Think WHO WANTS TO BE A MILLIONAIRE. The audience knows more than the contestant.

Or, as author James Surowiecki puts it, the many are smarter than the few :

• [Francis] Galton was a believer in the power of the elite, noting "the stupidity and wrong-headedness of many men and women being so great as to be scarcely credible." But at a fair, he noticed a wagering competition in which people bet on the weight of an ox. Eight hundred people participated; some were butchers and farmers, others just idle guessers.
  
  When Galton averaged the estimates, he expected the result to be way off. Instead, the crowd had come within one pound of the ox's weight.
  source: The Crowd is smarter than you think

• The same is true of jellybean contests, in which people try to guess how many jellybeans are in a jar. The collective guess is often closer than any individual determination.
  source: The Crowd is smarter than you think

• Linux, the open-source operating system created by Finnish programmer Linus Torvalds in 1991 but effectively owned by no one, is now the major rival to Microsoft Corp.'s (MSFT ) Windows. Independent computer programmers from around the world contribute to improving the operating system, and solving the problems that intrigue them, although Torvalds and his peers keep a tight rein on what changes are acceptable.
  source: Heeding the Herd Instinct
  

• Surowiecki [describes] the fascinating case of the May, 1968, disappearance of the submarine USS Scorpion on its way to Newport News, Va. The U.S. Navy had a general idea where the sub sank, but it was an area 20 miles wide and many thousands of feet deep. Naval officer John Craven hit upon a solution. He gathered a group of diverse experts and asked for their best guesses on why the sub ran into trouble, its speed as it fell to the ocean floor, the slant of its descent, and so on. Craven took all the speculations, ran them through a sophisticated mathematical formula, and ended up with the team's overall guesstimate. The Navy found the ship 220 yards from where Craven's group had predicted it would be, yet not one individual had picked that spot.
  source: Heeding the Herd Instinct
  

Together, we know more about teaching math to children--and teaching math to ourselves--than any one of us alone.

So consider yourself invited!

And if you have students or classes who'd like to start their own pages, we're looking forward to seeing them here.

-- CatherineJohnson - 18 Jul 2005

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