One day when my mother was busy I remember asking (since I could reach the wash basin by standing on the bathroom stool) whether I might get a drink from the toilet. My mother was horrified. I don't know if either of us ever realized that I used 'toilet' for the whole bathroom, as in 'go to the toilet', but for quite a long time I refused to fill a cup for myself at the wash basin.
Quite different. One day, when we were playing in the sandpile, and my mother was taking in dry laundry, at the time as I was learning letters (well before I went to school), I kept naming strings of letters and asking her what they spelled. "No, that's not a word." But when I said, does A S S spell 'ass', she told me not to spell it or to say it. Can I have been quite ignorant? True, it is very easy phonetics.
One day, at the grandparents, I asked my grandfather for an apple. He cut one in two, peeled and cored one piece, and said "Here's a half apple". Then he cut the second piece in two, and said "Here's a quarter apple for you and a quarter for me." The next day we got to sixteenths, which was about as far as my numbers went, except for just reciting by rote, which is merely preparatory. That year when I was four, at Thanksgiving we had the china with six bundles of flowers around the rim. While waiting my turn to be served, I kept looking at them and heard myself say "Three is six in half, and two is six in threes", to myself, not expecting anyone to notice. But they did notice. They didn't know what my grandfather had been entertaining me with (one advantage of being a first grandchild or an only child). Since then I have confirmed that almost any child between three and six can pick up the same insight. I never could figure out why the teacher taught the rudiments of fractions year after year.
I thought of apples and flowers again much later when I learned that early civilizations had worked duodecimally, rather than decimally.
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