INTRODUCTION AND OVERVIEW
Given that the empirical terrain of focus in this study is the secondary school subject- matter domain of Mathematical Literacy in South Africa, my intention in this chapter is to provide background information about the subject, to identify the rationale or intention for the introduction of the subject in the South African curriculum framework, and to provide clarification on the intended and implemented structure of knowledge and legitimate participation in the subject. I also investigate areas of divergence and commonality in the structure of knowledge and legitimate participation in the subject to existing local (South African) and international perspectives on forms and characteristics of mathematically literate, numerate and/or quantitatively literate behaviour. All of this is achieved through investigation of the dominant agendas and intentions prioritised in different conceptions of mathematical literacy, and the resultant structure of legitimate participation that is endorsed.
A key point that I highlight throughout this discussion is that there is a dominant orientation permeating much of the international literature on mathematical literacy, numeracy and/or quantitative literacy, and also within the literature on the South African school subject Mathematical Literacy, for the prioritisation of mathematical knowledge, techniques and structures (i.e. mathematisation processes and/or the imposition of a ‘mathematical gaze’11). This prioritisation occurs over an agenda for contextually relevant/appropriate/legitimate forms of participation and contextual sense- making practices in the development of mathematically literate behaviour: namely, the positioning of the mathematical terrain rather than the contextual terrain as the
organising principle of the learning process12. In the South African context – where the development of mathematically literate behaviour has been extricated and separated from the domain of scientific mathematics – this emphasis on mathematised forms of participation is disadvantaging learners who engage in the subject Mathematical Literacy and is contributing to the re(production) of a degree of educational and social disadvantage. The problematic nature of current practices in the subject is be analysed and theorised in detail through the work of Paul Dowling (1998) in Part 3 and Chapter 11 of the study (starting on page 167).
Although my primary intention in this part of the study is for analysis and discussion of the dominant agendas and intentions that characterise differing conceptions of mathematical literacy, a secondary intention also exists. Namely, in Chapter 5 below I present and utilise an analytic framework that I have developed to facilitate comparison and categorisation of differing perspectives and conceptions of the characteristics of mathematically literate behaviour. One dimension of this framework is focused on the dominant agenda and intention prioritised in a particular conception of mathematical literacy and the structure of legitimate knowledge and participation associated with these.
I contend that the components of this dimension provide a particularly important means
11 Refer to Part 3, Chapter 10 and sub-section 10.2.2 (starting on page 156) for an elaborated discussion of the notion of a ‘mathematical gaze’ as described from the perspective of Dowling (1998).
12 The idea for distinguishing between the mathematical terrain and the contextual terrain in terms of the dominant organising principle of an activity or learning process is drawn from the work of Ginsburg, Manly, and Schmitt (2006).
for differentiating different conceptions of mathematical literacy, and do so in a way that is able to account for both internal and external impetus that impact on the structure of participation or behaviour that is endorsed. Thus, the discussion in this part of the study provides an opportunity to demonstrate this framework and to test if the framework is able to provide a form of categorisation that illustrates differences in the structure of participation or behaviour legitimised in different conceptions of mathematical literacy.
Having presented the components of the analytic framework in Chapter 5, in Chapter 6 I then utilise the framework to provide an analysis and comparison of international literature and perspectives13 on general conceptions of mathematical literacy, numeracy and/or quantitative literacy, and the types of behaviour envisioned for these different conceptions.
In Chapter 7 I outline different meanings attached to the terms mathematical literacy, numeracy and/or quantitative literacy within the literature and provide a justification and motivation for my own privileging of the term ‘mathematical literacy’.
The discussion in Chapter 8 shifts to a specific focus on the South African conception of mathematically literate behaviour as encompassed in the school subject Mathematical Literacy. After providing a brief history of the subject, I use the same analytic framework outlined in Chapter 5 to analyse and discuss various facets of the subject. I also point out areas of commonality and divergence to international perspectives on mathematical literacy, numeracy and/or quantitative literacy.
The structure of this part of the study is illustrated in Figure 5 below:
13 By ‘international’ I am referring to literature that reference conceptions of mathematical literacy, numeracy and/or quantitative literacy that do not relate to the South African conception of mathematical literacy as encompassed in the South African school subject Mathematical Literacy. It is necessary to make this distinction because South Africa is the only country where the development of mathematically literate behaviour is given its own domain as a fully-fledged subject. In all other countries where mathematical literacy, numeracy and/or quantitative literacy is acknowledged and encouraged, it is done so in the context of the normal teaching of the discipline of mathematics. This important different in the way in which mathematical literacy in South Africa is conceptualised and positioned in the school and/or subject framework in comparison to international conceptions of mathematical literacy, numeracy and/or quantitative literacy makes an independent analysis of these two spaces necessary.
Figure 5: Overview and chapter structure of Part 2 of the study
CHAPTER 7 What’s in a name?
Mathematical Literacy, Numeracy or Quantitative
Literacy
Differing opinions on the meanings associated with the terms mathematical literacy, numeracy and quantitative literacy
My privileging of the term ‘mathematical literacy’
CHAPTER 8 Mathematical Literacy in
South Africa
Definitions, statements of purpose and curricular agendas for the subject Mathematical Literacy
A brief history of the secondary school subject Mathematical Literacy in South Africa Introduction: the unique South African situation
CHAPTER 5
A framework for identifying areas of commonality and divergence in the literature
Categories and sub- categories of areas of agreement, disagreement and/or comparison
Considerations of perceived orientation: intention and agenda
Summary of the categories and sub-categories used for organising, categorising and comparing the literature
Rationalising the use of the categories for the analysis of literature
Comparison of different conceptions of
mathematical literacy in relation to emphasis on:
CHAPTER 6 Review of international
literature
Considerations of mathematics Interplay of content, contexts and/or competencies Arena of application:
location and context
Components and/or features associated with courses, assessments, etc.
Purpose: intention and agenda