Students have been taught that math is about right and wrong, rather than trial and error
Over the three years Jordan Ellenberg was writing his book, he repeatedly encountered the same reaction to its subject. “I’d be at a party, and I’d tell someone what my book was about, and then I’d be like — ‘Hey, where’d you go?’” What topic was so awful and off-putting as to make people flee at its mere mention? Math.
Ellenberg, a professor of mathematics at the University of Wisconsin–Madison, has now published that book, How Not to Be Wrong, and rather than putting people off, it will make its readers want to stick around. Ellenberg tells engaging, even exciting stories about how “the problems we think about every day — problems of politics, of medicine, of commerce, of theology — are shot through with mathematics.” Understanding the role of math in these issues, he writes, “gives you access to insights accessible by no other means.”
Knowledge of math, Ellenberg enthuses, is like “a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world,” like “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.”
Sounds pretty great, doesn’t it? So then why does math fill so many of us with dread? I put that question to Ellenberg when we spoke by phone last week. “We teach math as if it’s about applying a prescribed formula, circling the right answer, and going on to the next problem without thinking about what it is we’re doing,” Ellenberg replied. “But that’s so not what math is. Math is a fundamentally creative enterprise, a fundamentally humanistic enterprise. It’s a lens through which we can see the world better.”
Ellenberg sees the results of rote mathematics instruction in his undergraduates: “It can be hard for my students to get into the mind-set of trying different things. Often, during my office hours, I’ll get a student who says of an assignment, ‘I didn’t know where to start.’ I tell them, ‘Of course you didn’t know where to start! You’re doing this for the first time, so try a few things and see what works.’ But this approach is foreign to students who have been taught that math is a series of formulas. They don’t realize that math is all about trial and error, about experimenting. That’s true of advanced math, but I think we can push that mind-set down into the earlier grades as well.”
Ellenberg acknowledges that his approach would require a paradigm shift. “People are not used to taking a loose and easy approach to math. They get very tight and tense around math because they have so much fear and anxiety about it,” he noted. In addition, he said, “People dislike math because they don’t like being told that they’re wrong. And it’s not incorrect to see math as a realm where there are right and wrong answers. But the thing is: knowledge in math does not come about because the teacher says it’s so. Math is a realm where people can demonstrate the rightness of answers to themselves. So if part of what creates the fear of math is wanting to avoid being wrong, then learning to like math is about learning to be willing to mess up.”
Paul is the author of the forthcoming book Brilliant: The Science of How We Get Smarter. Read more at her blog, where this post first appeared.