There's more to math than solving equations step-by-step.
A reader named Monika Hardy recently noticed that I harp a lot on the importance of math when blogging about education. (Guiltyascharged.) So, she sent me an excellent talk from the recent TEDGlobal event from this summer. The speaker is Conrad Wolfram, brother of Stephen Wolfram, the polyglot behind the applications Mathematica and Wolfram|Alpha, who runs the firm Wolfram Research. His idea: Math is made up of four parts, and our schools are only teaching one of them.
The elements of math, according to Wolfram are: posing questions, translating real world problems into mathematical language, performing computation, and translating mathematical answers into real world solutions. But, Wolfram asserts, we're only teaching computation. But, in today's world—which has progressed beyond paper, the abacus, and even the TI-81—we're still having children show the answers to quadratic equations step-by-mind-numbing-step.
Computers should be doing those calculations. That way, time in math class is freed up to show students how math undergirds everything in the real world. He says that the first country to design its curriculum around creating young adults who "feel mathematics" will benefit greatly in the modern world.
What about the processes needed to solve mathematical problems? Those can taught, as well, he asserts—by teaching kids how to program algorithms to solve equations.
Check out the video, it's really good stuff—at least, I think so.