When I started teaching Younger Daughter the times tables, she protested that she already knew them -- at least for 2, 3, 4, and 5 -- because she had been taught them at school. It turns out that what she knew is "skip counting" -- that is, "2, 4, 6, 8, ..." (Back in my day, when we weren't dying of the bubonic plague, we called this "counting by twos.") But if you asked Younger Daughter what 2 x 3 is, she had to think about it for a while, and the answer she came up with might or might not be correct. (She's getting better now, after a great deal of work on both of our parts.)
There's nothing wrong with skip counting, and it's a reasonable first step toward learning multiplication. This is typical of the new "fuzzy math" curricula (Younger Daughter's school uses "TERC Investigations") -- they include some reasonable first steps, but they don't follow through and actually teach the skills and facts you need to know.
The first unrelated-to-me kid that I tutored had a similar problem with adding fractions. I was impressed when she knew that 1/2 + 1/4 is 3/4. When I asked her how she knew this, she drew a little pie illustration. Again, this is a reasonable first step. But when I asked her what 2/50 + 1/100 was, she was completely stumped. That's because Trailblazers doesn't follow through and actually teach the algorithm for adding fractions.
Feh! The bad news is that the district of Upper Tax Bracket only adopted TERC Investigations a couple of years ago -- it'll take time for any kind of momentum to build against it. In the meantime, I'm teaching Younger Daughter math at home.
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