Becoming-topologies of education: deformations, networks and the database effect

Abstract

(national, regional, school, classroom) forces that operate through the 'system'. While these forces change, they work through a discursivity that produces disciplinary affects, but in a different way. This new-old disciplinarity, or 'database effect', is here represented through a topological approach because of its utility for conceiving education in an increasingly networked world.The increasing utility of topological approaches to understanding social phenomena was clearly demonstrated in a recent double-issue of Theory, Culture & Society. For its editors, attempts to understand the emerging social must engage with topology as "surfaces that are spaces in themselves are not only self-organizing and emergent, but their self-organization brings being and knowing, ontology and epistemology, into new kinds of relations" (Lury, Parisi, & Terranova, 2012, p. 20). Using a mathematical construct to conceptualize social spaces, which might otherwise be understood discursively, may appear unusual. The metaphysics of mathematics, however, has long engaged with the social, for example in Leibniz's concept of incompossibility (Deleuze, 2006), Hacking's (1990) theorisation of statistics, governance and normalcy and Badiou's (2005) argument that mathematics is ontological and has always been significant for understanding multiplicity, continuity and the changes of forms and figures.While this mathematical turn is important, particularly in the age of big data and the consequent impact of datafication on social ontologies and professional/personal subjectivities, the use of topology as a heuristic for articulating the becoming-self in education surfaces has only recently been used in wider education analysis (Lingard & Sellar, 2013;de Freitas, 2014). Using topology to understand cultures and societies is not new, since Euler's solution to the problem of the 7 Bridges of Konigsberg, theorists have been intrigued by the potential of topology to tell us something about the ways that environments, people and customs/cultures connect in productive ways. For example, Lacan was absorbed by the potential for topological figures to "theorise the relationship of scientific 1 We are very grateful to Sam Sellar and Andrew Murphie for their helpful feedback and suggestions on early drafts of this paper. We would also like to thank the reviewers for their helpful comments.

The power of relation-making: insights into the production and operation of digital school performance platforms in the US

“…tracking how often a teacher has used which parts of the platform and how long he or she stayed on a particular page). In other words, here the platforms start to relationally affectand thus discipline (Thompson & Cook, 2015)more and more teaching and learning settings, which to a great extent still operate within school buildings, physical classrooms, and in-person social relations, but become increasingly pervaded by the platform's logic, norms and values.…”

PISA for Schools: Topological Rationality and New Spaces of the OECD’s Global Educational Governance

“…In particular, we consider the identification of these discontinuities between participating schools and highperforming systems as providing the key impetus for local reform through system-to-school learning from main PISA (PISA to Schools). In this way, we see PISA for Schools reflecting the wider enfolding of global tests and discourses into local policies and policy-making processes (Thompson and Cook 2014), where the language of "elsewhere" is used to justify local reform. Our topological and relational analysis also emphasizes the importance of acknowledging the spatial as a lens for understanding education policymaking processes within the field of comparative education, rather than merely providing fixed territorial units of analysis centered on the nationstate.…”

“…In the case of PISA for Schools and other large-scale assessments that facilitate global comparisons of educational performance, we argue that these spaces are produced through a form of topological rationality. We draw on the argument of Lury and colleagues (2012) that a proliferation of practices-including measurement, comparison, ranking, and so on-is creating new connections between what can be measured and compared, producing a space of commensurability that relates each system (or indeed school) to others (see Thompson and Cook 2014). In this way, topological spaces emerge as "the site[s] of situated practices" (Amin 2002, 391), where distance and proximity come to be defined through mutable relations that are not fixed by external reference to territory, borders, or scales.…”

Emerging data infrastructures and the new topologies of education policy

“…Topology is primarily a mathematical concept that emerged in response to 'the perceived rigidities of geometric shapes and surfaces that take their cue from the clear-cut coordinates of Euclidean space' (Allen, 2011: 285). In education and geography, recent work on policy engages with mathematical or cultural topologies (e.g., Thompson and Cook, 2014), with a particular focus on analysing new forms of education policy governance emerging from the prevalence of data use across multiple scales (Lewis, Sellar and Lingard, 2016). Some work has looked to show how topology can supplement topographical approaches to understanding policy mobility by combining a focus on the materiality of, and interconnections between, places, and the spaces that emerge in the processes of measurement and calculation (Prince, 2016).…”