Thursday, September 24, 2009

Why Math? Why School?

Part I. Why Math?

Deborah Meier (author of The Power of Their Ideas) co-writes the Bridging Differences blog with Diane Ravitch. Meier's topic today is 'Why School?' She is discussing what she hopes students will learn in school. Deborah Meier has done amazing work, and I usually like what I read at her blog. But her conception of math seems terribly shallow to me:
Sufficient mathematics to make sense of what they find in the media—statistics, probabilities, forms of graphing, percentages, et al to a high degree of sophistication by the time they are 16. Basic arithmetic computation by 13.
I agree that one reason to learn some basic math is to be able to have intelligent opinions about national issues: Is it more costly to have single payer health care or what we have now? Is social security doomed because more and more of our population is the elderly? I would never have expected to be interested in a blog on the tax code, but Mary O'Keefe (who runs the Albany Area Math Circle) writes great posts about issues like this on her tax blog. How can you understand national budget questions if you get nervous about numbers?

So yeah, these are reasonable goals, but dreadfully insufficient.

Here's what I wrote in response:

Deborah, I have a deep respect for you and the work you've done. So I was distressed to see your opinion of what math students should know - mostly arithmetic and statistics. Well, that's a fine start, but it is not enough.

Shouldn't they know enough math to understand science? Shouldn't they see the beauty of math? Two books, accessible to anyone, that I'd highly recommend, are The Cat in Numberland, about infinity, and Powers of Ten. (I've blogged about a number of fun math books at my blog, Math Mama Writes.)

What Diana said above about literature and history applies to mathematics as well: We will teach mathematics because it is important and beautiful. We will teach it not because it will save our society, not because we "must" know particular techniques, but because we simply do not have it in our hearts to do otherwise.

I don't feel like I was particularly eloquent. If you think math is important for more than these basic uses, please go on over there and say your piece.

And I'd love to hear from you here. Why is math important? And what math is vital for schoolchildren to learn? I love math, but I don't feel clear on why people who don't love it should learn it (beyond the basics discussed above).

Part II. Why School?

Meier labeled her post 'Why School?' in response to Mike Rose's new book with the same title. I've enjoyed his previous books, Lives on the Boundary and Possible Lives, so I expect to like this one too. Whether it will answer some of the questions I find most difficult remains to be seen.

My personal vision of the ideal school is more like a kids' community center, where the children decide how to spend their time, and are surrounded by resources and adults who want to share in the learning adventure. Deborah and her respondents talk about what should be 'required'. I don't think it's possible to require students to learn anything. The best we can do in a system based on requirements is to show the students (who are usually still eager to learn, if it appeals to their own values and priorities) why our subject is vital. That's why I love the work Dan Meyer and Kate Nowak are doing making high school math topics relevant for their students.

These two questions go deep for me: Why Math? Why school?


  1. Let me add my voice for a FAR BROADER view of "why math?". I wrote about this very issue as the foreword to a post at Blog on the Universe:

    and it was re-posted at the Huffington Post under the title: Let's Ban English in School ... Except in English Class":

    Given that math is the language of nature, and that science and engineering are about an understanding of and interactions with nature, scientists and engineers need to speak nature's language .... and so should the rest of us. Why?

    Math - it powers the universe. You want to live life to the fullest as part of the universe? Get math. Good with cookies too.

    Want to see what you can do with math? On Sept 29 the NASA MESSENGER spacecraft will conduct a historic flyby of the planet Mercury. Math got it there. You want to participate in the mission? Done. It is being covered LIVE vis Web 2.0. And the code that's making the live connection possible, and your ability to read this? Math.

    MESSENGER coverage:


  2. Hi Jeff, Yes, math is a language, the language of science. And it underlies music and much art, though artists may only speak math subconsciously. And...

  3. And here's another viewpoint I just discovered . Seymour Papert wrote Mindstorms in 1980. It's hard to believe I'm only now reading it for the first time.

    Papert says (page 10): When I trace how I came to be a mathematician, I see much that was idiosyncratic, much that could not be duplicated as part of a generalized vision of education reform. And I certainly don't think that we would want everyone to become a mathematician. But I think that the kind of pleasure I take in mathematics should be part of a general vision of what education should be about.

  4. Hi Sue - my thoughts about this stuff are nowhere near settled but I did want to share one idea (kind of an elaboration of your Papert quote I guess):

    I think there's something really deeply empowering about mathematics. I believe the rich deep study of mathematics cultivates curiosity, profound resourcefulness, tolerance of frustration, persistence, and an amazing trust of your own mind. I think these are some of the really big reasons why it's an important part of education.

    The catch is that you could learn something called "mathematics" without learning any of this. The skills in an Algebra I course, or any specific mathematical skills, are totally unrelated to what I'm talking about. Students of mathematics have to engage in really deep reasoning and problem solving to get these benefits, not trusting expert sources of information but fighting for their understanding themselves. Since it's the skills, and not the struggle, that schools are answerable for, it's easy for math education to take place that doesn't yield any of these benefits.

  5. Hi Ben, Thanks for leaving a comment. I love the way you put that! I looked at your website just now. Very nice.


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