re: (Not Common Core)-- Why are they teaching math this way?

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You don't have an answer...figured that much.

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I do have an answer. Teach them 7+4=11 until they get it. I have no problems with offering them different tools to get there, but at the end of the day, they have to be able to answer the question, "What do you get if you add 7 and 4?"

It can be, "Oh, I know that 11 minus 4 = 7, so 7+4=11" - that's perfectly fine. But at the end of the day, single digit addition and multiplication, by rote, is the most efficient and effective path to doing more complicated mathematical functions.

I mean, we developed the atomic bomb and went to the moon with people educated like that - since we stopped doing that and started pussyfooting around in the classroom, promoting everybody, letting 1 + 1 = 3 if the child thinks that's the right answer - well, we just haven't achieved as much, as a nation, now have we?