 Finally, imagine an effective pedagogy for teaching arithmetic to children is known and we wish to introduce children to cardinal arithmetic. A reasonable start on a prescriptive theory for cardinal arithmetic for children might be to adapt as much of the successful pedagogy for full arithmetic as possible while anticipating that some of those methods will not survive the change in normative standards from Peano to (say) ZFC+. Some of those differences can be seen as a direct consequence of the change from one standard to another, while other differences may arise unexpectedly from the observed interplay between the change in task, that is, from performing full arithmetic to performing cardinal arithmetic, and the psychological capabilities of children to perform each task.