I agree with you wholeheartedly about the mixed signals thing. I definitely experienced that phenomena because of my science pursuits. I can also understand your point about how certain students would develop a "Well I'm NEVER going to do that..." attitude when shown certain specific examples of math. But a more practical applications approach - no matter how poor the examples - should still interest more students than a "I don't know why you have to do it, but just do it" approach.

I think your disagreement with me comes about in part because you are thinking in more concrete, specific terms than I am. You're correct that "You can use this math to build rocket ships" would probably not have helped me if I didn't have an interest in rocket ships. But a teacher wouldn't necessarily use just a single type of example. Beyond that, I'm saying that my teachers never explained the overarching concepts of math and how they were related or explained - in GENERAL terms - what it could be used to do. Each math 'concept' was presented as a discrete type of chore that you completed in order to satisfy some perverse deity for no apparent reason. Math was not presented as a language of logic and reason that could be used to solve practical problems, but as a completely made up busywork exercise. I might as well have spent my time memorizing Klingon grammar rules. I literally didn't realize calculus was the study of change until college, even after having passed a course in it! Maybe you had a better experience with math instructors, and it is just difficult for you to understand how woefully bad some practicing math instructors actually are?