The aim of this chapter, which draws upon data from a design researchproject based on Davydov’s principles of learning activity, is to exemplify the func-tions learning models can have in visualising students’ algebraic thinking whenthey collectively discuss algebraic expressions. The data are comprised of video-taped research lessons in grades 1 and 5, respectively. The analysis indicates that thelearning models enhanced the students’ joint exploration of the idea behind algebraicexpressions and thus materialised their algebraic thinking in the whole-class discus-sions in three ways: (1) materialising an argument, (2) materialising a problem, and(3) materialising a collective memory.