Several notions have been proposed to understand the specificity of schooling and its persistence across time and space, despite several attempts to reform it. In this article, the author analyses more closely the notions of the "grammar of schooling", "forme scolaire", and "school organisational culture". These notions have also been used to address the global expansion of schooling and the adoption of similar structures and visions, in a process coterminous with westernisation and colonialism. The author reads the three of them together and analyses with some detail what they say about schooling as well as some of their blind spots. She then presents two alternatives to what she perceives to be their shortcomings: first, a historical and anthropological approach to school culture; and second, Bruno Latour's notion of networks and assemblages. While the two of them are not exclusive of each other, they have tended to grow different intellectual projects that are discussed here. While acknowledging that theorising might be a risky project, the author argues that researchers have a lot to gain from navigating these turbulent waters, producing a grounded, local theory that illuminates the "more than one, less than many" configurations of schooling.