Technology-mediated interactions and datafication are increasingly central in contemporary social dynamics and institutions, including teaching and learning processes. In order to fully understand the complex entanglements of human and non-human actants that emerge in postdigital education, it is essential to imagine new methodological approaches that are sensitive to the multidimensional nature of education--as a socially and materially-situated phenomenon that increasingly takes place across distributed contexts. The overall goal of this paper is to propose and operationalise a new methodological approach for the study of technology in education. It draws on the notion of relational topologies to improve our understanding of educational settings and, ultimately, how learning unfolds. The proposed approach relies on a multi-paradigm enquiry strategy, based on the idea of using "topologies of digital data practices" in combination with the three dimensions that articulate design-for-learning processes according to the Activity-Centred Analysis and Design (ACAD) framework: epistemic, social and set designs. While the article focuses on presenting the elements of the approach from a theoretical perspective, we illustrate its application through the data collected in a small case study that will serve as a testbed. The topologies of relations we present in this article show uses of technology--as described by participants in their own learning experience--that involve different spaces, devices, and personal situations. In doing so, we reveal how humans and non-humans are entangled in hybrid, unstable and generative ways. The article concludes with some remarks on the value of the proposed approach for studying technology in education and its potential to explore the state-of-the-actual in this field, with the ultimate goal of helping inform educational research, practice and decision-making.