Today we were told about the early morning fish markets in Japan. Those bidding in the tuna auction have to decide what is on the inside of the tuna before it is cut open. All they have to go by is as cross section where the tail is cut off. Those with a good tuna eye are able to pick the good fish and so end up making more money. Those without a good eye for what is on the inside don't get the money.
What's this got to do with math education? It goes back to the idea of using problem solving to teach mathematics. In order to use a problem in this way you must be able to see what math can be learned, not just what math can be used to solve it. Our ability to distinguish between these two ideas will determine our success when using problem solving in such a powerful way. This ability is a talent. For the sake of my students I hope this talent can be learned.
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