But they're important in the context of real life.
So, yes, we should keep these classes, keep having kids go through algebra and calculus and geometry...
...But you shouldn't be bound by arbitrary rules. Algebra is important, but if you find "x" by doing something other than some arbitrary thing where you subtract both sides, etc., you shouldn't get an F in the class.
Same with calculus, geometry, everything. The importance is the thinking and the logic, and what real-life application you can take from your knowledge. Making hard rules for these math courses, for example, definitely hurts this and does some of the things this article claims.
But true, honest exploration in math and thinking about it is very important, and if it's free and done in an honest way there is no question about whether it's necessary or not.
Richard Feynman covered this better than I ever could: http://www.youtube.com/watch?v=5ZED4gITL28