Patient Problem Solving
Last year, I remarked on a TED talk from mathemagician Arthur Benjamin, who argued for the displacement of Calculus by Statistics in the hierarchy of high school mathematics. This year, TED has sponsored a talk by high school math teacher Dan Meyer, who discusses what, in his view, are the major problems with the way mathematics is currently taught to kids, and what can be done to fix things.
His opening is spot on: "I teach high school math. I sell a product to a market that doesn't want it, but is forced by law to buy it." He goes on to argue that the problem with math education, a problem exacerbated by most textbooks, is that it discourages what he terms patient problem solving. Problems in textbooks rarely reflect the types of problems one encounters in real life: textbook problems usually supply you with just the right amount of information, and the question is frequently just a matter of plugging values into an appropriate formula. More complicated questions are frequently presented in multiple parts, so that students rarely have to think long and hard about any one thing. Instead, they are offered bite-sized pieces of a larger problem, any one of which is relatively simple. Taken together, the net result may be the solution to an interesting problem, but by holding students' hands like this along the way, they never develop a taste for solving difficult problems.
This hand holding, Meyer argues, trains students to become impatient when they encounter an actual problem. If a question isn't broken down into easily digestible pieces, any one of which can be solved by plugging and chugging into one of a short list of formulas, students are trained to throw up their hands. In a world fraught with problems, however, this does a disservice not just to students who study mathematics, but all students.
The video is a little over 10 minutes, but if you have the time I'd encourage you to watch it. Meyer talks about potential solutions to this failure of our educational system, and compares the current state of affairs to watching episodes of Two and a Half Men. And despite the presence of a fraction in the title, the comparison is not favorable.
(Hat tip to Patrick for sending me the link.)
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