Abstract
The issue of subjectivity has recently occasioned a lively discussion in this journal opposing socioculturalism and Lacanian psychoanalysis. By confronting Luis Radford’s cultural theory with Jacques Lacan’s psychoanalysis, Tony Brown sought to show the limitations of socioculturalism. This article takes advantage of that discussion to develop a critique of Radford’s theory of objectification, taken as an exemplary sociocultural theorization of the teaching and learning of mathematics. It does so by extending the criticism made by Brown at the level of the subject, namely by showing what is lost in socioculturalism when it reduces the Hegelian notion of dialectics to a relation between constituted entities; but mostly by exploring the possibility opened by contemporary theory to posit the discussion around subjectivity in the political. While socioculturalism assumes the possibility of a synthesis between person and culture thus making education possible, it will be argued that a theory which assumes the impossibility of education is in a better position to, on the one hand, conceptualize the resistance of many towards the learning of mathematics, and on the other hand, to address the ongoing political failure in achieving the desired goal of “mathematics for all”.
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Notes
Recent theoretical developments in mathematics education research are also founded on the need to articulate the relation between individual and social. For instance, Anna Sfard (2008), through the exploration of Wittgensteinian philosophy and in order to surpass the traditional divide between thinking and speaking, introduces the notion of commognition as a way of conceptualizing the relation between cognition and communication; also, Walshaw (2004) and her search for a conceptualization in Lacan and Foucault that could aid the interpretation of subjectivity.
In Pais (2015), I provide a critique of Brown’s use of Lacan’s apparatus in mathematics education research, which complements the critique of Radford’s theory developed here.
My use of Hegel’s theory is informed by Žižek’s works on Hegel.
Ernesto Laclau, Chantal Mouffe, Fredric Jameson and Alan Badiou are among the ones who have been articulating insights from Lacanian psychoanalysis with a Marxist critique of political economy.
This tendency to allocate “cogitation” in the object (such as artefacts) was already criticized by Glasersfeld (1996). He denies that (radical) constructivism ignores the role of social interaction in the construction of knowledge, however the “other” “constitute ‘exist’ for the individual subject only to the extent to which they figure in that individual’s experience” (p. 309). That is, the meaning of an artefact is not deposited in the artefact, as Radford argues (2008a, p. 451), but posited by the subject. Also recent research in situated cognition (Watson & Winbourne, 2008) has called attention to the way some studies within socioculturalism overestimate the formative influence of artefacts and situational configurations on mental functions, “as if these were embodied in tools” (Stech, 2008, p. 20).
Walshaw (2011) and Walkerdine (1998) made the same critique apropos of the theory developed by Cobb and Hodge (2007) and Lave (1988) respectively. They take the position that their work leaves intact the characterizations of identity, consciousness and agency put forward by traditional social science. These understandings, in turn, provide a limited perspective of how mathematical identities are constituted within the realities of the classroom and the wider sociopolitical context. As a way to surpass these limitations, both Walshaw and Walkerdine introduce the Lacanian subject, as one where there is more at stake than the rational links between individual and social, namely, the Freudian unconscious.
What one should render problematic here is that the big Other, precisely as pure artificial schemata it has effects on reality: “precisely insofar as it is a ‘dead scheme’, we must presuppose it as an ideal point of reference which, in spite of its inexistence, is ‘valid’, i.e., dominates and regulates our actual lives” (Žižek, 2008b, p. 61). Culture has thus this paradoxical nature: although it is not to be found anywhere in “reality”, is nonetheless effective and regulates our lives. When responding to Brown’s book, Roth (2012) raised the issue of corporeality. Roth does so in order to emphasize how the body precedes any given language or symbolic system. Yet more interesting than exploring how every “language” needs a body, is to investigate how the immaterial, the fictions, affect the body. The typical Marxian example of a system without a body is capital. Marx’s characterization of capital as an “automatischem Subjekt”, an oxymoron uniting living subjectivity and dead automatism (Žižek, 2012, p. 250), presupposes a “subject” that does not exist as a living-one, but nonetheless has real (automatic) effects on reality.
By posing dialectics as a relation between two entities, Radford misses the full potentiality of this notion. If we recall how Hegel refers to the dialectical process, we can say that there is no dialectic between parts. Rather, dialectics is itself the motor that generates the parts, it takes precedence over the poles, it does not occur “between” constituted entities.
Towards the end of his life, Lacan (e.g., 2007) moved from an analysis of the psychic apparatus centred on the Imaginary and Symbolic, to an apparatus revolving around the Symbolic and the Real. The latter is only slightly mentioned in the response of Presmeg and Radford (2008) to Brown’s article. This is also why they fail to catch the radical emancipatory spirit of the Lacanian subject.
Less than a handful of people take into consideration the economy of schools in mathematics education research (Pais, 2014).
Indeed, to withdraw promotion from schools it is sufficient that teachers stop stamping people with letters and numbers. Technically, this can be done tomorrow, saving a huge amount of resources and people’s time (a significant part of all the labour that revolves around schooling is spent in assessing and controlling students’ performance). Why is it not so? Because there is more at stake in school than just the transmission of knowledge and competences. People in school learn the economic rules for the production and seizure of surplus-value (Baldino & Cabral, 2013, 2015). To question school’s credit system is to question an entire economic structure in which we all participate. Such a radical change is often experienced as impossible.
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Acknowledgments
I am thankful to Roberto Baldino for rectifying my diligent misunderstandings of Hegelian philosophy, to Tony Brown for a tireless review of previous versions of the manuscript, and to Sylvia Violet for her generosity in proof-reading the text.
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Pais, A. At the intersection between the subject and the political: a contribution to an ongoing discussion. Educ Stud Math 92, 347–359 (2016). https://doi.org/10.1007/s10649-016-9687-6
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DOI: https://doi.org/10.1007/s10649-016-9687-6