This paper examines how learners interact with variations in representations presented in a computer environment. In particular, it explores how analysis of learning in terms of the notion of strategic theories can provide insight into learners’ cognitive processes when using such representations. The study reported here looked at problem-solving using concurrent mathematical representations (numbers, graphs, algebra). For each task, the set of representations was presented in one of three instantiations. These were: Static (non-moving, non-changing, non-interactive); Dynamic (animated, following keyboard inputs); and Interactive (directly manipulable using a mouse). A variety of data was collected from 18 participants: learners’ shifts in attention were recorded using an unobtrusive eye-tracking device and screen capture software; keyboard and mouse actions were logged automatically; utterances and gestures were video recorded; and notes and sketches were recorded in real-time. This rich data was analysed in an integrated way, with the aim of characterising learners’ strategies. The results show that participants tend to use multiple strategies over the course of task completion, and that the number and type of representation influence the strategies used. It is argued that this form of strategic analysis offers a systematic way of understanding learning journeys.