This paper addresses a gap in our understanding of cogni-tion with external representations: what memory struc-tures are acquired and how they change during learning? The focus will be on line graphs. We adopt Representation Interpretive Structure Theory (RIST) and its modelling no-tation (RISN) as an approach to answer those questions. RIST is a schema theoretic account and RISN operational-izes its assumptions. Models for stages in the gradual ac-quisition of growing interpretive sophistication are built, from basic precursor components to advanced interpreta-tions. Learning mechanisms are proposed to explain the transition between the stages. During learning, the memory structures undergo localized incremental changes and more global radical restructuring of the networks.