Excellent post. I often wonder if anyone ever bothers to really understand how children learn. They are natural learners full of curiosity. It's when that natural interest in life around them is shut down, or worse, punished. The government now wants kids to start school at age four, when they have proven that programs like "Head Start" has no affect on how their grades are at high school graduation. Their brains aren't even fully developed until age five. I'm also against all the institutional type thinking. Sitting quietly at a desk being lectured to or standing in lines all day is contrary to a child's nature.
My boys were very active physically and it was hard for them to sit still. I talked to a retired teacher and she said jokingly, that boys shouldn't have to go to school until they are 12, because most of them are so active. My kids when they were toddlers watched Sesame Street and game shows. They would play around with their toys while I tried to get my morning chores, laundry etc done. Although a little afraid of "Count Dracula" my oldest would count along with the puppet. When he was about three, he would bring me pencil and paper to draw things for him. One time he wanted "three threes". I wrote down three number three numerals. He said no and yelled three threes. I tried three groups of three has marks. He got frustrated and stomped his feet crying "no...three threes". I couldn't understand what he wanted me to do and he was very upset at me. Finally I thought, no way, but, I wrote down the number 9. He smiled and nodded at me. I was floored that my three year old was thinking in terms of multiplication.