That fits with my non expert intuition. If you don't get the basics of arithmetic it is incredibly hard to grasp the idea of "equals" as a pivot point. Divisio

That fits with my non expert intuition. If you don't get the basics of arithmetic it is incredibly hard to grasp the idea of "equals" as a pivot point. Division by hand helps to give us a hint that numbers can be broken up into constituents and still be the same. You internalise a whole set of behaviours, typically via repetition, and it unlocks understanding beyond itself imo