This chapter focuses on an inferential view on elaborating concepts in mathematics classrooms. A framework is going to be presented and used, which helps to analyse and to reflect on the processes of teaching and learning mathematical concepts. The framework is based on Wittgenstein"s theory of language-games and especially its core, the primacy of the use of words. Concerning the theory of inferentialism by Robert Brandom, the inferential use of words in language-games can be regarded as an indicator of the understanding of a concept. Together, the theoretical framework combines the role of judgements and their connections via rules in inferences in order to describe processes of concept formation.