Alan H. Schoenfeld

Yeah, so it goes back to they're getting it pretty quickly.

The question is, what is it they're getting? We know from past research, mine and others, even dating back to the 80s, Alan Schoenfeld's work out of Berkeley, you know, he went into classrooms, similarly, very well taught mathematics classrooms, and found that, you know, even though everybody said this was a great lesson, students understood, they said, we understand, we understood everything that the teacher taught.

Again, they had the same Problem, as I had when I was teaching, is that if you explore understanding or you throw them a little curveball or change a parameter, their understanding was shallow.

So it seems that just directly telling leads to understanding, but depending on how you measure it, the conceptual understanding is quite shallow in many of the studies that I've looked at.