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Friday, March 28, 2008

What's the matter with math today?

What’s the matter with math education today? No, it’s not that kids don’t know the basics, despite what some people say. And it’s not that teachers are teaching “fuzzy math,” despite what some people say. Paul Lockhart has the correct analysis:
If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with crushing ideas that constitute contemporary mathematics education.
This sentence comes from “A Mathematician’s Lament,” an essay by Paul Lockhart, a professional mathematician. The link to this essay was found in Keith Devlin’s regular column in MAA Online, a publication of the Mathematical Association of America. (Devlin is best known for his radio columns, Saturday mornings on NPR’s Weekend Edition, and is less well-known as the author of The Numbers behind Numb3rs, which will be the topic of another post in this blog. But I don’t want to discuss Devlin here; I want to discuss Lockhart.)

Every math student, every parent of a math student, every curriculum developer, and especially every math teacher should read Lockhart’s essay. It’s not that it’s perfect, for of course it has many flaws, but its point of view is so provocatively on target that it will provide essential fodder for critical discussions. It zeroes right in what’s important in mathematics and on the misplaced emphasis of the way it’s taught in school (or skool, as my friend Brian would write):
I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.

If your art teacher were to tell you that painting is all about filling in numbered regions, you would know that something was wrong. The culture informs you — there are museums and galleries, as well as the art in your own home. Painting is well understood by society as a medium of human expression... But if your math teacher gives you the impression, either expressly or by default, that mathematics is about formulas and definitions and memorizing algorithms, who will set you straight?
I could keep quoting thought-provoking excerpts, but I’m not going to do so; just read Lockhart’s essay yourself!

But wait! I can’t resist quoting his “completely honest” course description for the typical Algebra II course as taught in American high schools:
The subject of this course is the unmotivated and inappropriate use of coordinate geometry. Conic sections are introduced in a coordinate framework so as to avoid the aesthetic simplicity of cones and their sections. Students will learn to rewrite quadratic forms in a variety of standard formats for no reason whatsoever. Exponential and logarithmic functions are also introduced in Algebra II, despite not being algebraic objects, simply because they have to be stuck in somewhere, apparently. The name of the course is chosen to reinforce the ladder mythology.
Fortunately things aren’t quite this bad at Weston. But it’s still painfully close to the truth. Solutions, anyone?

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