Where the Learner of Mathematics Is Socially Positioned in Textbooks

Posted on March 23, 2012 by

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Dowling, Paul. 1996. “A Sociological Analysis of School Mathematics Texts.” Educational Studies in Mathematics 31 (4) (December 1): 389–415.

Methods:Results of language of description as applied to mathematical texts in England SMP 11-16.  Work is illustrative than demonstrative. (p.389)

These series account for the bulk of the mathematics curriculum in the last three years of compulsory schooling (years 9-1 1).  The main focus of my analysis was on the upper and lower series, the ‘Y’ and ‘G’ series, respectively (p.390)

Findings:

  • Mathematical knowledge-which,in its textualised form, I want to refer to as message- is distributed to the voices such that esoteric domain message and public domain message are associated, respectively, with superordinate and subaltern voices. The text is comprised of textual strategies which position voices (positioning strategies) and which distribute message to the respective voices (distributing strategies). But the text is a cultural product which is understood to be producing and reproducing a social structure,which I shall refer to as an activity. The activity,in this case school mathematics, regulates who can say or do what. That is, it comprises subject positions and practices. In the text, subject positions and practices are realised by voices and message,respectively (p.393)
  • Generalising and localising are textual strategies that have a particular importance in the language of description.This is because they derive from a modality of practice which can be indexed, but not defined, by the opposition abstract/concrete.  The distinction that I want to make is between practice that is highly organised at the level of language, and practice that generally lacks systematic organisation in language.Esoteric domain mathematics is an example of the former.It is able to generate texts which are relatively context-independent.
  • The G text positions its reader by projecting its reader voice on to junior clerical work and onto infantile behaviour (comic reading)…the Y text positions its reader voice by producing a denotative mapping onto mathematical work through the invitation to join the community of mathematicians (p.401).
  • The Gtext, then, positions its reader voice within a particular comparatively low status, career trajectory and distributes public domain message to this voice:mathematics is presented as being for participation in thepublic domain.  The Y text positions its reader as the subjectof a gaze which objectifies the public domain setting.  The distributing strategy movesthe reader away from this setting towards the esoteric domain.Mathematics is presented as describing the public domain,but not as a requirement for participation in it (p.395).
  • The use of opennarratives- giving minimal settingdetail,fast-switching between settings, and irony ensures that the public domain takes no hold in the text. At the same time, it constitutes a generalising of a mathematical gaze, a triangulation which pinpoints the esoteric domain as the centre of subjectivity of the activity.  Again, whereas the Gtext presents mathematics as being for participation in the public domain, the Y text invites the reader into the esoteric from which location they can describe the non- mathematical world (p.403).
  • School activities are…vertical activities and their practices exhibit high discursive saturation (p.409).
  • ‘Language’, in the chapter heading,might signify simply a code, like a computer language (p.396)
  • In terms of subject positions,the location of the evaluative principles of pedagogy must be with the teacher, by virtue of their necessarily superordinate relation to the students. Texts which realise this hierarchical relation are referred to as pedagogic texts.These texts (re)produce activities (p.409).

My Evaluation:

The analysis while insightful appears to be guided by nothing more than his own semiotic interpretation.  What would be useful would be to see is what students thought about the textbook, what they actually encountered, and what they ultimately took from using the book.