Originally posted by Reid:
def.Do you care to elaborate on why you feel this way?
Teachers have a profound, but understated, influence upon their students. The risk isn't just that teachers will teach the material incorrectly (which they often do, cf. the ever-rising emphasis on standardized testing) but rather that teachers will communicate their poor attitudes and anxieties about the material. Reluctant, apathetic teachers will also express frustration at having to answer questions or give additional help to students, teaching children that it is socially improper to seek additional help. Beyond being obvious as all hell, this is (increasingly) well-documented in the pedagogy literature. For example, the paper I cited.
In other words, I feel this way for the best possible reason: because it is empirically correct to feel this way.
Edit: ^- answers the part about pedagogical incompetence.
About mathematics being useful to everybody: I'll give you two arguments that should completely convince you.
1.) It is useful in a literal sense. It depends on what you're doing, but I can come up with a scenario for everything. Calculus is the study of areas and rates. Linear Algebra is the study of direction. Combinatorics is the study of counting things. Statistics is the study of uncertainty. If you deal with any of these things, there is a place in your life for higher mathematics. If you don't deal with any of these things, you are probably catatonic.
2.) Mathematics is a part of our culture, especially as a technologically-advanced civilization. We should study mathematics simply so that we can understand the attitudes and beliefs that pervade our culture. We should study mathematics for the same reason we should study English literature and history.