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

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So when yours was given questions like Q1 in the first post of this thread, what do his teacher mean by 'double facts'?

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It meant this...

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They simply use doubles as an easy frame of reference, as most people intuitively do memorize those. At no point was he ever asked to memorize doubles.

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Both of mine were given complete units on visualizing but then completely memorizing double facts, 5 facts, and 10 facts. Then, as you say, those memorized facts become the framework for double -1 etc...

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Mine were not...which was my point. Everyone is/was not being taught to memorize these.

He learned to count by 5's and 10, but I wouldn't call it memorization.

This is actually one of those things which makes sense intuitively to me. If you already, likely, know that 8+8=16 than quickly pulling that 8+9=17 because 8+8=16+1=17 makes perfect sense. Doesn't it? Or are you advocating memorizing every addition fact from 1+1 to...I'm not sure what?