Math is dead. Long live Mathematics!

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.

http://video.ted.com/assets/player/swf/EmbedPlayer.swf

One Innovation Enhancing Learning

Karl Fisch keeps an excellent blog and is the co-author of the video “Shift Happens”. He’s experimenting with flipping homework and classwork in his math class, and it’s making a difference already (read Fisch’s early observations here). A couple of my math colleagues are finding this works as well, and their comments are the subject of a future blog post here.

For now, Daniel Pink offers Kudos to Fisch for doing something we all find challenging: innovating. Note that innovation doesn’t mean you’re the first to do something, rather, innovation is about taking an idea and doing it for the first time yourself. Trying something new is a great way to learn what works and what doesn’t, and we need plenty more of it in education.

Fisch also has a day job — at Arapahoe High School, near Denver. This year, in addition to his other duties, he’s begun teaching algebra to 9th and 10th graders. And he’s taken a novel approach: Instead of lecturing during class time and assigning problems as homework, he’s flipped the sequence. He now records lectures on video and puts them on YouTube for the students to watch at home at night. Then spends class time working on problems with students.Read more at www.danpink.com