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Many kids also have the experience of being full of wonderful ideas, that when they try to share, go flat, because the agemates (and sometimes the Teacher) have no idea what they are talking about.

Yes, yes! This keeps happening to my son! Last year, he wanted to talk about infinity and a mathematical operation he invented called "zap". He says he invented zap to make an "easier kind of math". Examples: 2 zap 3 = 23, 4 zap 8 = 48. He even invented a symbol for zap--a little lightning bolt. He loves to talk about numbers as in "Mom! 10 is 2 and 3 and 2 and 3 because it's two 5's and 5 is 2 and 3 so 10-4 is 6 because 4 is two 2's and if you take them away two 3's are left and that makes 6." Other kids his age just kind of look at him blankly.

Cathy