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  1. I have my third grade math book from the nineties downstairs. Maybe I'll look this up.
  2. I think the problem with EM is that it's a huge math program even without throwing in "btw, do all the math facts." And a lot of it advised drill via games, which is tricky to organise with one kid, let alone thirty. AFAIK Math Makes Sense, our Canadian folly, doesn't include drill.
  3. I may be coming at this from a very place-specific situation. Right now we've gone head-over-heals into conceptual math in my province (and several other provinces) and we're trying to pull back. So most of the people that I meet day-to-day are suffering because the teacher thinks that multiplication tables are optional niceties that parents might or might not drill at home, not because they didn't get the concept explained. They probably did get the concept explained, but they're so underwater they can't internalise it. http://blog.scs.sk.ca/schmitz/math%20makes%20sense%205.pdf Think
  4. Not taking sides on what children do or do not do in the grammar stage (because I don't care), but Euclid &c. were intended to be studied later on in education, and thus I don't think they make your point here. I think knowing that 4*6 is itself useful, in addition to understanding that multiplication is commutative, but ymmv.
  5. I strongly disagree that everything understood will be retained, although it may be true for people who are very gifted in a given area. The best results in educational studies result from good explanation followed up by significant targeted practice. Countries that generated these conceptual math programs (Singapore, Japan, Russia) supplement them with drill, often in amounts that would make Americans weak in the knees. My own kids do Singapore, but my daughter is still not particularly strong in math. I think people overestimate the extent to which the texts make a difference. I beli
  6. I grew up with traditional math and understood all this stuff. Maybe my mother was very bright. Conceptual math makes explicit what traditional math may not. Some people don't need explicit, and skilled teachers have always demonstrated the rationale behind the procedure. Unfortunately elementary school teachers are frequently weak on math. I'm not at all sure that a deep understanding of arithmetic is necessary for higher math. In general I think people fail at math for want of practice, not for want of explanation.
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