Derivative of test scores.

A good teacher should make your scores improve. The absolute numbers are much less meaningful.

No, it really depends on the teacher. My precalculus teacher (probably the best math teacher I've ever had) gives progressively harder tests/quizzes as we learn more about each topic. He ignores the textbook and writes the tests himself.

(Incidentally, we've recently been covering derivatives.)

What do we want to measure in students? Skills, creativity, "intelligence"...?

Standardized metrics are themselves dubious when we are dealing with highly chaotic systems (see: combinatorial explosion, etc) with drastically different properties.

I don't know, nor do I think a good metric necessarily exists. Teaching doesn't fit in neatly with the typical production metrics we use in industry, eg. widgets per hour. Those outputs are directly measurable.

But what is the unit of output for a teacher? Test scores could only hope to measure teaching quality indirectly. It'd be like using record sales to assess the quality of a musician... and we'd all agree that Britney and Mariah aren't the best musicians going around.