Digital platforms have become central to interaction and participation in contemporary societies. New forms of 'platformized education' are rapidly proliferating across education systems, bringing logics of datafication, automation, surveillance, and interoperability into digitally mediated pedagogies. This article presents a conceptual framework and an original analysis of Google Classroom as an infrastructure for pedagogy. Its aim is to establish how Google configures new forms of pedagogic participation according to platform logics, concentrating on the cross-platform interoperability made possible by application programming interfaces (APIs). The analysis focuses on three components of the Google Classroom infrastructure and its configuration of pedagogic dynamics: Google as platform proprietor, setting the 'rules' of participation; the API which permits third-party integrations and data interoperability, thereby introducing automation and surveillance into pedagogic practices; and the emergence of new 'divisions of labour', as the working practices of school system administrators, teachers and guardians are shaped by the integrated infrastructure, while automated AI processes undertake the 'reverse pedagogy' of learning insights from the extraction of digital data. The article concludes with critical legal and practical ramifications of platform operators such as Google participating in education.