Teaching mathematics to young children

It is my belief that facts are only memorized when there is a motivation to do so, and that by far the best motivation is relevance to something the individual cares about. Thus memorizing facts on their own is hard, but doing interesting problems which require those facts will lead to natural memorization through repetition.

Therefore I would recommend activities that require math but are not rote practice. For instance, dice games such as backgammon, yahtzee, and board games require the numbers up to 6 to be repeatedly added. Under this approach the child should progress from using the number line, to mentally visualizing a number line, to simply memorizing the sums and differences through natural repetition.

As a final comment, I would rather that a child laboriously compute solutions from first principles rather than progress too rapidly to memorization of results without understanding how they were obtained. In the first case they are much better equipped to handle problems that go beyond what they have previously encountered.