Edtech Digest today runs an interview with one of the Wolfram brothers, part of a research group that designs software to help people learn.

Here’s his November 2010 Ted Talk

The real and only important problem pointed out in this talk is that there are four steps to math, according to Wolfram, but we are spending the bulk of our time teaching kids to do the part of math that computers already know how to do well. It’s like we ignore the fact that we have computers at our disposal, and we’re forcing kids to reinvent the wheel of their own education, as if it was really going to teach them something. Wolfram says we should spend the bulk of our teaching time on these three highlighted areas:

And here is a segment of his interview with edTech:

Victor: In your 2010 TED talk, you say, “we have a real problem with math education right now”—how would you characterize that problem in U.S. schools, is it the same internationally? What’s wrong, essentially? Why? What do you suggest we do about it?

Conrad: There are different layers of the problem. Let me try to peel them off from the outside. To start with, most people–parents, employers, students and teachers—aren’t that happy with math education. It’s hard to find people who say “math in America is great” … Why is this? Well, math is more and more important so the pressure on it to deliver has gone up, yet students’ abilities don’t seem to have gone up; and very few find math fun either! Why is this? In my view a key reason, bluntly: we’re teaching the wrong subject. A chasm has opened up between the subject of math in education and math outside. I think of math as having 4 steps:

1. Posing the right questions

2. Real world –> math formulation

3. Computation

4. Math formulation –> real world, verification

In education, we spend perhaps 80 percent of the time on step 3 by hand, yet it’s rarely used outside above the most basic arithmetic. Computers (and don’t forget phones, iPods and iPads) do that bit—and usually much better than any human could!

So let’s do the same in education. Let’s teach the other steps much more, with harder, more realistic problems. There are some cases where hand calculating is still useful—like estimating—but that’s the exception not the rule. The default assumption should be “computers do the calculating”.

This isn’t just a U.S. problem; it’s everywhere; and the country that solves this first will get a great boost in technical competency and its important economic and societal consequences.

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1 COMMENT

  1. Where are those sims?!!

    Great discussion topic. Obviously we need to rocket up blended learning; and maybe we should use programming instead of math to teach logical thinking. But what about this notion of skipping the calculations?

    Here’s a funny thing about this. Practicing computation sure seems a fine way to gain understanding about problem formulation and de-formulation.

    Admittedly this is a high end example, but it also describes something you’d definitely not describe as mental calculation (the type of math Wolfram says we should practice calculating).

    About halfway through university, the schedules for our learning both math and physics conflicted in a way. On one hand, were on schedule to learn from the math department differential equations. On the other hand, the physics curriculum demanded differential equations at the start of the same semester. The physics department was used to this, and as oft happened, they taught us the math first. But they taught us differently.

    Which approach then better helped us understand how to use diffy-q’s?

    Against intuition, the math department focused on a plug-in, programmatic approach. “Short-cuts” if you will, that included memorizing certain solution formulas. Sort of like a computer would do. (With a computer, of course, no need to memorize the formula just feed in the vars.)

    The physics dept though, needed us to understand more than a couple simple solutions: they needed us to fairly quickly explore the energy functions for a bunch of different quantum mechanical systems, e.g. a hydrogen atom, a free particle, a long cylindrical surface (copper wire).

    Now, I’m certainly jealous of students who have access to the visualizations the computers offer. Yet…

    To my mind, we learned much more about using diffy-q’s by calculating them the hard way. While you couldn’t complete 10 problems in the same hour timeframe allowed by the plugins, I thought by doing learning the long way, we understood the math formulations much better.

    The PISA analysis from last week maybe hints at this?

  2. Where are those sims?!!

    Great discussion topic. Obviously we need to rocket up blended learning; and maybe we should use programming instead of math to teach logical thinking. But what about this notion of skipping the calculations?

    Here’s a funny thing about this. Practicing computation sure seems a fine way to gain understanding about problem formulation and de-formulation.

    Admittedly this is a high end example, but it also describes something you’d definitely not describe as mental calculation (the type of math Wolfram says we should practice calculating).

    About halfway through university, the schedules for our learning both math and physics conflicted in a way. On one hand, were on schedule to learn from the math department differential equations. On the other hand, the physics curriculum demanded differential equations at the start of the same semester. The physics department was used to this, and as oft happened, they taught us the math first. But they taught us differently.

    Which approach then better helped us understand how to use diffy-q’s?

    Against intuition, the math department focused on a plug-in, programmatic approach. “Short-cuts” if you will, that included memorizing certain solution formulas. Sort of like a computer would do. (With a computer, of course, no need to memorize the formula just feed in the vars.)

    The physics dept though, needed us to understand more than a couple simple solutions: they needed us to fairly quickly explore the energy functions for a bunch of different quantum mechanical systems, e.g. a hydrogen atom, a free particle, a long cylindrical surface (copper wire).

    Now, I’m certainly jealous of students who have access to the visualizations the computers offer. Yet…

    To my mind, we learned much more about using diffy-q’s by calculating them the hard way. While you couldn’t complete 10 problems in the same hour timeframe allowed by the plugins, I thought by doing learning the long way, we understood the math formulations much better.

    The PISA analysis from last week maybe hints at this?

    recatchpastillsux

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