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Lacan, subjectivity and the task of mathematics education research

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Abstract

This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud’s psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan’s subjectivity initially in relation to the work of Piaget and Vygotsky who have been widely cited within mathematics education research, but more extensively it is shown how Lacan’s conception of subjectivity provides a development of Peircian semiotics that has been influential for some recent work in the area. Through this route Lacan’s work enables a conception of subjectivity that combines yet transcends Piaget’s psychology and Peirce’s semiotics and in so doing provides a bridge from mathematics education research to contemporary theories of subjectivity more prevalent in the cultural sciences. It is argued that these broader conceptions of subjectivity enable mathematics education research to support more effective engagement by teachers, teacher educators, researchers and students in the wider social domain.

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Notes

  1. Žižek has extensively outlined Hegel’s influence on Lacan. For instance, Žižek (2000) offers Hegel’s example of a plant being akin to a human with intestines on the outside. Whilst a plant draws nourishment through its roots a human draws nourishment through symbolic networks and in a sense becomes understood through the filter of her participation/implication in these networks, which are external to her. In Hegel’s philosophy objects are apprehended in relation to what the cognition brings to them, but the mind itself is then conceived of as being constituted out of these apprehensions. The act of cognition results in an aspect of the object being partitioned off according to how the human apprehends it. The “in-itself” of the object becomes the “in-itself only for consciousness” (Hegel, p. 55, Hegel’s emphasis). That is, Hegel argues that the object “in being known, is altered for consciousness” (ibid). And this aspect in the object corresponds to an aspect of the human mind, “the pure apprehension” (ibid). That is, “the pure apprehension” mirrors the “in-itself only for consciousness” of the object. Thus in Hegel’s formulation: “Consciousness simultaneously distinguishes itself from something, and at the same relates itself to it, or, as it is said, this something exists for consciousness: and the determinate aspect of this relating, or of the being of something for a consciousness, is knowing (Hegel 1977, p. 52. Hegel’s emphasis). Lacan’s conception of the mirror phase (Lacan 2006, 75–81) echoes Hegel’s couple of the “in-itself only for consciousness” and “the pure apprehension” with regard to how a human develops an understanding of who she is. However, having taken this Hegelian step in constituting the human subject, the picture as regards how the human apprehends objects becomes rather more convoluted since Hegel’s second object, “the pure apprehension”, becomes a function of a fantasy self. That is, all objects apprehended are tainted according to the human’s conception of who she is and, specifically, her conception of how she fits in to the social network. The composition of that social network defines the objects of mathematics and the correctness thereof.

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Acknowledgements

A number of people assisted me in thinking through the ideas presented in this paper: Dennis Atkinson, Roberto Baldino, Tamara Bibby, Tania Cabral, Nesta Devine, Una Hanley, Tansy Hardy, Rob Lapsley, Kathy Nolan, Ian Parker and Margaret Walshaw. Also engagement with referee comments was an exhilarating experience.

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    Tony Brown

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Brown, T. Lacan, subjectivity and the task of mathematics education research. Educ Stud Math 68, 227–245 (2008). https://doi.org/10.1007/s10649-007-9111-3

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