3 3 2014 ~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?
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.
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."...
I recently visited students in fourth, fifth and sixth grades at a school in New York to talk about the ideas of modern math, ideas they had never heard of before. They were young enough that no one had told them yet that math was impenetrable, that they wouldn't get it. Their minds were still uncluttered with misconceptions and prejudice. They hadn't yet been humiliated by poorly trained math teachers for making mistakes in front of their peers. Every question I asked them was met with a forest of hands.
I used a Rubik's Cube to explain symmetry groups: Every rotation of the cube is a "symmetry," and these combine into what mathematicians call a group. I saw students' eyes light up when they realized that when they were solving the puzzle, they were simply discerning the structure of this group.
We next studied the majestic harmony of Platonic solids using dice. And I told the kids about the curved shapes (such as Riemann surfaces) and the three-dimensional sphere that give us glimpses into the fabric of our universe...
read full article at: http://touch.latimes.com/#section/-1/article/p2p-79479491/
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