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Abstract
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.
Notes
1. See for instance Lynn, 2010 orWhitin & Whitin, Citation2002.
2. See O’Halloran, Citation2007.
3. See Radford, Citation2009.
4. Although there isn’t room here to address this complex relationship in full, it is worth noting that the standard philosophical treatments ofmathematics (formalism, logicism, intuitionism, naturalism) are at heart concerned with the ontological status ofmathematical entities and the epistemological issue of how one comes to know these entities and to what extent mathematical statements capture, represent or exhaust these entities.
5. It is important to mention that the critique I offer in no way intends to play into the recently reheated debate between ‘student centered’ versus ‘teacher centered’ instruction, triggered in part by the 2008 National Mathematics Advisory Report which reiterated this unfortunate binary. I fully support Boaler’s critique of the report, and I agree with her when she says that ‘Researchers in mathematics have worked to understand and analyse the different aspects of effective teaching, and few have concerned themselves with trying to show that one extreme approach is better than another (Boaler, Citation2008, p. 589). In addition, it’s important to say that I use these videos in my own work with pre-service mathematics teachers, and that the videos are of great value to the profession. I offer this critique as a way of opening the conversation up about communication in classrooms.
6. On the other two occasions ‘think’ is used modally to indicate the degree to which a student believes in what they are saying.
7. In the Logic of Sense, Deleuze (1969/1990) describes the confining circle of denotation/ manifestation/signification as that which fails to address the event (sense) of the boundary between language and content.
8. Another reading of Colin’s contribution is that he is more confident and speaks without the use of a modal ‘I think’ to hedge his assertions (rather than an ‘I think’ that reports on thinking).
9. I follow Lecercle (2002) in the use of this term to underscore the ways in which we grant signification infallible referential power.
10. Deleuze points to a nomadic mathematics that troubles and threatens axiomatic mathematics. Although algebraic methods might be leveraged in either tradition, they operate all too often as a confining and legislative discourse in school mathematics. Of interest here is the tension between Deleuze and the work of Alain Badiou, who pursues a more axiomatic and set theoretic approach to mathematics.