In a conversation with a friend recently, I got into the topic of math. Yes, it's not much of a surprise. I'm passionate about it.
What struck me was something she said about the graduate-level statistics she had taken. All she could recall about it was that it was stressful, and she had gotten through it by memorizing until she had finished the exam, then dumped everything from her brain.
This is not unusual, and I think it's the biggest failing of our math education model. Our kids (and most of us as adults) never get to see the story that numbers can tell us. To me, the beauty of mathematics is in the picture it can reveal. To see it, you don't need to memorize a bunch of formulae. Just look them up when you need to; that's what I do.
To see the story behind the numbers, you need to understand the concepts they're describing.
Standard deviation and confidence intervals aren't a bunch of meaningless calculations to be performed. They tell you about the phenomena they describe. They reveal patterns. They show what your gut is telling you (or if it's lying to you). Calculation without understanding is like putting letters in order without knowing what the words mean. Where's the value?
So why do we force ourselves to memorize math formulae? Are we more interested in developing the ability to calculate, or the ability to think? Is the proper assembly of letters the same as the ability to compose a story? Do we ask our musicians to be able to hit the high notes every time, or is it better to listen to a performance that evokes am emotion?
Don't get me wrong: calculation is critical to good math. But it isn't the whole of educating good mathematical thinkers. We need to develop the ability to interpret, understand, infer, and evaluate. How else will we grow as a society of critical thinkers who can understand our increasingly data-rich existence? I'm much more interested in getting a student to tell me what the numbers mean, rather than have them recite a formula. If you can just look it up online, is it really that crucial to memorize?
Critical thinking isn't something you can find with an internet search.
It's reminds me of the typing classes I had when I was in grade school. Were they teaching computing, or were they teaching how to operate buttons efficiently? I don't want to fill my classroom with button-pushers, or calculating machines, or any other type of operator.