In fact, jonette11, the examples you mention are painfully typical. And, sadly, this sort of thing has grim daily consequences -- especially for mathematically gifted kids.
Because math teachers generally know so little about their subject, they're all too apt to teach it mindlessly. Lacking the understanding needed to evaluate alternative methods of solution, they insist on rigid adherence to the One True Method, as set forth in the textbook or teacher's manual. Getting the right answer is not enough: a child must also demonstrate that he got the right answer by following all the "right" steps in exactly the "right" order.
But often, despite the protestations of the teacher, there really is no one "right" way to solve a problem -- and it is exactly the most mathematically talented kids who find this sort of completely unjustified pedagogical fascism especially maddening. A child who can correctly solve a certain genre of math problem a hundred times in a row -- even under considerable time pressure -- should not be bothered about his methods. Whatever they are, they're clearly not inferior to the teacher's One True Method, since the results to which they lead are not inferior. And demanding that the kid be able to explain his methods to the teacher is obviously unreasonable when that teacher can't even explain the One True Method the textbook prescribes.
In fact, one of the most characteristic indicators of mathematical talent in a young child is the spontaneous formulation of idiosyncratic methods of calculation. Such a child often finds his private methods impossible to put into words, and an incompetent teacher will often penalize him for this, no matter how spectacular his arithmetic accuracy.
This is unreasonable and foolish, of course, but it's also very common. And it all just traces back to mathematical ignorance in the teacher.
