To make an analogy, your idea is that a runner needs to learn stride techniques, physics and biology first and doing base physical training without understandin

To make an analogy, your idea is that a runner needs to learn stride techniques, physics and biology first and doing base physical training without understanding these is pointless. This does not work in athletics, nor does it work in math. Somebody who cannot even run 100m is not going to benefit from understanding how carbs convert to ATP and how that ATP is consumed to fire muscles or how muscles and ligaments in the legs can store and release energy or how drag slows you down etc. These are all good to know for an athlete to improve further, but not for somebody who just started running. And people had been evolving to run for millions of years! People have not evolved for math. Their innate math ability is similar to falling after making few steps in regards of running analogy. They need a whole lot of boring and painful base training to be any good. What we get with "but they need to understand!" is people who can barely walk 1km without losing their breath insisting that when children get fun carbon shoes and tasty carb gels they will run much better than children who are made to run laps until they drop.