Yesterday, DS7 forgot to bring home his math worksheet. But he wanted to work on a math worksheet. So, we found some free worksheets online and flipping through topics and he wanted 6th grade statistics. So, I print a sheet out with questions on mean, mode, and median and some "find the mean" problems.
OK, so mild surprise to me, he knows the terms and knows how he is supposed to calculate mean. But he has some problems wrong from misreading to mistranslating (thinking the problem had 5 rather than 4 items, etc.)
So, that is one of the acceleration problems. Mean, median, mode are math terms and calculating averages, not bad. Really, hardly more knowledge in most of K-5 math than rules in a game like Monopoly. But, there are a lot of secondary skills, heuristics, sanity checks, etc. that are supposed to develop through practice, play, and exposure to various problems and such.
From above, in each of DS's mistakes the mean value was outside the bounds. I pointed this out and we talked about sanity checks and rereading problems. So, 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.
