The problem which this paper addresses is the difficulty of knowing students in large diverse classes in pedagogically useful ways. The paper discusses how the phenomenographic methodology can be employed to address this problem. It describes how phenomenographic studies and their results can enable teachers to "know their students" at a collective level in terms of a set of qualitatively distinct idealised types rather than at a personal level of individuals with their particular characteristics, and demonstrates the pedagogical utility of this kind of knowing. The means used to describe the approach and to demonstrate its utility when teaching large classes is to present, as a case study, a phenomenographic investigation into the learning practices among students in a large, diverse cohort of entrants to an engineering programme in South Africa. General principles are drawn from the case study and are discussed as they apply to the teaching of large classes.