David Cox said:
"The question, as I see it, is this: Can we do both? Can we teach students math—real, interesting, thought provoking, man-this-stuff-is-cool, math—and still have them show growth on whatever assessment is put in front of them?"That's an awesome question, Dave. There are three problems with our current state exams in NY anyway that complicate the issue.
#1 There is way too much content tested for a course that is supposed to be done in one year. I think most of us would agree that authentic learning takes time, but if you take the time to do it right, you can only cover maybe 2/3 of the stuff tested. We have to make the choice of exposing students to all the content by frog-marching them through it, or teaching it in a way they really learn it and conceding there will be stuff on the test they've never seen before.
#2 Many of the questions strictly test knowledge of notation and vocabulary. A kid could know the math inside and out but still miss these.
#3 Many of the questions have a gotcha nature that are clearly not intended to assess understanding. For example, this week one of my students couldn't understand why she picked the wrong answer on a multiple choice trig question - she had done everything right, but her calculator was in radian mode instead of degree mode. Those weasels had made the radian-mode answer one of the distractors, AND, this wrong answer was reasonable in the context of the question.
These are my frustrations around NY exams that make me feel like I can't both teach for understanding and teach such that the exams show progress. It remains to be seen how the common core assessments address these issues.