Economic and Game Theory
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I want to make the hypothesis that the choices made during student collaborations in classrooms occur in a manner that is similar to the Prisonerís Dilemma. For instance, when students are collaborating about an object (e.g. a lesson related to a curriculum standard or teaching objective), the resultants are:
Object non Object
Collaboration 5, 5 10, 0
Collaboration 0, 10 1, 1
For the sake of this example the total utility (e.g. a collaborative achievement score) of the collaborative effort is 10 units. If the two students collaborating on an object were placed in different rooms to explain their results and each did so correctly, then the utility value is equally shared (5,5). If neither student can explain the results of their collaborative effort in terms of the curriculum object the assumption is made that no collaboration occurred in the direction of the curriculum objective. Thus the utility value is 1,1 because the two students did collaborate (though not in the direction of the curriculum objective, thereby receiving the least amount of points available). Finally, for values of 0,10 and 10,0 one student did all the work and no collaboration occurred - only one student could explain.
This matrix suggests that students would always rather collaborate (in some fashion) and receive a 5 or a 1 as a collaborative achievement score rather than risk receiving a 0 for no collaboration.