I wouldn't say my nephews are geniuses. But boy! They are smart for their age! Today, the older one enters Grade One. I look back at my own first day of school (I didn't go to any pre- and kinder school.), and I don't think I knew then a quarter of what my nephews know now.
My Grade One nephew can read, can count, can argue, can be fierce in street games, can play strategy games like Cut the Rope, Push Cars, and Lorax, never mind that he scores more than 1.5 million in Temple Run.
My three-year old incoming pre-schooler can count, knows all the channels in cable as the TV remote custodian, "reads" interactive books, creates folders in iPad and re-arranges icons in and out of folders (And he learned it on his own), plays "Mahjong" better than my sister (He will hate any teacher who will give "match/ put similar things together" tests.). He knows "download," "delete," "complete," "game over," "next level," "internet," "wifi"...
I can only hope that the school will provide the right environment where they can acquire skills and knowledge as they do at home. I don't expect that they get brilliant teachers, only patient and caring ones who will teach only what they know to be 100% accurate and right.
I hope their learning at home will not be stunted by their going to school for some formal education.