The subject must be active, must transform things and find the structure of his own actions on the objects. One is acting on material things. But the other means doing things in social collaboration, in a group effort. This leads to a critical frame of mind, where children must communicate with each other. This is an essential factor in intellectual development.
Cooperation is indeed cooperation.
A characteristic phenomenon in intellectual difficulties of pre-school children is that they have difficulty conceiving of any point of view other than their own. The best idea I have heard from a pedagog at the International Bureau of Education in Geneva was made by a Canadian. The teacher must provide the instruments which the children can use to decide things by themselves. Children themselves must verify, experimentally in physics, deductively in mathematics. One participant asked what Piaget thought of having children of different ages in a class together.