It starts very early with things like mental calculus, where you try to get kids to compute things like 99 times 101, 98 times 102, finding tricks and rules to make the computation "easier". We could instead teach them to follow mentally some multiplication algorithm, but instead we try to promote some exploration and looking for pattern.
In chess, similarly you can train for puzzle to develop some vision without having to calculate, like multiplication table.
The education system must also take care not to prevent it from adapting to further changes by being too rigid. If the cat can't get out of the box, the box won't ever grow bigger.
But you can't have too many cats getting out, or you'll soon have an empty box and hangry cats.
I don't know what the goals should be, far from me the idea of proposing to teach, I only show paths that can be taken.