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Problems with Conventional Math Problems

Posted in Knerds on April 22, 2010 by

David Yourdon, a Content Dev @Knewton, proves we’re not just obsessed with the GMAT, LSAT, and SAT.

The academics team at Knewton has been buzzing about a video that one of our expert teachers, Chris Wu, sent around this morning. It’s a TEDx talk by Dan Meyer, a high school math instructor in Santa Cruz. The talk focuses on the virtues of what Meyer calls “patient problem solving” — where fewer formulas and inputs are fed to students and more active problem formulation is required of students.

For example, rather than giving students a train’s average speed and the distance the train needs to travel and asking them what time the train will arrive, why not ask them for the train’s arrival time and let them, in a group conversation, determine what information is needed to solve the problem? When they realize they need some kind of distance measurement, make them consult maps to find the distance in question; when they need a rate, let them research a train’s average speed. Students will learn to manipulate equations in the process, but more importantly, they’ll learn to think creatively about the real world. The result, as Meyer says, is that “the math serves the conversation; the conversation doesn’t serve the math.”

Math and science education is a hot topic in the US these days, and as the Obama administration prepares to institute new school standards that will set the curriculum in 48 states, we must improve not only what we teach but also how we teach. Part of the “how” fix boils down to making the educational experience less monolithic. In an earlier post on this site, Kalyan Dudala bemoaned the lecture format that has hounded him since his undergraduate days. A three-hour lecture on organic chemistry may work for some students, but it certainly doesn’t work for most. People learn at different rates and in different ways.

Motivation is also an issue. The lecture format is designed, in part, to allow the teacher to verify that you came to class. But fear of punishment doesn’t make somebody a good learner. Once we’ve done away with one-size-fits-all lectures and customized the student experience, we will still need to make sure that students are engaged. In other words, it’s not enough to make sure that everyone can successfully plug values into formulas. Teachers must also communicate why these particular math and science concepts are being studied. Sean Carroll put it well in a recent New York Times interview: Students need to see that the quantitative aspect of science “can be in the service of interesting rather than boring problems.” If they do, the subject becomes inherently worthwhile. On the other hand, if math and science are presented as a series of rote equations, students are unlikely to learn the concepts. Or — just as bad — they’ll learn them, but they won’t grasp the fact that in life, the things you need in order to solve a problem are seldom handed to you. Nor, for that matter, is the problem.

Of course, some people do approach reality best through the medium of abstract equations. That type of intelligence — which spawns the most profound scientific breakthroughs — can and will be ministered to as well. In fact, that’s the beauty of where math and science education appears to be headed. If, as Dan Meyer says, “math is the vocabulary for your own intuition,” then the curriculum of the future will essentially amount to letting you speak your mind — and clearly.