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I think you summed this up in one word: automaticity. We got to bolster their automaticity so that they don’t expend their cognitive energy on thinking how to do
this territory is moderated
The only way to get to automaticity is to drill, drill, and more drill. I get that about learning kanji and it applies to mathematics also in the grammar school levels. In Japan, I got to see a soraban school at work and it is drill and more drill but the kids knew how to use mental soraban by the time they were finished. Yep, automaticity!
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