The 2015-2016 South African higher education students' movement proved historical for our country in bringing to our dinner tables: issues of higher education transformation and decolonisation; institutional culture(s); curriculum reform; the need to foreground and make inclusive assessment in education; the coloniality in our knowledge production, and more. Influenced by the emergence of the student movements and the critique they have brought to South African higher education, we bring to the fore the often silent critical reflections on the purposes of higher education in general, and in South Africa especially, as they relate to teaching and learning. We propose that the purposes of higher education in relation to teaching and learning ought to respond to (1) context, (2) democratic difference, and (3) cosmopolitan perspectives. We argue that discourses, phases and logics about South African higher education have tended to disregard and, at times, blur the context and differences as well as cosmopolitan perspectives. Using the notion of Ubuntu-Currere, we re-imagine how teaching and learning could respond to context, difference and cosmopolitanism with examples from the South African higher education experience.