Individual intention is defined as the purpose to produce change by one's own agency and without counting with outside support of other people. By "intention", it is implied that the individual seeks to make a choice that will make a difference, whether good or bad.
Social function is the composite of individuals who get together for the purpose of accomplishing a common goal. This entails that all the people involved in a project will act as separate sub-systems which, working together, interact with each other and give ideas for assuring success. By "function", we refer to the manner in which one thing is accomplished through its dependency to something that will make it happen.
This being said, there is a complementarity between individual intention and social function in the field of education. The individual intention lies in the personal motivation and drive of the professional who aims to reach mastery of both content and pedagogy. Just because "the system" asks you to get a certificate, or an endorsement, should not be the only reason for a teacher to aim to become a whole professional at what he or she does.
The result of individual intention is, more often than not, that the organization becomes more solid, since all of its individual parts is functioning at their peak.
This is a good example: A teacher has been hired by an organization to train future ESL teachers. The individual intention, if well-founded, would make the teacher want to obtain every single resource available, and go beyond the call, to ensure that the other teachers are as solid and sure of what they are doing as she is.
The social function of the organization that hired the teacher is the provision of ESL teachers that are qualified and well-trained. Hence, the individual intention of the teacher in question has moved forward the social function of the organization by imparting what is most needed.