“... to children who don’t reflexively know the basics,...”
Exactly! The basics become the mental equivalent of ‘muscle memory and as such form the basis of more complex calculations.
Have you ever noticed how fast the guy at the deli (usually the owner) used to provide change WITHOUT using the change function built into the machine? Back in the day, BEFORE the cash drawer finished sliding open he’d broken down the change to the number of even units and then the fraction then dug out the fraction and then the bills (usually in that order). He sure as heck wasn’t parading ranks of numbers around in his head.
I briefly worked at a roadside hot dog and burger joint called Callahan’s Road Stand in New Jersey (Joisy). Employees stood inside what amounted to a horseshoe-type counter area with customers crammed in on all sides calling out their orders - 2 cheeseburgers, 1 with onions, 3 dogs, fries, 3 cokes - 2 large, 1 small, etc. Employees were expected EXPECTED to be able to “ring all this up” in their heads, take the correct money and return the correct change. All employees rang up their sales (just the total) on a single cash register. It was fast, fast fast and the lunch rush could last up to 2 - 2 1/2 hours.
No sweat...