This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.

Video data has now become the most common form of data for educational researchers studying classroom interaction and school culture. Software protocols for analysing vast archives of video data are deployed regularly, allowing researchers to annotate, code and sort images. These protocols are often applied by researchers without reflection or reference to the extensive philosophical work in film and media studies. Without exception, this research treats the video image as movement-image or picture, a recording of ‘raw data’, indexical of a (...) given time-space relationship. In this article I situate this kind of research within the history of scientific cinema, drawing on Deleuze's books on cinema, as well as his ideas on colour and figure from The Logic of Sensation, to propose an alternative way of analysing video data. One of the central claims of Deleuze in Cinema 2 is that the time-image reconfigures bodies as expressions of force – the body becomes a ‘shock of forces’. I argue that such an approach allows us to study the student body as less a phenomenological organism with built-in ‘I can’ cognitive and motor capacities, and more an indeterminate crystalline contraction and expansion of intensity. I present an example of how to study classroom video data as time-image, and explore the implications of such work for education research. (shrink)

Thinking with Spinoza about education involves thinking with and beyond his authored texts, situating his work within the tradition of Western thought, and exploring his contribution to the philoso...

The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question ofcommunication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching and learning. Moreover, the nature ofcommunication in mathematics classrooms remains highlyelusive and problematic, due in part to the distinct relationship the discipline has with verbal language and (...) thought. I first discuss current attempts to better address the embodied nature ofcommunication in mathematics classrooms, and argue that these remain overly logo-centric and language-centric in their conception of thinking. I then show how the work of Deleuze and Guattari on thought as a radical disruptive event can be used effectively to critique current pedagogical practices that privilege a narrow conception of communication in the classroom. I examine a set of exemplary classroom videos used in mathematics teacher education to argue that the current approach fails to honor the highly creative and disruptive nature ofthinking. (shrink)

Using the work of philosopher Henri Bergson to examine the nature of movement and memory, this article contributes to recent research on the role of the body in learning mathematics. Our aim in this paper is to introduce the ideas of Bergson and to show how these ideas shed light on mathematics classroom activity. Bergson’s monist philosophy provides a framework for understanding the materiality of both bodies and mathematical concepts. We discuss two case studies of classrooms to show how the (...) mathematical concepts of number and function are themselves mobile and full of potentiality, open to deformation and the remapping of the possible. Bergson helps us look differently at mathematical activity in the classroom, not as a closed set of distinct interacting bodies groping after abstract concepts, but as a dynamic relational assemblage. (shrink)

In this essay Elizabeth de Freitas follows Tim Ingold's groundbreaking anthropological work on lines and their cultural and material significance to argue that the line is the engine of theory, be it the drawn line of inscription or mathematical measure, the exclusionary line of delineation, or the undulating generative line of flight. De Freitas focuses on contemporary theories of perception that deploy the line — and mobilize the force of theory — so as to encode and reconfigure the student's body. (...) She draws on the work of Gilles Deleuze to develop a topological approach to the line, and argues that such an approach aligns with current philosophical approaches to social interaction that might be termed “topo-philosophy.”. (shrink)

Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, (...) devoted to exploring the ontology of mathematics as it plays out in different contexts. This book will appeal to scholars who are interested in particular mathematical habits - creative diagramming, structural mappings, material agency, interdisciplinary coverings - that shed light on both mathematics and other disciplines. Chapters are also relevant to social sciences and humanities scholars, as each offers philosophical insight into mathematics and how we might live mathematically. (shrink)

Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue that the concept of event—rather than object—better captures the vitality of mathematics, and offers new ways of thinking about mathematics education. In this paper I draw on two different but related (...) theories of event articulated in the philosophies of Alain Badiou and Gilles Deleuze to argue that the central activity of ‘problem solving’ in mathematics education should be recast in terms of a problematic of events. (shrink)