Over at her Guardian blog, Grrlscientist just posted a video where Conrad Wolfram suggests that instead of teaching hand calculation, it would be better to teach children mathematics through computer programming. I think Wolfram is more than simply wrong - he's dangerously wrong.
In the video, Wolfram argues that in the real world, mathematics is essentially a four-step process:
1: Pose the right question
2: Figure out the mathematical formulation
4: Apply answer back to real world.
Wolfram argues that education is too focused on how to do step three by hand, and insufficiently focused on the other three steps, which are clearly more important in the real world. He suggests that using computers to do the calculations in school would be a "silver bullet" (his words) that would go a long way toward fixing math education.
I think Wolfram is perhaps confusing his world with the entirety of the real world. I'm not sure that computer calculation is always as immediately available or convenient in the real world as his suggested teaching method would require.
That's a partial view of one of the swimming pools I supervise. The two people in the picture are lifeguards, engaged in the process of painstakingly scrubbing the walls and floor of the pool in an attempt to knock off as much of the mustard algae as possible. While they're doing this, I want to figure out how much algaecide will be needed to address the problem.
Unfortunately, I don't know the pool volume, and that's kind of important to know if you want to know how much of a chemical to add to reach a given concentration. I've got that information - and a computer - in my office, which is not at the pool. I don't need an exact volume - as long as I'm within 5% or so it will be good enough. That's hand calculation territory, provided I can remember enough geometry to do the job. (The pool is essentially an irregular hexagon in shape at the surface.)
My world is a touch more blue-collar than Wolfram's. That's the case for a lot of people, many of whom need to use math on a regular basis, and need to do so in places where computers are not normally available, and not normally necessary. Computer-based math simply adds unnecessary complication.
And it does so with potentially devastating costs to society.
We already - at least here in the United States - live in an environment where the gap between the rich and the poor continues to increase as an accelerating rate. Rearranging mathematics education to depend more heavily on computers works great if and only if you have easy and regular access to a computer.
This may be another area where Wolfram is confusing his own world with the real world.
In the real world, many children and many schools still do not have adequate access to computers for the sort of education that they're doing now, much less a new math curriculum along the lines Wolfram proposes. His new math curriculum would simply provide another way to leave those students farther behind.