As a student, high school often frustrated me. Math classes were particularly painful to sit through, for exactly the reason Tom Henderson savages, from the other side of the classroom, in this interview at Technoccult:
Many students want teachers to “show me the steps.”
They want a sequence of steps that they can perform that will give them an answer. This is not unreasonable; they know that their performance on exams, and therefore their performance on the All-Seeing Grade Point Average, is largely determined by being able to Do The Steps.
But “The Steps” are cargo cult mathematics.
The Steps are seeing the sorts of symbols that count as “right”, and trying to replicate that dance of steps. It turns out that the easiest thing in the world is to look at a student’s work, and tell the difference between “Knows what’s going on, made mistakes and dozed off” vs. “Can memorize steps, has no idea what’s going on.” […]
Many students want to know the formulas, so that they can float them on top of their short-term memory, ace the exam, and then skim them off. Why do they want to know that?
Probably because, for their entire mathematical careers, math has been a sequence of Steps, and if they get them wrong, they get red pen, bad grades, No No No Look What You Did. Plus, bonus, there is no apparent relevance of these algorithms other than To Get The Answer.
I don’t mean to sound condescending—because, as Henderson says, the system encourages Memorizing The Steps, and my classmates were, on the whole, far from dumb—but this is just the sort of flogging my ears and brain endured year after year. After a week, you knew exactly which students cared only about their grades and would never take a broader view of mathematics. They clutched their formulas and struggled with problems framed in any novel way.
And AP classes were the worst of them all: entire courses building toward one exam. A year’s worth of learning, reduced to a digit, 1-5. Nothing else mattered. The Steps invaded other classes, even those, like English, that should have inspired deeper thinking. (Yes, even critical essays were reduced to tired, AP grader-friendly formulas and checklists; in essence, we learned SEO for AP English.)
At some point, the system has to change. Just look at what schools have wrought: Students unprepared for collegiate rigor and who value only the end result.
“If you are not so worried about presenting yourself as absolutely unique, then it’s O.K. if you say other people’s words, it’s O.K. if you say things you don’t believe, it’s O.K. if you write papers you couldn’t care less about because they accomplish the task, which is turning something in and getting a grade,” Ms. Blum said, voicing student attitudes. “And it’s O.K. if you put words out there without getting any credit.”
A “show me the steps” mentality, in any discipline, encourages uniformity, not originality; this glut of plagiarism, then, shouldn’t be surprising.
In any case, Henderson’s Punk Mathematics book, which spun out of the positive reaction to the above interview, sounds brilliant, and I’ve pledged my support, as much for the ethos as the book itself.