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.

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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."

Instead of introducing kids to the basics, introduce them to the great works.

Though it has become a naturalized part of music-making since the first one was built in 1710, the pianoforte (its name means "soft-loud") was a technical marvel for its time, a machine that changed music in ways that are hard to imagine. Computer pioneer Alan Kay once observed that any technological advance is "technology only for people who are born before it was invented,' and in the case of the piano, this applies to no one alive today. Seymour Papert, the MIT researcher, concluded, "That's why we don't argue about whether the piano is corrupting music with technology." Four hundred years later, few can play the piano well, but just about anybody can sit down at a piano, pluck out a simple tune and perhaps even sing along. Devlin realized that foremost among the piano's virtues was its ability to enable just about anyone to play real music from day one, on the same instrument that professionals use. You could go from absolute beginner to Carnegie Hall soloist course of a decade or two. The piano delivers instant feedback on your performance, allowing you to easily gauge your progress. You must touch the piano to play music, but the more you do, the more you'll learn, naturally, about melody, harmony, consonance, and dissonance. It is, in a word, immersive.