One of those little "why I homeschool" anecdotes. Or, why prime numbers are the unfairest numbers of all.

From Language Log, an anecdote in a post that's not about schooling, but about the cultural development of number words.  

(The boldface is mine; I just included a paragraph on either side to give a teeny bit of context for the writer's observation.)

... I'd like to point out that comparing exact quantities is only one aspect of the way that people "perceive exact quantities".  Once the "cognitive technology" of number is established, there are many other properties of particular exact quantities, or classes of exact quantities, that may become cognitively salient.

Once, a five-year-old of my acquaintance, stimulated by kindergarten exercises in counting and comparing, announced a discovery: there are a "fair numbers" and "unfair numbers". Fair numbers, he explained, are when if you have that many things, you can share them with a friend so that you each have the same. With unfair numbers, somebody always gets more. (This was not part of the lesson plan — in fact, I learned about it because his teacher perceived his enthusiasm for unscheduled discoveries, expressed in idiosyncratic terminology, as distracting and even disruptive.)

After you've understood something like the distinction between even and odd numbers, it seems to me that it becomes (to one degree or another) part of the way that you "perceive exact quantities"....

"Okay, Junior, now as an exercise, I want you to extend the property of "fairness" to the general case of n friends..."