Through the Education Lens

Crossing the Math Chasm

CJW, November 17, 2010 11:29 AM


"We've got a real problem with math education right now.
Basically, no one's very happy.
Those learning it think it's disconnected, uninteresting and hard.
Those trying to employ them think they don't know enough.
Governments realize that it's a big deal for our economies, but don't know how to fix it.
And teachers are also frustrated.
Yet math is more important to the world than at any point in human history. So at one end we've got falling interest in education in math, and at the other end we've got a more mathematical world, a more quantitative world, than we ever have had.
- Conrad Wolfram

By C.J. Westerberg

What is the expression in the news business?  If something happens once it is news, twice it's a trend, and three times it's a cover story.

Within minutes of viewing Conrad  Wolfram's TED talk, , I thought this was "cover story time" and not because of the title, "Teaching Kids with Computers," which in many ways de-emphasizes a key point in his presentation which centers on teaching kids math through posing the right questions, defining the problem and understanding the problem. 

How many impassioned pleas by math teachers and students do we need to hear about this very same point?   It seems our math education is so back-end loaded with the emphasis on getting the right answer that we give short-shrift on understanding the question.  How to pose the right question?  What question is the problem asking?  What information matters in this question?  Case in point: how many of us "lost" our high school math knowledge as soon as the SAT exam pencil was put down, unless we continued it in higher education?  Did we ever really "get" it?

One need not go further than The Daily Riff series on Singapore Math and here (used by leading math countries, such as Singapore and Japan),  which places a huge emphasis on the ability to properly define the problem including the finding and sorting of information that "matters" in the problem.   Or, visit math teacher Dan Meyer's viral video talk which centers upon the need to refocus math education on problem posing with advice such as "let students build the problem".

Wolfram tackles the questions of "why math?":
So let's zoom out a bit and ask, why are we teaching people math? What's the point of teaching people math? And in particular, why are we teaching them math in general? Why is it such an important part of education as a sort of compulsory subject? Well I think there are about three reasons: technical jobs so critical to the development of our economies, what I call everyday living. To function in the world today, you've got to be pretty quantitative, much more so than a few years ago. Figure out your mortgages, being skeptical of government statistics, those kinds of things. And thirdly, what I would call something like logical mind training, logical thinking. Over the years we've put so much in society into being able to process and think logically; it's part of human society. It's very important to learn that. Math is a great way to do that.

So let's ask another question. What is math? What do we mean when we say we're doing math, or educating people to do math? Well I think it's about four steps, roughly speaking, starting with posing the right question. What is it that we want to ask? What is it we're trying to find out here? And this is the thing most screwed up in the outside world, beyond virtually any other part of doing math. People ask the wrong question, and surprisingly enough, they get the wrong answer, for that reason, if not for others. So the next thing is take that problem and turn it from a real world problem into a math problem. That's stage two. Once you've done that, then there's the computation step. Turn it from that into some answer in a mathematical form. And of course, math is very powerful at doing that. And then finally, turn it back to the real world. Did it answer the question? And also verify it -- crucial step. Now here's the crazy thing right now. In math education, we're spending about perhaps 80 percent of the time teaching people to do step three by hand. Yet, that's the one step computers can do better than any human after years of practice. Instead, we ought to be using computers to do step three and using the students to spend much more effort on learning how to do steps one, two and four -- conceptualizing problems, applying them, getting the teacher to run them through how to do that.

Wolfram expresses how math educators should use students for the following four functions of math but to spend far more time on steps 1,2 and 4, whereas our present system spends the vast majority of time on 3.  Probably the most contentious issue of his talk is about the "basics"  of calculation - how much provides enough foundation for the critical thinking and problem solving he addresses as the "real" mathematics education.

  1. Posing the right questions
  2. Real world math formulations
  3. Computation
  4. Math formulation -- real world, verifications

And, finally, he calls for computer programming to be an essential component of a solid math education.  You have my vote on that one.

Let us know what you think.  Wolfram's wrap-up:   

We can engage so many more students with this, and they can have a better time doing it. And let's understand, this is not an incremental sort of change. We're trying to cross the chasm here between school math and the real world math. And you know if you walk across a chasm, you end up making it worse than if you didn't start at all -- bigger disaster. No, what I'm suggesting is that we should leap off, we should increase our velocity so it's high, and we should leap off one side and go the other -- of course, having calculated our differential equation very carefully.


Related posts in The Daily Riff:
Singapore Math:  Can Solving Problems Help Solve Our Fear Of Math?
Singapore Math:  Is this Our Most Visual Math?

Dan Meyer:  An Amazing Time for Math in This Country

See Wolfram Alpha


Published November 17, 2010 The Daily Riff

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