The more personal the competition, the more it affects the learning. The best competition is with oneself. More difficult tasks improve through cooperation. Students learn a great deal from each other. They learn more rapidly from familiar peers than from those who are strangers.
Group work improves quality rather than quantity.
The gain in the group is only in relation to the interaction that goes on. If the group is working as individuals, there is little gain. Groups of more than 5 often increase stratification to the point where the problems outweigh the advantages. There is a general level of complexity best for each learner, depending on age, intelligence, and purpose in learning. Each person has a relatively fixed normal memory span.