In this theoretical article, we propose a conceptualisation of noticing, drawing on our enactivist perspective, which takes account of what is now known about human cognition, and from which we draw out implications for how noticing develops. We review past work on mathematics teacher noticing and note the dominance of a paradigm of taking noticing to comprise: attending, interpreting, and deciding. We argue this framework draws from a computing model of mind, which is outdated. We use a vignette, from a lesson and stimulated recall interview, to elaborate an alternative. We suggest that noticing is: embodied; layered; mutual; and meta. We then further exemplify these characteristics by showing how they can be used to analyse a vignette from a teacher discussion of a video recording (of the first vignette). From these ideas, we then consider how it is possible to educate teacher noticing, and how it can develop through a focus on critical events.