they can accelerate as fast as they can, but school and online videos are rarely going to offer the direct metacognitive support for the secondary skills they did not give themselves time to develop.
Curriculum focused standardized tests are more often going to focus on the direct testing of specific element knowledge and application. They can become poor indicators of actual mastery that would include the full range of secondary skills.
WOW. Thank you, ZenScanner, for that. THAT. That is what I have been trying to put my finger on with mathematics instruction and what distresses my DH and I about the way her school is tending to do things.
This is a real problem with flipped classroom methodology in practice, too-- it neglects the same heuristic factors. I do think that the only way that most students-- even PG students-- pick those things up is by NEEDING them, or seeing someone else apply them in real time.
There's no teachable moment quite like "Wait-- WHA?? Why did you just do that??"
