There is a technical distinction between human learning and human development. (For a more complete discussion, see Furth and Wachs, Thinking Goes To School, 1975, Oxford U. Press.) You can learn something without actually understanding what it means or how to use it (see examples below). Whereas, simply put, development refers to the full integration of a body of knowledge and its application, like an ability that can be applied in a wide variety of circumstances. Hence, we don’t actually learn how to walk—we develop the ability to walk; and once we develop walking, we can pretty much walk anywhere.
Similarly, babies develop language. They understand the concept—that certain sounds have specific meaning that can be communicated to other individuals—well before they learn what those sounds (words) actually are. We may teach a child any number of words—in fact, this is usually quite helpful. For example, a toddler says “abble,” and the parent says, “Yes! Apple!!” In this case, the child has “learned” that the name of the fruit is apple and yet is still in the process of “developing” the ability to say “apple” instead of “abble”.
So why don’t people learn calculus naturally? Because most of us do not develop the underlying schemas needed to make sense of the math we are supposedly being taught. Even algebra throws many people for a loop, because the system we have memorized (i.e., learned, not developed) is represented by numerals, and algebra replaces many of these numerals with letters. When we are then taught that ax means “a times x”, it is as if we have entered a whole new world, where none of the old rules apply. With time and patience, children can grasp these new concepts, but they can’t do it on someone else’s timetable, and many can’t follow along and simply give up.
Because they are in control, self-directed learners develop their understanding as they learn. Yes, they benefit from instruction (when they are open to it and are interested in what an instructor has to offer), but only when they have the underlying mechanisms for making sense of the new material. Otherwise, it is like giving a lecture in Russian to the average American adult: No matter how “smart” she is, if she doesn’t understand Russian, she’s not going to get much out of the lecture.