Group work and student collaboration during problem solving sessions are teaching methods which positively affect learning outcomes and socialisation. It is extremely complex to find a way of applying these methods to make them appropriate for and interesting to the new digital generation of students. This paper proposes a model which enables social network collaboration between primary school students within the system for mobile game-based learning of mathematics. It also suggests technology and proposes a general model which enables researchers to access anonymized data, teachers to keep track of student progress, and students to keep track of their own progress relative to other students, all at the same time. A microblogging social network service is integrated in the system in a way that enables sending messages without additional authentication and thus facilitates dynamics of the system. The proposed model enables mining of anonymized data streams originating from both the game and the social network. In this paper the model is used for the analysis of concepts which students most often publish, and for the analysis of their correlation with other activities within the system. Social network posts are analysed with the aim to detect students capable of taking advanced classes which cover more complex areas than the regular curriculum.