Thank you so much, HK. Really helpful, and I (and, I'm sure, others) appreciate it! :-) The math is tricky, and your explanation is terrific.
#5 made me smile but also reflect on our B&M experience in a "fancy" school district, where the game was a little different: the school trumpeted how fabulous the curric was but omitted the substance. So the "three times a week of Mandarin instruction!" turned out to be an underpaid contract teacher who tried and failed to keep order in class and managed only to teach the kids (in three years) not much more than a Chinese song to sing for the parents at assemblies! Or the "enrichment" math program that involved insanely complicated crafts projects like hundreds of tesselations drawn with precision but without really explaining the math of it -- the kids were supposed to "intuit" that bit! :-)
