I'm thinking a lot about this history of math class
Polyphemus, the cyclops in the Odyssey, written maybe 3000 years ago, keeps track of his sheep by putting a pebble in a bowl for every sheep. Why not count them? Because he lacked the terms for enumeration. So, he uses a pebble to stand for each sheep.
That seems simplistic, silly. But, in fact, remembering what numbers are, where they come from historically, what they are not, and to consider how mathematics was constructed historically is not only interesting but might help you do math better.
In the 19th century mathematicians were trying to understand infinity. Polyphemus' technique, without the terms "one two three four," turns out to be useful for understanding why Euclid's axiom that the whole is greater than the sum of it's parts is not actually true.
There is so much to cover in this class this fall, I'm very excited. Pineapples, hungry mice, clay balls, dice, the lines on your hand, flowers, throwing popcorn... Should be fun.
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