Archimedes, the famous Greek scholar who lived in Syracuse, was frustrated by a problem the king had given him. The king suspected his goldsmith was cheating him; the king had given him gold to fashion a crown, and he thought the goldsmith was mixing in cheap metals. Archimedes knew that he had to measure the volume of the crown to solve this problem, but it was an irregular shape. He went to relax and take a bath and think.
When he sat down in his bathtub, he noticed that the water level rose. The volume of water displaced, which could easily be measured, was exactly equal to the volume of his irregularly shaped body.
“Eureka!” He shouted, hopping out of his bath and running through the streets of Syracuse jubilant and naked. We are all familiar with this feeling, and call it many different things: “moment of clarity,” “aha feeling,” “light bulb moment,” or “epiphany.”
Paul Lockhart, in his fantastic A Mathematician’s Lament, talks about how math is actually a creative, artistic discipline; mathematicians do math because it is a pleasure. But the way we teach math kills that pleasure for the vast majority of students. Most people who “love” math love that “aha!” they get when they solve a difficult problem.
This feeling goes way beyond math and science. People will remember forever the moments they make deep insights about themselves or about people in their lives. Most entrepreneurs can describe a moment of clarity when they conceived their business idea.
There is no general agreement among psychologists as to what is going on in the brain during these moments. There seems to be a common process: a person is frustrated by a problem, tries several different solutions and fails and then takes a break. Eventually, in an unpredictable way, he is hit with the answer.
Two aspects of this process are important to education: one, it is pleasurable. Finding problems pleasurable will encourage students to be independent. Two, students remember the insight far longer when they discover it themselves.
It is the unpredictability of the process that makes it difficult for the classroom. The attached lesson plan tries to cultivate the “eureka” feeling. Let me know how you like it.
I'm an entrepreneur and I teach math, history, economics, and fitness. I'm looking for arguments.