i feel like they want them to be ready to enter 3rd grade in order for them to enter k one year early.
I totally feel your frustration. I remember virtually everyone I talked to about the possibility of my DD entering K early said something like "Well, just because she can read well doesn't mean that she's ready for K now" even when they knew nothing else about her abilities. I think the knee-jerk reaction of many school officials (but not all) is to say no to early entrance and to think that you're just another one of those parents who thinks their kid hung the moon.
But, I do have to say that, even though they don't expect a child who is wanting early entrance to K to have 3rd grade skills, they do generally expect them to have end-of-first grade skills pretty much across the board in all subjects. Their theory is that a child who is accelerated should be towards the top of the class into which they are accelerated so that they can continue to feel successful and not struggle at all. Otherwise, the argument generally goes, other forms of enrichment are generally sufficient. Just the messenger . . .
