This article considers relations between inheritance, disobedience and speculation in art practice and art education in schools and other sites of teaching and learning. In recent decades educational practices such locations have been subject to doctrinal cultures of audit, standardisation and competences, invoking what Michael Hampe terms the "homogenization of the interpretation of experience." In contrast the article advocates the idea of speculative pedagogies that remain open to the unknown potentialities of students' and teachers' learning encounters and invent a future when such a future, demands thought. Speculative practice and the idea of disobedience are elaborated through contemporary art practices, then applied to pedagogical contexts and processes of learning. Focusing upon the relevance of how a learning encounter matters for a student and the obligations required of a teacher, the article then considers an ethics and politics of pedagogical work through the idea of idiotic events and Isabelle Stengers' notion of the cosmopolitical proposal.