I am studying Calculus in a classroom. It is taught by a qualified University of Minnesota Professor.
Most people I know expect such an experience to be hell.
It surprises me that it is hell.
When I first encountered calculus in the 1960's, it was a mysterious, almost mystical unknown. Only Certain Geeks could approach the temple and few became qualified calculusers. Because of my interest in Science Fiction and scientific approaches to solving social problems, Calculus was never far from any topic I was really interested in. But I always assumed it was, like playing classical piano at the concert level, a skill reserved for a small, deserving minority of people.
Over time, this image of exclusive Olympian existance began to break down. Clues came here and there in articles, stories, conversations. By and large the reputation of Calculus as really hard and unpleasant, reserved for "souless iron-butt repressed drudges" -- the reputation remained intact.
Finally about fifteen years ago I was developing some graphic software, and had learned to code curves and fill areas. By coincidence I came across a short article on calculus that explained it in terms of computer graphics coding. It was an amazing "aha" moment. I knew about slopes of lines and approximating irregular areas with lots of tiny regular areas. I had enough basic geometry and algebra to dimly get the rest of what I was reading.
Calculus was about changing tanget lines along a curve, and approximating the area under the curve with rectangles, in its operational essence. I won't go any deeper into it than that.
After reading the article it felt like a great weight had been lifted from me. I had carried the burden of "not qualified for calculus" around for years as a subtle sabotage of my interest in science. I had attacked the finite maths, such as statistics, probability, set theory, boolean logic, etc, with gusto, because I was qualified for that...I had done well in basic classes and was not impressed with any mystiques.
From time to time after that experience, I would come across something that required thinking a bit in calculus concepts, and I wouldn't be daunted. But I didn't actually tackle the curriculum. I just felt more comfortable, and when the time came to ask questions, I felt as though I could ask them without making a fool of myself.
Recently I decided to bite the bullet. I need operational knowledge of calculus at a much deeper level than before. So I registered for pre-calculus last semester. It consists of trigonometry and the algebra of polynomial and rational functions, for the most part. There are other things. But holy damn, it was hard. I thought my computer experience would serve me in two respects: one, I had written code that created graphic demonstrations of most of the concepts involved, from quadratic equation solutions to animation of sine functions. So I assumed that I would get the concepts easily and could anchor my work on exercises in a secure conceptual understanding.
Not so. The presentation of the detailed aspect of the ideas was never connected to the more abstract level. We marched through horrendous black-board filling exercises in expanding and factoring ugly algebraic expressions. I felt as though I was being dragged behind someone's pick up truck on a chain, and they didn't care if my head was still on when they came to stop five miles down the road.
My romantic notions of the beauty and power of math encountered the ugly truth of math pedagogy. It was taught as a method to separate the class into clear groups: the minority who can function in the hostile environment of rapid, forced manipulation; the majority who can struggle along without raising their heads; and the "unqualified for calculus" who would drop out during the first 10 weeks or so, unable to make any sense or headway in the typhoon of symbols.
After the first two weeks my fascination and infatuation with math was completely scoured out of my little pan of math capacity. All that was left was room enough to fight my way through the increasing pain of homework. Each morning and evening I sat at the dining room table, with index cards, summary sheets, page markers, algebra review books, sheets and sheets of paper scribbled with the scars of a thousand little wounds called "problem solving" by the books and teachers but called torture and indoctrination by the insecure student.
My pride in my programming prowess turned neutral, then to a kind of oblique shame. The class was taught with pencil and paper and, if necessary, cheap math calculators: no graphing or algebraic automation allowed. No computers. We were doing the same drill that students of pre-calculus had done in the 1960's, even the 1930's. No concession was to be made to any social or intellectual shift in attitudes toward the role of math in society. This was meant to be hard. That message was underscored by the stunning rigidity of the class rules. No homework was accepted late, period. No make up tests allowed, period. No excuses were accepted for anything, period.
Since I was struggling so hard to get the problems done, and especially the midterm test problems within the time limits that energetic 19-year olds found daunting, I began to wonder if I would even pass. After my experience of hysterical blindness during the first midterm, and subsequent resignation to handing in half the problems, I was sure I would fail.
But the curve saved me. I had just enough on the ball to be one of the stragglers in the middle group of head-downers. I never quite fell out of the herd, and ended up in fact with a B- despite barely scoring over the mid point of each major test.
The curve saved my participation in math, and allowed me to proceed to the next level of calculus. But the system failed me significantly in not recognizing and responding to my basic problems with algebra.
I have been in calculus for three weeks. The calculus is easy.
The algebra is hell, and there is no relenting from it. It marches like cloned extraterrestrial insect soldiers from Starship Trooper, filling the horizon with its black homicidal whirr of horizontal asymptotes and drone of rationalizing denominators.
Despite my alarmed remarks, the Professor smiles when I say I really need review in Algebra to keep up. "The Calculus is easy, " he grins, "The algebra is hard."
And that is the essence of the situation. Whomever designed this curriculum did not do it from the assumption that a mathematically literate citizen is a better citizen. They designed it to keep the rabble out of the hallowed temples of Math. And as they succeed, and frighten the reasonable, terrorize the faint, and only inspire the unbalanced, they do Math and civilization a great disservice. Keeping an abyss between the math literate and the average educated citizen is not longer an intriguing by-product of our rapid technological ascent in the West, a subject for essays on C.P. Snow's "two cultures". It is a disease. It can be cured.
It might kill me first.
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