I was in the doctor's office the other day, getting blood drawn, and the phlebotomist asked me what I was reading since I was carrying a book (I'd rather read when sitting in an examination room waiting for the doctor than stare at those charts of nasty medical illustrations on the walls and wondering which disease is eventually going to kill me).
I told him it was a book about math (which I'll review in a couple of days when I finish reading it). He then asked if I taught math and I told him I was a geologist we talked for a bit. He told me he was never very good at math (as most people will tell you if they see you reading a book about math for fun), and one his memories from a high school math class was his teacher yelling at the class - "You know why you kids do so badly on the test? It's because you can't follow directions and that's what math is - following directions!"
He was done drawing my blood, so I didn't continue the conversation, but I was horrified that a math teacher would yell at his class like that. Not because he yelled at the students - good for him, they probably deserved it and never followed instructions - but because he told them something I think is totally false. Math, real math, is not simply "following directions". I would contend just the opposite - that teaching math this way is the worst possible way to do it (to be fair, of course, I'm just going by some one's memory of a long-ago math class, reality may have differed).
Also keep in mind, in what follows, is that I'm not a math teacher. I'm a geologist that likes math and think it's terribly interesting (I also find myself teaching elementary algebra to college students in my geology lab when they can't solve certain problems). Take what I say with a grain of salt (perhaps a math teacher could chime in if they're reading this).