Why The Sociology of Mathematics Education?

Why The Sociology of Mathematics Education? Activity, Strategy and Dialogue

Paul Dowling

Culture Communication & Societies Institute of Education, University of London

The position that I want to develop in my lecture is, at least in part, a tactical response to what I perceive as an impending crisis in educational studies in the UK. Arguably, the crisis has its roots in the new forms of governance, which have shifted away from the state provision of services and towards the surveillance and regulation of services that are increasingly out-sourced. The efficiency and scope of this surveillance and regulation is achieved via the recruitment of the rapidly developing and expanding technologies of information and communication. These technologies, of course, include those that are commonly referred to as information and communication technologies. However, their general characteristic entails the minute precodification of the objects of their scrutiny. On a day-to-day basis, we feel the impact of such technologies in, for example, the automatic switchboards, which, in some cases, allow us no route to communicate at all other than through the touch-tone keypads on our telephones. These new technologies of bureaucratic informatics are now being turned on us so that the intellectual field in which we operate is increasingly penetrated and dominated by them. The effect of this new informatic accountability is to urge us to exchange methodological and theoretical rigour for fast-track, quick-fix remedies that must make extravagant claims to act directly on the improvement of teaching and learning in schools. The result would appear to be the dissolution of the languages which have hitherto constituted the disciplines of educational studies and so the potential for the productive interrogation of educational practices. These languages once also constituted the visible guarantees of competence of the academic: to be a sociologist of education might be taken to entail familiarity with, say, a canon of texts (admittedly fuzzily defined and, to a certain extent, of dynamic composition) and their associated terminologies and principles of description. The academic, now, is urged to abandon this now redundant expertise and seek authority in their diplomas and official affiliations which, we know only too well, were never any guarantee of anything (well, not much).

The bureaucratic dissolving of the academic languages is of course being mirrored in schooling itself, which is also increasingly subject to informatic fragmentation through regulation and surveillance. However, and at the risk of sounding controversial, some of the supposedly critical responses to such curricular denaturing are, arguably, themselves contributing to the same process. In particular, I am referring to the liberal democratising of education powerfully proposed by Piaget and taken up by successive generations of pedagogic constructivism. For Piaget, culture is relative. Therefore, the authoritative imposition of a cultural product, in the form of a discursive of practical schema, is, in his terms, socio-centric. As such, Piaget claims that it must inhibit the development of rationality which can occur effectively only where relations are non-authoritative. Authority, for Piaget - power for others - is dispensable and with it the voice of the pedagogue as subject of the discipline as the content of pedagogic action. I contend that this form of liberal constructivism concurs with informatic fragmentation in the dissolution of academic expertise, if in nothing else.

My position, along with Marx, Freud, Foucault and others, is to construe power not as a dispensable condition, but on the contrary, as a sine qua non of subjectivity: power constitutes rather than (or, shall we say, in addition to) constraining the subject. My tactical response, then - tactical in de Certeau’s sense of the strategies of the subaltern - is, firstly, to present my own sociological language which, through its explicitness and (it is to be hoped) its coherence can attempt to validate its own utterances. In this validation, it also attests to the competence of its speaker. In its deployment, the facility of the language is the production of sociological analyses of texts, the term ‘text’ being interpreted in its broadest sense to refer to any closed corpus of data. The language was inaugurated through a dialogue within the theoretical field which constitutes educational studies and through a dialogue with the empirical field of educational practice. The choice of school mathematics as the focus of my work was motivated by virtue of its own highly explicit grammar and because of my own professional investment in the activity. My original empirical setting was the secondary school mathematics scheme, SMP 11-16, although in this paper I shall also refer to one or two other mathematical settings which will serve as illustrative overtures to the presentation of the main structure of the language itself.

The language that I shall introduce is constituted as a cultural product - a discursive schema. In order for it to develop beyond the status of idiolect, I must attempt to apprentice others into it pedagogically. I am therefore constituting a conception of pedagogic action as authoritative.

Issues and questions

I have already raised the issue of my perception of an impending crisis in educational studies, which is leading to the dissolving of academic languages within the field. To the extent that my perception is shared, this is clearly a major problem for educationalists generally and for those of us involved in mathematics education, in particular. My first question, then, is strictly a political one: In an era of academic barba/erism, how can we/should we identify, develop, deploy, disseminate and institutionalise existing and new languages of description—coherent theoretical frameworks—in order to produce and market rigorous and coherent analysis of the empirical field of mathematics education?
I contend that a text is constituted as a tactical or a strategic recruitment of available resources in the production and reproduction—(re)production—of the social structure of the activity within which the text itself is produced. I further contend that the social structures that characterise research activity are, in general, quite distinct from those characterising the practices of schooling. This being the case, there is no simple transferability of products between research and professional practice (or, incidentally, between mathematics and its non-mathematical public domain incorporating domestic and working practices and so forth). The relationship between mathematics education research, on the one hand, and the professional practices of mathematics education in schooling and other settings, on the other, is therefore one of dialogue; any attempts to collapse the distinction between these two fields can only confound the dialogue. My second question, then, is in two parts: Are educational research and professional practice in mathematics education (and, correspondingly, school mathematics and the non-mathematical practices which it recruits) properly conceived as distinct activities or as a single field of practice; if the former, how can we achieve a dialogic relationship which is productive within both?
I define a pedagogic activity as entailing the transmission and acquisition of a privileged discourse, narrative, skill, or comportment under conditions whereby the principles of evaluation of texts are located with the transmitter. I want to hypothesise that apprenticing transmission is properly conceived as textually oriented. That is, transmission constructs an apprenticed acquirer position to the extent that it makes explicitly available the esoteric domain principles that generate valid texts. However, this can be achieved only in the presentation of texts for interpretation by the acquirer. Apprenticed acquisition, on the other hand, is essentially grammar-oriented. That is, the apprentice is confronted by texts that they must interpret in terms of their generative principles. To simplify: the teacher deploys principles in the generation of texts, which are presented to the student; the student must read the text with a view to accessing the teacher’s principles. This is because it is the principles rather than or, at least, in addition to the texts themselves which constitute the content to be transmitted. My third question is: To what extent does this interpretation of pedagogic activity enable reconciliation between the notion of pedagogy as a transmission, on the one hand, and pedagogic constructivism, on the other?
My understanding of sociology is that it is concerned with patterns of relations between individuals and groups—the social—and their production and reproduction in cultural practices. My analysis of mathematics education, in particular, describes this particular set of cultural practices as constituting a range of myths concerning the relationship between the mathematical and the non-mathematical and of distributing these myths such as to (re)produce an intellectual/manual hierarchy. My fourth question is: (How) can mathematics education in itself or in its incorporation into alternative curricula ever be anything other than (re)productive of a hierarchical division of labour?