Map is not only the result of geospatial environment cognition, but also a tool for geospatial environment cognition. The new concept advocated by Constructivist cognitive theory is highly consistent with the concept of map service in the era of Internet plus space-time big data. This paper analyzes the geographic information transmission process from the perspective of constructivism, and constructs the geographic information transmission process model. Based on the traditional map cognitive process model, a map cognitive process model based on constructivism is constructed. According to the four elements of “situation, cooperation, communication and meaning construction” advocated by Constructivist cognitive theory, a map service function model based on constructivism is constructed.