I carry a large bitter chip on my shoulder because my sight division got broke by "showing your work" for Long Division in like 4th grade. Maybe a year or two later I would've understood how I did it, and it might've survived that crucible.
That sucks.
I also remember things I've read here and elsewhere about students graduating from high school with shaky understandings at best of such important topics as division, the meaning of an equals sign, etc. I also credit that focusing on rote teaching of an involved process like long division might confuse and dishearten students, and get in the way of learning the underlying concepts (besides potentially missing out on a chance to develop problem-solving skills). I get it.
Still, looking at the videos on the following page, I think DS would literally
scream if he were forced to sit through something similar:
http://investigations.terc.edu/curriculum_clrm/earlyalgebra/earlyalgebra.cfmNow, it might well be that the general didactic approach used by these teachers would work fine for him, just that he'd have to be able to go at a faster pace, and of course not have to learn what he already knew that way. The students do seem engaged well enough in those short videos.
ETA: I think that the last video on this page also would cause extreme frustration for DS:
http://investigations.terc.edu/curriculum_clrm/mathpracticestandards.cfmI might be missing the point of it, but I think the approach in this particular video is garbage. I don't think these students are becoming stronger mathematical thinkers in any substantial way, or even really getting better at multiplication here. I think it would be demeaning for a lot of students to be forced to verbalize a lot of this extremely basic stuff, such as that 30 is 3 10s. I think that that particular video mainly shows wasted instructional time.
But that's not an indictment of the entire curriculum, just an example of one way that it might be implemented poorly. Actually, now that I think about it, this sort of approach might make it difficult to implement in-class enrichment for the brighter students. It's so... plodding, and the students seem to be expected to plod together. But in a classroom filled with students with a similar pace of learning, even that might not be an issue.
