This paper contains a discussion of how the concept of critical aspects and the principle of compositionality can provide a powerful tool to analyse and understand the communications that occur in the classroom. It is grounded in data collected in a longitudinal study. The content chosen is algebra. It is argued that the critical aspects and the principle of compositionality should be considered as a methodological principle that describes how communication in the classroom should be designed. Here, I present the power of using variation theory whose main purpose is to generate an understanding of critical aspects and compositionality in practice.