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Thursday, August 07, 2014

How our 1,000-year-old math curriculum cheats America's kids

Photo: Elizabeth Lippman
UC Berkeley math professor Edward Frenkel writes, "Imagine you had to take an art class in which you were taught how to paint a fence or a wall, but you were never shown the paintings of the great masters, and you weren't even told that such paintings existed. Pretty soon you'd be asking, why study art?" continues Los Angeles Times.

That's absurd, of course, but it's surprisingly close to the way we teach children mathematics. In elementary and middle school and even into high school, we hide math's great masterpieces from students' view. The arithmetic, algebraic equations and geometric proofs we do teach are important, but they are to mathematics what whitewashing a fence is to Picasso — so reductive it's almost a lie.

Photo: Los Angeles Times

Most of us never get to see the real mathematics because our current math curriculum is more than 1,000 years old. For example, the formula for solutions of quadratic equations was in al-Khwarizmi's book published in 830, and Euclid laid the foundations of Euclidean geometry around 300 BC. If the same time warp were true in physics or biology, we wouldn't know about the solar system, the atom and DNA. This creates an extraordinary educational gap for our kids, schools and society.

If we are to give students the right tools to navigate an increasingly math-driven world, we must teach them early on that mathematics is not just about numbers and how to solve equations but about concepts and ideas.

It's about things like symmetry groups, which physicists have used to predict subatomic particles — from quarks to the Higgs boson — and describe their interactions. Or Riemannian geometry, which goes far beyond the familiar Euclidean geometry, and which enabled Einstein to realize that the space we inhabit is curved. Or clock arithmetic — in which adding four hours to 10 a.m. does not get you to 14 but to 2 p.m. — which forms the basis of modern cryptography, protects our privacy in the digital world and, as we've learned, can be easily abused by the powers that be.
 
We also need to convey to students that mathematical truths are objective, persistent and timeless. 
They are not subject to changing authority, fads or fashion. A mathematical statement is either true or false; it's something we all agree on. To paraphrase William Blake, mathematics "cleanses the doors of perception."
Read more...

Related links
Edward Frenkel's homepage - Department of Mathematics
Love and Math: The Heart of Hidden Reality By Edward Frenkel

Buy the Book 

Source: Los Angeles Times


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