In modern society we've learned to specialize: we are whatever is it is we do for a living and teachers are teachers - we must leave our kids' education in their hands. Way back when there were no schools, parents were also their children's teachers. This was in every way a more constructive and productive relationship, since parents had not only a full understanding of their children, but also cared for their development and well-being more than anyone else. There's no way any teacher will ever care for a child as much as their parents do - let's face it, this is a reality we just don't want to look at because it will mean more responsibility and work for ourselves, and no one wants or needs that.
If you are having trouble with your teenage child, feeling he or she is useless, and if you are no college calculus professor, then you may have noticed the problem a little too late. The key is to always be observant from your child's early schooling, so that you may begin taking corrective actions. I live in China where the encouragement system has nothing of encouraging - the students are ranked continuously and the students know at all times how they rank, not only in their class, but in their grade. Knowing you are among the top 5 must produce an indescribable feeling of success, and superiority. Falling into anything below 20 (cause it's easy for there to be more than 70 students in one class in China) must surely lower your defenses, make you shrivel and die. It's a ruthless system. Luckily you are not in China.
The key to raising a physically and emotional child is to learn what your child is learning in school and act as your child's after-school tutor (and coach). You need to help with difficult questions, not by giving the answers, but by providing guidance. In order to do this you will in time learn you will have to know your subjects inside out. This is the easy part, though.
Now for the heavy lifting. This is where you become your child's coach. Coaches direct the play, but more importantly bolster the players self-esteem. Making someone believe they can is an art that takes practice. It's not about telling the players they are awesome when they are awful. It's about praising the little extra efforts made that got the team that one extra point. A coach constructs a state of mind in which the player believes there's always room for improvement.
Employ positive reinforcement - always positive. Take mistakes as normal steps towards success. Be patient, good wine needs time. Think any improvement is a great improvement, and praise it as such. Praise works miracles.