This is scary stuff for math professors, but with the arrival of amazing programs like Wolfram Alpha, we’re going to have to start paying attention to the signs of change.  I talked to Conrad Wolfram (at Wolfram Alpha Homework Day) when he was still formulating what he wanted to say at this TED Talk.  I think it’s worth 18 minutes of your time to watch Teaching kids real math with computers.

Here’s an outline of the Conrad Wolfram’s argument (which I am paraphrasing/quoting here):

What’s the point of teaching people math?

1. Technical jobs (critical to the development of our economies)
2. Everyday living (e.g. figuring out mortgage, being skeptical of government statistics)
3. Logical mind training / logical thinking (math is a great way to learn logic)

What IS math?

1. Posing the right questions.
2. Convert from real world to mathematical formulation
3. Computation
4. Convert from mathematical formulation BACK to real world

The problem? In math education, we’re spending about 80% of the time teaching students to do step 3 by hand.

Math is not equal to calculating, math is a much broader subject than calculating.  In fact, math has been liberated from calculating.

Should we have to “Get the basics first”?  Are the “basics” of driving a car learning how to service or design the car?  Are the “basics” of writing learning how to sharpen a quill?

People confuse the order of the invention of the tools with the order in which they should use them in teaching. Just because paper was invented before computers, it doesn’t necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.

What about this idea that “Computer dumb math down” … that somehow, if you use a computer, it’s all mindless button-pushing.  But if you do it by hand it’s all intellectual.  This one kind of annoys me, I must say.  Do we really believe that the math that most people are actually doing in school practically today is more than applying procedures to problems they don’t really understand for reasons they don’t get? … What’s worse … what they’re learning there isn’t even practically useful anymore.  It might have been 50 years ago, but it isn’t anymore.  When they’re out of education, they do it on a computer.

Understanding procedures and processes IS important. But there’s a fantastic way to do that in the modern world … it’s called programming.

We have a unique opportunity to make math both more practical and more conceptual simultaneously.

Personally, I’m all for it.  But how?  That’s the question.  How to shift and incredibly complex and interconnected system of education? How to train tens of thousands of teachers and faculty to teach a new curriculum that they themselves never learned?  Hmmm … it seems that we might need some help, maybe a new paradigm for education itself.  It’s coming.