Learning analytics systems often use interactive visualisations to display information. Interactivity is typically used by visualisation designers to reduce cognitive load for users. However, our research suggests that interactivity holds significant value beyond the reduction of cognitive load. Informed by theories about meaning, perception and experience, we propose that interactive visualisations promote emergent meaning-making processes which should be accounted for in the design of interactive learning analytics visualisations. We present findings from a qualitative study of four teachers engaging with interactive visualisations in an Australian university. The study used a think-a-loud protocol and a semi-structured interview which were coded according to theory-informed constructs of dimensions of meaning and interaction opportunities. Our findings suggest that interactive visualisations that had been designed with regard to meaning-making stimulated users to engage more deeply with the data and explore it at different resolutions, from overview to detail. The interactive visualisations afforded more opportunities for users to gain understanding and insights they found meaningful. While this is a small study, we argue that it opens up promising avenues for further investigation; provides a practical approach to gather further useful data about interactivity and meaning-making; and suggests new principles that may be helpful for designers of interactive learning analytics visualisations.