Identifying local proof ‘modules’ during proving

Given that understanding a proof entails students breaking the proof into components or modules and then specifying the logical relationship between each of the modules, in this paper we focus on what proof modules can be identified during the process of learning deductive proving in school geometry. Through an analysis of observations of grade 8 geometry lessons, and corresponding to three level of understanding characterised as elemental, relational, and holistic, we identified three structure ‘modules’: 1) vague ‘chunks’ of propositions, 2) small networks with universal and singular propositions by universal instantiations, and 3) series of small networks.