CHAPTER 3
POSITIONING THIS STUDY IN THE FIELD OF KNOWLEDGE
The field of production is the field in which discipline-specific or domain-specific expert knowledge (Singh, 2002, p. 572) is constructed and positioned by role-players such as academics and professionals in the field.10 Since the primary intention of this study is the development of a theoretical language to describe a particular conception of the knowledge required to engage both mathematical and contextual domains of practice, a major component of this study is, thus, located in the field of knowledge production. This knowledge production is in specific relation to domain of knowledge associated with a specific conception of mathematically literate behaviour and also to the localised empirical site of practice of the secondary school subject Mathematical Literacy in South Africa.
To facilitate the development of this language of description and to provide a rationale of the need for this language, it is also necessary to temporarily shift the object of study.
This shift in the object of study facilitates analysis of literature relating to conceptions of mathematically literate, numerate and/or quantitatively literate behaviour in general and, specifically, to the South African conception of mathematical literacy embodied in the secondary school subject Mathematical Literacy. This latter site of analysis requires a reading of various curriculum and related supporting documents for the subject. Thus, Part 2 of the study (c.f. page 29 below) – in which the bulk of the analysis described above takes place – facilitates a shift of focus in the object of study to a site
characterised by Bernstein as the official recontextualising field (as a sub-field of the field of recontextualisation). Once the internal language of description is developed, a gaze is cast from this internal language – through an external language and associated methodology of textual analysis – over empirical textual resources (textbook section, curriculum section, national examinations, and course notes for a teacher education course) relating to the subject-matter domain of Mathematical Literacy (c.f. Part 7 starting on page 381). This process is also located in field of recontextualisation, albeit this time in the pedagogic recontextualising sub-field. A word of clarification and caution is, however, necessary. It is essential to reiterate that the primary intention of this study is the development of a theoretical language to describe a particular
knowledge structure – which takes place in the field of production. Any attempt to shift the object of study outside of this field – for example, through the analysis of
curriculum documents or pedagogic texts – is always in service to this knowledge development intention. As such, although focus shifts to different sites in the official recontextualising field in the analysis of subject-related documents, this shift is made to further facilitate and strengthen the developed internal language of description.
As regards the field of reproduction: this is the field in which teachers make use of the
“privileged and privileging texts created in the field of recontextualisation” (Singh, 2002, p. 577) to interpret and implement the curriculum through classroom and assessment practices. Although in this study I draw on my own experiences of teaching in the subject- matter domain of Mathematical Literacy and on my interactions with other teachers of the subject in providing an analysis of the literature and curriculum documents and in outlining approaches to pedagogic practice for the subject, the key area of focus of this study does not fall within this field of reproduction. Rather, I step periodically and somewhat superficially into this field to inform the knowledge construction process of a
10 Bernstein distinguishes between two primary forms of knowledge – hierarchical and horizontal knowledge structures. These knowledge forms are differentially distributed to different groups of people to produce differential power relationships (Singh, 2002, p. 573). Hierarchical and horizontal knowledge structures, together with horizontal and vertical discourses, are discussed briefly in Part 3 of this study (c.f. Chapter 10 and sub-section 10.1.1.2 starting on page 150 below).
language of description within the field of production and the testing of this language in the field of recontextualisation.
The positioning of this study in relation to Bernstein’s pedagogic device is illustrated in the diagram shown in Figure 4 below:
Figure 4: Positioning of this study in relation to Bernstein's Pedagogic Device
Importantly, the location of this study primarily within the field of knowledge production signifies that any claims made only provide a limited perspective on the practices associated, specifically, with the subject-matter domain Mathematical Literacy and, more generally, on the traits associated with mathematically literate behaviour that are seen to stem from participation in this subject. In particular, since the study does not delve into the field of reproduction, little or no validated commentary is possible regarding the classroom practice of teachers or learners and/or how such participants may further re- contextualise the legitimised knowledge developed in the field of knowledge production.
Field of Reproduction Pedagogic Device
Recontextualisation of Knowledge
Reference to knowledge in these fields is only made to support the language of description
developed in the Field of Production Primary area of focus
of this study Field of Production
Language of description of the structure of knowledge in Mathematical Literacy
Field of Recontextualisation Official
Recontextualising Field
Analysis of curriculum documents
Pedagogic Recontextualising Field
Analysis of textual resources through the lens of the language of description