conditioned to dislike the stuff. Now, I’m not one to pass on the blame, and I’m certainly not innocent in the matter, but I feel pretty strongly about this. It’s just plain wrong the way Math courses are taught these days, or at least it seems that way to me. They pry open your head, then shovel, hammer, and drill into your brain what’s needed to pass standardized tests, and then you regurgitate it back out so the school gets the funding it wants to do more cranial construction. They don’t really give you the proper foundation, based on principals and Mathematical laws that help you build your understanding and power to reason. It’s more often the short-cut, trickery method that magically gets you to the answer faster than really knowing how. It’s kinda depressing…

I actually excelled at Math prior to High School. Then one fine day, the year before moving up to 8th grade (which was High School for me — sub-freshmen, they called us, the lowliest of the low), I was given the choice: during activity period, I could take Pre-Algebra with the rest of the brainy kids, or continue on with band (I had been playing the saxophone for the past 2 years and was on my way to the lead sax player). That’s not a choice any 12-year-old should have to make, especially on their own — choose between music and higher learning? It’s just wrong on so many levels., but that’s how it played out — I’m not even sure my parents were involved in the decision. My choice… my tragic flaw… was band.

This (as well as several other factors) set the stage for Mathematical disaster. 8th grade came around, and while most of my classmates took Pre-Algebra that year, I was encouraged to take Algebra I with the other kids who chose Pre-Algebra over band the year before. On top of that, my instructor was an ornery old man who was in his last year before retirement. On top of that, he was also the wrestling coach, and had no love for lazy, long-haired hippies (or rather, grunges, which I was awkwardly becoming). On top of that, my 2-years-elder, “bad influence” friend was in the class with me. I got a D the first grading period — maybe the instructor did have some sympathy for me after all — and F’s every grading period thereafter. So my first foray into the world of higher Mathematics was an utter failure. To add salt to the wound, I quit band prior to entering High School for fear of the terrible things that would surely happen to me if I remained a “band geek”.

Despite failing Algebra I, I was signed up for Algebra II the next semester! How this farce was allowed to play out, I will never fully understand (yay poor, small-town, public schools?). Not only that, this time I was stuck with another grizzled old guy, this time the football head coach (which is tantamount to godhood where I grew up), no less. The odds were stacked against me again, yet somehow I eeked out an overall grade of D in that course — enough to pass me through to the next level of the inferno.

War-torn, battered, beaten, and bruised, I went into Geometry class ready to bomb as before. This time I had your classic matronly, hair-in-a-bun, reading-glasses-on-the-end-of-the-nose, highfalutin, Grade A Math teacher. The kind that whacks your knuckles with a meter stick if you foul up. I’m not sure if the old broad liked me, or if I just liked Geometry, or maybe, just maybe I started to actually care… I came out of Geometry with a solid B+. Could it be that I was overcoming the odds? Could it be that I had won out, despite the system railing against me?

To be sure, before I could graduate, I had to pass Algebra I. So I went into my Junior year, with Algebra II and Geometry squared away, but no Algebra I (aren’t these supposed to be sequential, hierarchical learnings — you need to understand the first to learn the subsequent ones?), so I had to go back and prove my mettle in the introductory course. Once again, I prevailed, and exited Algebra I again… this time with an A.

I took no other math courses in High School. Despite my poor grades, I still earned an Advanced Studies diploma. I even scored a 650 on the Math portion of the SAT (without a calculator, no less — no one told me I could use one!). Even though in the end I came out partially on top, my learning path was so crooked, so incomplete, I still didn’t really understand much of anything I had “learned”.

Today, I’m a much better student, but I still struggle with Math — not really because I’m bad at it, but because I didn’t learn it properly. It’s very frustrating, to say the least.

Resources

If, like me, you were given a poor shot at Mathematics… If, like me, you want, or need, to improve your skills… then I hope this list of links will be of some help to you.

• Khan Academy — If you haven’t heard of Khan Academy, where have you been? This may be the best single resource on the internet for Math (and many other subjects as well). Spend a lot of time here.
• MIT’s Calculus Revisited Course — This, and many other MIT Math course materials (and other topics including Computer Science!) are available for free online.
• Free Math Books Online — with a Calculus subsection. Lots of free e-books on Math (and, again, other subjects).
• How to Read Mathematics — some insight on how to read and interpret equations and such.
• How to Ace Calculus — an interesting take on how to change your mode of learning Math to do well in Calculus.
• What is the proper way to learn Mathematics? — a question I asked on Quora. It’s a pretty straightforward answer, but be the subsequent comment helped me feel like I was not alone.

I’m sure there’s many other great resources available on the web, but these are links I stumbled onto mostly by accident and bookmarked knowing that I would need them some day.

Have any other Calculus, Mathematics, or other Learning links to share? Let me know — I’m going to need all the help and support I can get!