I was recently working on a project that involved a lot of math, and was reminded – unpleasantly – of my regrettably formative high-school years. You see, despite being quite good at most things involving the English language, decent where world and American history are concerned, no slouch at what is still referred to as “home economics”, and decent enough where most things involving science, technology, and computers are concerned, I just barely graduated from high school. Why? Math, or rather, the way math was taught and graded in the school district I went to.
More and more, I’m becoming convinced that schools in America are systemic failures. Over the years, they’ve shifted from preparing students for the “real world”, to teaching a carefully-defined (by a committee, natch) “curriculum”, and more recently just teaching what is on the standardized tests, and no more. “No Child Left Behind” has a lot to answer for, but even before it came into being, the education system was painfully flawed.
In math, for example – which is where I had problems – the point is not to teach that, say, 128 + 256 = 384, or that 3 * 18 = 54. Rather, the point is to teach the process, how to figure out what A plus B equals. And that’s fine, of course – except that there is more than one way to get from A, or B, to C.
See, in my math classes in junior high and high school, the answers to the problems weren’t really important. That we had actually figured out what one-fourth of 360 is was less important than that we could demonstrate that we knew the approved way of figuring it out. What was really important was that we “show our work”, a phrase that was the bane of several years of my life.
This wouldn’t have been a problem, except that I approach math differently than what was mandated by the school district. As such, even though I was getting the right answers – and showing how – I was still failing, because I wasn’t doing it the “right” way. And, let’s face it, because I was too stubborn to drop what I – quite rightly – viewed as a superior approach to math.
Say, to keep things simple, that a problem on a test is the quite simple 8 * 12. Now, the “correct” way to do this is to put the 12 over the 8, and figure out 8 * 2 and 8 * 1, then add the numbers together as required. That’s “showing your work”, and how you get a passing mark on that problem, at least in the backwater hellhole I went to school in.
How I did it – and still do it – goes something like this – and all in my head: twelve is ten and two; eight times ten is eighty, that’s a no-brainer, and eight times two is sixteen, also a no-brainer. 80 plus 16 is 96. That’s just how I see it, and I think it’s a better way than the slow and clumsy method I was “supposed” to be using. The problem is, though, that there was no way to express on paper what I was doing in moments in my head, which would be “correct”. 80 + 16 = 96 was “wrong”; (8 * 10) + (8 * 2) = 96 was “wrong”; even 8(10+2) = 96 was, of course, “wrong”.
In the real world, of course, it really doesn’t matter how you figure out that A plus B equals C, so long as you consistently come up with C, and not D or E. In high-school, though, you do it the proscribed way, or you fail.
I’m not trying to defend what I admit was several years of (principled, admittedly) bone-headedness on my part; the story, I think, illustrates a major flaw in today’s education system, which has lost sight of what’s actually important…