Photo: Ianqui
BY MICHAEL V. COPELAND
The way most of the world teaches math today doesn’t prepare anyone for living and working in a world where the first-language of problem solving is increasingly math, says Conrad Wolfram. Take the quadratic equation and doing long division by hand. Wolfram likens teaching these age-old math stars to learning outdated processes of photography, like how to load a roll of film or use a darkroom, in order to take go out and take a photo with your smartphone.
And despite a growing discussion on the importance of math education (and all the hang-wringing in the United States in particular over poor performance on standardized tests) virtually nobody is talking about what it actually means to learn math today.
Along with his brother Stephen, Wolfram leads Wolfram Research, the company behind Wolfram|Alfa, Demonstrations, and Mathematica. He’s also the founder of computerbasedmath.org, an organization dedicated to retooling math education for real application in a world where more and more students have access to the greatest math tool invented since the protractor – the computer.
“The mistake that’s being made by nearly every government across the world is that they say you’ve got to learn to make all of the tools before you use them, which is a fundamentally a flawed belief about life, in my view,” Wolfram says. “The result of that mistake is that they don’t teach people many tools… If the only tool you have is a hammer, then everything looks like a nail. That’s exactly what we’re doing with math.”
Wolfram’s goal at computerbasedmath.org is to establish a new curriculum of math education that is grounded in mathematical questions you might encounter in the real world. For example, one problem might ask students “Are girls better at math?” Another: “Should you buy laptop insurance?” Unlike the problem sets of today, which are based far more in math procedures and equations, this type of question involves the essence of mathematical thinking.
A student can set up the problem, ask the right questions, and just as important, find the right data or numbers to help answer those questions. The questions get turned into math, and the calculations are specified. That’s where the computer comes in. Instead of spending a lot of time hand calculating, the grunt work is turned over to the computer to complete almost instantly. It’s the student’s job to go back and validate the answers.
If you think getting to that answer requires writing a smart bit of software, you would be right. Wolframs’ approach requires that students learn at least the basics of coding. Essentially, it’s about learning how to use the main tool available for solving math problems: the computer.
“The relationship between composition and English is a bit the same as the relationship between coding and math,” Wolfram says. “Code is the way you write down your understanding of the technical world. If you can’t do some level of coding, you’re going to have real trouble expressing yourself in a meaningful way technically. It’s actually more central to people’s skillset than even the people promoting coding believe it is. It should be part of primary math.”
Solving real-world problems also increases the appeal of math, Wolfram says. Rather than having this sneaking (and correct suspicion) that you might never use the quadratic equation, math becomes a key ally in understanding and navigating the world.
“What we’re doing in education today is we’re using an abstraction to frighten people off,” Wolfram says. “We’re saying here’s a completely abstract problem, go out and solve it. But we won’t tell you how it’s related to anything. Most people are frightened by something that seems outside of their experience.” But by no means does Wolfram want to dumb down math education. On the contrary, CBM is meant to make it possible for people to solve much more conceptually difficult, in-depth math problems.
Wolfram and CBM are not without detractors. The main argument against this new model of math education is that by using a computer, students won’t understand the algorithms and formulas running underneath. They’ve swapped one abstraction for another.
To that, Wolfram says that there is a general misunderstanding about the subject of math. “Of the people who disagree with me, none disagree with my characterization with how math is done in the real world. They just think that you should be teaching some proxy to that to get to that point,” Wolfram says. “I’m saying take the real subject and teach the real subject. I don’t really get why they think the proxy is a better way to get to that than the real subject.”
Which gets us back to whether you should buy laptop insurance. The short (math-based) answer is, it depends. If you are short on cash, and your computer means everything to you – practically every student out there – yes you should, Wolfram says. But if you can afford to drop the money for a new machine, every time you drop your machine on the floor, take a pass.