Similar teaching is needed for students. They should be taught to work together and help each other. For, in another associated file, I discuss "Teach Web Workers", which is cooperative
working, in contrast to the old hierachical style of working.
The hierarchical style is TRIBAL, long "out-of-step" with our TECHNOLOGICAL SOCIETY. This has been paralleled by COMPETITIVE SPORTS.
Mathematicians have useful language for this in a vast field known as "game theory". A "zero-sum game" is a game or activity in which one person or one "side"or team must LOSE in order that the other CAN WIN -- the WIN and LOSS CANCELLING OUT. But mathematicians also speak of "nonzero-sum games" in which more than "one player can win".
Now, all of the major religions teach "nonzero-sum" attainment of "heaven" or whatever. Democracy
exploits a similar notion. And Capitalism in a Market Economy exploits a similar notion. And a recent book, Nonzero Sum, The Logic of Destiny, by xxx xxx, produces considerable evidence that "this is the way of Evolution". (The baloney about "Survival of the Fittest" did not derive from the biologists and mathematical evolutionists who have developed the field -- but from a philosopher, Herbert Spencer, founder of "The Liberatarian Movement".) So the most important "forces" of our Society differ markedly with the zero-sum impetus of Sports and hierarchical workforces.
The new business and production style is the "web", wherein worker-power derives from connections to others who provide information and assistance, while disseminating and advancing the worker's ideas and achievements. (x-General xx xx, Commandant of The Marines has intorduced it there!) Students need to prepare for this, which may be widespread by the time many arrive in "the workforce".
However, many will raise another objection: that this could allow "cheating" on test. I faced that problem 45 years ago. My solution: Every student receives a different test. (I discuss this, and related topics, ONLINE in blakpage.htm.)
Once, at The University of Maine at Orono, I conducted a Statistical Final for 123 students and each student received a different test!
And I did this on an old-fashioned typewriter. It would be a cinch with computers and existing software.
There's another good reason for doing this. I don't want students to believe that "mathematics is written in stone". It's the PATTERN of the PROBLEM that's critical -- not the particular language used to convey it. When my students compared their test papers later -- with different numbers and other attirbutes -- they had to realize this.
So this disposes of the two main arguments against "ensemble playing" by students in the learning process.
FULFILL BY FILLING SOCIETY'S NEEDS! Happy teaching!