There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not contain interactions among students and we discussed the possibility of improvement of the models for collaborative learning. [Funding for this paper was provided in part by KAKENHI from Japan Society for the Promotion of Science (JSPS). For the complete proceedings, "Proceedings of the International Association for Development of the Information Society (IADIS) International Conference on Cognition and Exploratory Learning in Digital Age (CELDA) (Madrid, Spain, October 19-21, 2012)," see ED542606.]