I was taught that the one way to know that you actually learned something is not passing a multiple choice test, but can you actually teach it to someone else.
But the thing is that many teachers aren't passing math knowledge onto someone else. They can't, because they don't have it themselves.
I'm no fan of multiple choice tests (and Pearson) for many reasons. I agree that high scores aren't evidence of the kind of knowledge needed to solve complex problems. But poor scores ARE strong evidence of lack of knowledge.
Future teachers have the lowest or near-lowest average SAT and GRE scores. They struggle to pass 9th-grade-level state certification tests that they know are coming for years --- there's no excuse for that.
I agree that knowing HOW to teach something is very important, but a person has to have the knowledge first. The teaching corps seems to make excuses on this point by claiming that soft skills around the knowledge are what's really important. That's not true. Both things are important.
I'm sorry about your struggles, but the facts are that certification tests aren't set at a high level.
If they look hard or unfair, it's because of lack of knowledge, and people who have that knowledge can see this very easily.
