November 21, 2010
Mike Gwaltney
algebra, Creativity, education, engagement, learning, math, Real-World, Relevance, Rigor, school, TED
7 responses

Recently I watched a TED talk which got me thinking about Mathematics in a way I hadn’t before. To cut straight to the video, scroll down.

Let me be clear at the start of this post: I’ve had a difficult relationship with the academic subject area called “Math”. I did well in it until high school, when math work became a fairly complicated process of memorizing and calculating. I wasn’t very good at committing formulas to memory or at seeing how they had application to anything real.

So I became a Math Dropout as an upperclassman in high school, surrendering to the complexity of Trigonometry and Pre-Calculus. I instead doubled up on History, Social Science, and English classes and joined that group we call “Humanities kids”, or the ones who aren’t “good at math.”

From what I can tell, my experience in math class isn’t unique. I hear many students say that math is hard – they get long lists of problems to solve using complex computation, none of which they see as relevant to their lives, and by the time they’re in 10th grade many start self-identifying as “dumb” when it comes to math.

That so many students leave high school thinking they aren’t smart enough to understand math is really a shame. “Mathematics” comes from the Greek *máthēma* which means learning, study, and science. It is a way of deducing truth – an absolutely essential human ability. Yet when a smart 17-year old kid says to me “I can’t do math”, I never think he’s really telling me “I can’t learn”, or “I can’t think scientifically”, or “I don’t know how to seek truth.” Rather, I think he’s saying he isn’t good at calculating answers from book problems. The capitulation to the false dichotomy of smart/dumb in math is in fact a misunderstanding of what math actually is. But it is a misunderstanding that I hear math teachers and policy-makers reinforce all the time. How has education so tragically misunderstood math?

Conrad Wolfram explains in his TED talk that math education has become nothing more than a multi-year practice of hand and paper computation. He suggests that what we need is a return to the understanding of what math actually is: a way of thinking quantitatively to solve problems:

Mathematical thinking is an important way of problem-solving in the real world. Math education should take both common and extraordinary problems humans encounter today, and teach how these can be seen quantitatively: “Should I buy a house?” “What is the most sustainable way to power our city?” The 21st century may require more quantitative thinking than any before it and yet we rarely present math in real-world terms in education – most high school math classes spend an inordinate amount of time (or all the time) in computing answers to book problems, and never get to the bigger picture of using math in a real world context. Math has been reduced to simple computation, divorced from its larger purpose and removed from real-world context. Is it any surprise that many smart people conclude math isn’t for them?

Wolfram suggests that by using computers to do Step 3 above, we can free up math education to be more effective and authentic to its purpose. Computers are an incredible tool for solving numeric problems, so why not use them? Why shouldn’t a Calculus class be about learning how to use it in the real world of Engineering, where engineers use computers all day long? If Engineering is about using math to solve real-world problems (i.e. “How can we better build levees in New Orleans?”), why don’t we create math classes where students use computers to do the time-consuming computational steps thereby freeing up their time to focus on identifying, quantifying, applying, and verifying? Wouldn’t math be a more engaging and wholly valuable experience if it mimicked the real-world? I agree with Wolfram that we must revise our thinking of what math education should be. Much less time should be spent teaching computation and much more time should be outside the room, finding real math problems and testing solutions for them. We must transform math class so that it becomes a place where the focus is on learning to identify those real-world problems which might have quantitative solutions, and to suggesting and verifying solutions for them.

Don’t get me wrong, I’m not saying computation is not important, rather I am saying that computation is an essential process for which a powerful tool has been created, and should be used. There are basic abilities and concepts of computation which must be mastered, of course. But when math education recognizes that computers can do the more complex and difficult computation and therefore help the larger quest for solutions to meaningful problems, I think math class will be transformed into a more authentic version of itself – a discipline that is engaging to students and preparatory for real life. It will become a discipline that doesn’t leave so many smart people tragically mislabeled as “dumb” or under the delusion that math doesn’t matter.

Enjoy Wolfram’s talk. I welcome your comments.

Comments

Mike Gwaltney

I’d say you’ve got one of the best explanations of his idea I’ve seen. As a math teacher myself, I have the same assessment of the subject, and I’d like to see how we can improve it.

I think we’d have to find a school which could do away with the computationally based curriculum we have, and teach kids how to use (and understand) appropriate tools to do those calculations.

Thanks for your comment David.

If we can think of a continuum of teaching math with the “old way” and the “ideal” on the other end, perhaps we can start moving the instruction toward the ideal, within the existing conditions. I’m thinking of my colleagues who would say that the SAT doesn’t allow for reform in Math – perhaps students would better understand SAT problems if they got more real-world practice with them. I think if Math teachers want students to truly understand, instead of just memorizing, students should have to transfer the computing ability to real-world problems. That’s at least a start down the road to ideal…

Great post, I agree that we need to deemphasize the calculating portion of our curriculum. On my blog I respond to this video by encouraging STEM teachers to use programming in their classrooms for modeling and understanding of algorithims.

http://brokenairplane.blogspot.com/2010/12/math-and-curriculum-reform-for-21st.html

http://brokenairplane.blogspot.com/2010/12/math-curriculum-programming.html

We don’t want the pendulum to swing too far the other way and have a large portion of our population be able to use computers to do the work for us while not understanding how it works.

If the emphasis is on topics like factoring equations as a matter of understanding and not practice in algebraic manipulation, then it would shift how we help students learn topics such as this.

Once again, great post and thanks for facilitating conversation about this topic.

Thanks for the thoughtful comment, Phil. I love your blog posts on this topic and I’m certain your students benefit from your very deliberate attention to their thinking ability. Good stuff.

Your point about watching just how far the pendulum swings is an important one, and it needs restating, so thanks. I think it’s important though for us not to be hesitant to reform math education (and other disciplines as well) in the face of sometimes irrational fears that the “machines” will take over and that humanity will lose all ability to think for itself.

Thanks again for the post. Cheers.

I agree with Wolfram’s comment that math, as taught now, consistently denuded of real life applications, teaches a form of disciplined thinking. Gardner’s “disciplined mind.” I think that skill is broadly applicable within and beyond mathematics and serves an important role in the whole education of children.

That said, I wholeheartedly agree with the idea we need to increase the braoder conceptual problem solving we do in math, even for younger children, and emplyoing computers to do the heavy computational work makes sense to me. After all, what world are we preparing our students for? A place where they will have to compute logrithms by hand? I don’t think so…

I’m with you, Mike- I had a rough experience with math during junior high, and decided I wanted to study other areas more in-depth during high school.

This video instantly made me think of a poster that hung in my geometry teacher’s classroom (and undoubtedly many others). At the top it said, “When will I actually use this?” above a giant chart, connecting math concepts to occupations. It was kind of a wake up call, and yet I wondered if those concepts would be better learned in the occupation itself, or years before in school.

I think there needs to be a balance. Using computers is great, and quick, but if one totally relies on a calculator or a computer, he or she will have no idea how to solve a problem when technology fails or isn’t readily available. Friends of mine actually like to sit down and do math problems, in order to break from screens and make sure they still know it. Shouldn’t you know how a computer is doing this, the order, and why it’s necessary? Total reliance on machine computing concerns me.

That being said, math definitely needs to be correlated to its real world applications, and not just a poster. I had to do a math assignment while painting murals in college, in order to get accurate quotes, percentages, etc. Our Multivariable students at OSG are asked to find their subject matter within the news, daily life, etc.

In other words, a balance needs to be struck. Giving up on hand computation completely, in my mind, devalues the processes and motivation which made those tough problems much more possible to solve with just one’s mind.

Math classes do incorporate real world applications into the lessons. They’re called “story problems”, and in my experience they evoke far more terror from students than factoring polynomials.