[wcarey]

The approach you describe definitely does not work for all children. The vast majority (that I've taught) are better served by a scaffold of increasingly complex metaphors and definitions. The fact that the metaphor of repeated addition wears thin actually highlights the idea that different sets of mathematical objects have different operators for most students in a way that just telling them that ahead of time does not.

The changing of the rules is good preparation for scientific study where our understanding actually changes over time and we have to internalize new models regularly. I taught my chemistry students that quarks only combine in pairs or triplets, until one year Fermilab released evidence that quarks combine in quartets and quintets while I was teaching the unit. How could I avoid telling my students that what I'd taught them before was incorrect? Literally no one knew. So the practice of revising our ideas has utility.