Re: Point #5, I think we also have to beware of throwing the baby out with the bath water. It’s tempting to say that because research in education is messy and not as fundamentally precise as, say, research in medicine or physics, then it can tell us nothing about how people learn. I think you and I would both agree that this is too extreme, and yet I hear this all the time when I write or speak about education research — from researchers in the hard sciences, and yes in mathematics as well, who completely dismiss educational research because of perceived methodological flaws.
The truth about education research seems to be somewhere in between. It is very hard to use empirical studies to learn things about how people learn because we are dealing with human beings, not drug trials or electrons that we can directly control. And yet this research does tell us something. The trick is in doing the best we can with the methods we have and being fundamentally honest about what the results do tell us and what they do not tell us. It’s a hard business because we only make discoveries about learning in bits and pieces and we need an entire community to stitch the pieces together into a coherent whole — but those discoveries do actually happen.