> Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deri

> Think of stuff like the quadratic equation, or formula for the surface area of a cone. How many of us were just taught these magic formulae without first deriving them? Why do we start talking about pi without first explaining how it's calculated? If we're waiting until children are capable to derive those equations before we get them to use those a bit, then we're waiting for very long. And if you just keep telling them to add numbers and multiply numbers together for many years in a row without giving them any interesting problems to go with it, there'll be no one interested in math by the time they'd usually have the abstract maturity to deal with the more foundational modern math problems. We don't ask Computer Science students to write an OS before using one, we don't ask carpentry students to build a hammer and cast nails before using them.