Yesterday’s post by Dan Meyer hit all the right buttons for a comment frenzy.
Even worse, at this moment in history, computers are not a natural working medium for mathematics.
For instance: think of a fraction in your head.
Say it out loud. That’s simple.
Write it on paper. Still simple.
Now communicate that fraction so a computer can understand and grade it. Click open the tools palette. Click the fraction button. Click in the numerator. Press the “4″ key. Click in the denominator. Press the “9″ key.
I’m sympathetic to anything that brings media studies analysis onto our teaching techniques, but the mixed targets and strawmen examples confuse me. The first example sounds like a struggle with typesetting mathematics in Word (or some other word processor). Yet for software that actually understands fractions, I can get away with typing “4/9” and I am done. Simple, and at least as quick as pen and paper.
The key there is which software we’re talking about. Some software is horrible at communicating mathematics. This can even vary wildly between versions; Word 2007 is significantly more useless than Word 2010 when it comes to typing in math equations.* On the other hand, something from Wolfram is going to get math because it was built with math as its focus. If you give Wolfram Alpha “4/9”, it will not only make it look right, but it understands it as an irreducible number and will inform you that 1.333333333 is only an approximation.
So maybe we can’t treat all software as equal when thinking about it as a medium?
On the other hand, there are things which even W/A will only understand if typed in a cryptic format, or with excessive parentheses to keep things unambiguous. I don’t know if that’s really getting to the heart of what Dan’s complaint is about, though.
Do you want to know where this post became useless to Silicon Valley’s entrepreneurs, venture capitalists, and big thinkers? Right where I said, “Computers are not a natural working medium for mathematics.” They understand computers and they understand how to turn computers into money so they are understandably interested in problems whose solutions require computers.
Okay, so full disclosure, I have a Computer Engineering degree and I like doing recreational programming from time to time. However I’ve also tried to teach kids with little-to-no computing background how to do math on Geogebra, and watched them flounder, and I get that there’s truth in here.
The thing that confuses me is that mathematics is the medium by which computers operate. This doesn’t mean that the reverse is true, but it does mean that it’s weird to me to think that computers are a bad tool for doing math when that’s the very domain in which they live and breathe. (Or one branch of mathematics, at least.)
So we’re closer to but not quite at Dan’s real point which is that computers are lousy at assessing mathematical ability. His strongest examples, the ones which are carrying his message, are not really about computers as a communication medium but about computers as an assessment machine. This is where it starts to actually make sense to me. I don’t see any reason why a computer would be a poor medium to use to communicate mathematical reasoning to an actual human teacher – kids can type their math essays as well as they type their English ones. Where this falls apart is when we use computers as more than a medium, but rather as an analysis tool to do the assessing for us.
Assessment defines what students are told is valuable about a subject. If all you assess is computation, students will get the message that computation is all that matters in mathematics. And computers are only good at assessing what they’re already good at doing – computation.
If we tell students that math ability is only about doing what computers can already do better, we’re clearly not going to convince them of the importance of math.
So, I don’t think this discussion has ruled out computers as a medium to communicate mathematics. But it definitely highlights that in education, just as in applied mathematics and engineering, we can’t expect a computer to do the thinking for us.
* Word 2010, in fact, does let me type “4/9” and typeset it properly – if I’ve made an Equation object, which is an extra click.