Photo180 - Recursive Process

I attended the Wolfram sponsored - computer based math summit today and Friday in NYC at unicef hq. No picture today but I will share a question that is going through my head. If you'd like to comment then I'd be truly flattered. What role does learning how to calculate have in learning mathematics? Can the calculating part of mathematics be reduced/eliminated without harm?

(Eg. By calculate I mean, find the roots of a quadratic. By hand? Or with technology.)