That is the exciting, interesting thing, but you have got to learn this boring gradeschool maths first. For instance, if they had considered this important, and, say, found a graduate student to come in to the school to talk to the children for a few hours a week, then they would have been able to do without formal instruction, and the children would have learned even more. Here you are asserting the truth of the proposition we are trying to establish. It is that that would have made them learn more. At first, a baby's primary task is to interpret the sensory chaos that surrounds him.
Eyes focus, brain begins to hear sounds, and then to break sounds into words.
Words become associated with things and with concepts. The examples you give here are examples of actual theories being different, not of differences in the way the child learns. Although different theories are needed, the logic of scientific discovery is the same for all those theories. The substantive theories change, but the nature of learning must be the same for everything. There is nothing that hangs on that question about what one should learn first, unless you think that the children will make the wrong decision about what to learn first.