1.) If you get used to be a consumer of solutions (via rote memorization or by always googling the answers or asking someone else) you will never become a problem solver.
2.) Math is useful.
In my humble opinion, the real problem with education is that we usually give credits only to correct answers and mainly to the number of correct solutions, but this should'nt be so.
To get to the point here is an advice for heart care that can be applied with much success to the goal of becoming a problem solver:
If you are out of shape and you daily walk 20 minutes you will be rewarded with a great benefit for you heart, and it will be much greater that the effect on others with strong hearts.
So my advice for becomming a good problem solver is: It doesn't matter that you are out of shape, that you feel dumb or stupid. Try to solve one small problem, it doesn't matter whether you succeed or not, that exercise will produce in you an excellent result and if you persevere you will become a good problem solver. So that is, close your ears to any other solution to your problem and put yourself at working at it. (Sorry for the English)