A study of the Mathematics teacher?s professional knowledge, of the concept of function, is presented. The study accepts that the relation personal significance, between subject - object, is mediated by the institutional significance. The case study was carried out with a group of seven Middle School Mathematics teachers who had recently participated in an in service training program on the topic. The results show the complex relationships, with respect to the function object, between personal significance and the institutional significance developed throughout the in service program, and proves that the possibility of change in the professional knowledge of a Middle School Mathematics teachers depends on the changes in the institutional conception about Mathematics and its didactics.