Stacy Transancos has a lovely new piece up on her blog "Accepting Abundance", entitled "Little Aristotles".
Her little Aristotle can, in a couple of years, move up to a proof of the isoperimetric theorem.
Mom can take some pennies, and a length of string.
Mom can ask her little Aristotle to find a way to enclose the most pennies inside the string.
Won't take long for the little Aristotle to have proven the isoperimetric theorem in a physical way that the mere memorization of a mathematical formula could never do.
Then- and I would argue only then- will little Aristotle be properly prepared to tackle, later on, the formal proof of what she has already obtained, on her own, as a matter of true knowledge.