I don't know that I agree with this. If you don't like just following rules, then you want to try to understand why the rules work and make sense. E.g. why are you allowed to add "x" both sides of the equation or divide both sides by 2?
The rest of it is like what BrentRitterbeck says. You just need to do enough problems to be able to look at a problem and say to yourself "I think this technique will work."
Proofs in algebra aren't usually very enlightening with respect to the theorem they are trying to prove, but they can teach you a new technique (e.g. proving the quadratic equation can teach you how to "complete the square").
Comments
I don't know that I agree with this. If you don't like just following rules, then you want to try to understand why the rules work and make sense. E.g. why are you allowed to add "x" both sides of the equation or divide both sides by 2?
The rest of it is like what BrentRitterbeck says. You just need to do enough problems to be able to look at a problem and say to yourself "I think this technique will work."
Proofs in algebra aren't usually very enlightening with respect to the theorem they are trying to prove, but they can teach you a new technique (e.g. proving the quadratic equation can teach you how to "complete the square").