If students testing at the X percentile on a standardized Algebra test at the end of Algebra I end up at the end of Geometry testing at 1.1X in one teacher's class and at 0.9X in another teacher's class in the next classroom, it seems we have a pretty good hint which teacher is better.
I strongly disagree. Students can understand different subjects better than others. They can become different (better or worse) students from one year to another, for instance, because of home(less) and family situation, have friends in this class but not that class, or like the hot teacher but don't like the old, ugly hippy.
Sure, there are some subject areas that don't lend themselves to standardized testing (for example, various performing arts), but these don't seem to be the areas that are resulting in American High School graduates being non-competitive.
So what you're saying is, those subjects in which there aren't standardized tests are areas where we are competetive. Hmm... sounds like you made the opposite argument here. Feeling and intuition are just as important in "rigorous" fields such as math as in liberal arts. Can you point me to a computer that can solve all our number theory or mathematical logic problems?
... end up being frustrated by not being rewarded for their performance...
I agree. However, using standardized tests is most commonly seen as a method for punishing poor performance, so why would they be supportive of that?
Things equal to nothing else are equal to each other.