While that statement is a bit premature, I guarantee you will hear a chorus of teachers belching that from their 1970′s era podiums in the coming months. One of the coolest features of Wolfram|Alpha, being able to do annoying calculus problems at the drop of a hat, is going to mean cheating galore. This point occurred to me immediately upon using W|A, and I tweeted that its usefulness would be much greater for high school students, but this was just brought to my attention again by an article in the Washington Examiner. Computational physics teacher John Dell makes the following point:
“It no longer makes a lot of sense to spend lots of time teaching students to perform calculations that machines can do better.”
If you ask me, it never has made much sense. Physics tests where I couldn’t use my graphing calculator were the dumbest things to me. I imagine very few physicists these days do any serious calculations without the aid of a computer. Why spend three hours chugging through something that a computer can give an answer to in 3 seconds. It’s just dumb.
On the other hand, learning calculus is more than just coming up with an answer. It’s easy to do simple calculus, any kid with pre-algebra knowledge can do it as long as they know what variables, fractions, and exponents are. But that will only get you so far.
At the very simplest level, you might say the point of learning something is being able to apply it to a future problem. Calculus does you no good if you never learn what sort of problems you can apply it to. Stuff that you learn that has no application is trivia, and while that may be useful for winning Jeopardy, it’s not much help in real life outside of cocktail parties. Most kids feel that the math they learn after ‘rithmetic is trivia.
What if instead of a class of children who give up learning higher math because of brain bending pages of complex equations, you had a class of children who grew up knowing how to ask the right questions of software to solve real world problems? I think we need to step back and ask ourselves if what we’re teaching children we’re teaching them just because it’s somebody’s notion of “what kids ought to know” or if it is applicable to real problems. Teaching trivia has a non-trivial effect.
While I see no reason for students to live in the 19th century, I do see merit in their understanding how machines solve problems. I feel the same way about formulas: a student should at least grasp the intuition underlying a formula–and ideally be able to walk through its proof–before using it as a shortcut. I’ve seen what happens when students rely on shortcuts they don’t understand: they return negative numbers as areas and volumes and have no idea why that might be a problem. :-)
Yeah I think there’s a balance here that unifies understanding what sort of solutions a problem can have, with not having to learn something that seems really esoteric if a computer can do it for you. Of course there will still be those children who want to learn how to do it, and they will probably grow up to be scientists. Or, at least, academics.
I think kids who want to learn something will learn it, if you give them opportunities. Forcing them to learn something rarely has the desired effect. I wonder what percentage of people in a random sampling of a mall on a Saturday afternoon can solve a quadratic equation, tell you what the boundary between the Earth’s crust and mantle is called, or what the heaviest element is that will undergo fusion in a star. I learned all of those things before high school, but only the first has been useful to me. Is my life better for knowing them? Doubt it.
But I think this is an area where people will say children should be exposed to a variety of things so they know what there is to be interested in. They may never have heard of geology or astrophysics without it. Maybe that’s true, but it’s getting close to my dreaded “what kids ought to know” problem.
I don’t have the solution really, just the sense that there’s a problem. Maybe we’re doing it the best way it can be done, though I doubt it and the thought depresses me! :)