Ethical clearance was granted by the Research Office of the University of KwaZulu-Natal for this thesis. The upgrade of this thesis from the Masters to the PhD program contributed to the length of the thesis.
LIST OF TABLES
DEDICATION
ACKNOWLEDGEMENTS
INTRODUCTION AND STUDY OVERVIEW
BACKGROUND INFORMATION, MOTIVATION AND GUIDING RESEARCH QUESTIONS
I argue that each of the domains of practice in the knowledge domain of mathematical literacy is characterized by uniquely identifiable discursive resources. This theoretical language was developed in response to a specific problematic scenario that exists in the specific empirical terrain of the subject domain of mathematics literacy.
SCOPE, KEY FINDINGS AND LIMITATIONS OF THE STUDY
All of the above points to the originality, usefulness and importance of the contribution of this study to the existing literature on the subject of Mathematical Literacy. This process particularly illustrates the usefulness and validity of the language for identifying, describing and comparing the criteria according to which participation in different empirical activities related to the knowledge domain of mathematical literacy is legitimized and endorsed.
STRUCTURE OF THE STUDY
THEORETICAL (AND OTHER) ANTECEDENTS
INTRODUCTION AND OVERVIEW
RESEARCH METHODS, PARADIGMS AND MATHEMATICS EDUCATION THEORIES
Positioning this study in an interpretive paradigm
Positioning this study as a form of qualitative research
Continuing this line of thought, there should be no doubt in the reader's mind that this research is directly influenced by my own interests, perspectives, and values. Rather, a qualitative analysis is necessary due to the distinctive and unique nature of the subject of Mathematical Literacy in the South African context.
Positioning this study within the field of the sociology of mathematics education
For this reason, the object of scrutiny in this study—namely, the knowledge structure that characterizes the specific relationship between mathematical content and real-world contexts envisioned for pedagogical practice in the subject of Mathematical Literacy—simply does not use one. This kind of analysis is driven by my own personal interest in understanding the way in which different groups of participants perceive the 'reality' of the subject - and in particular to favor a version of 'reality' in which preparation for life is prioritized over learning from mathematical knowledge.
THIS STUDY AS THE DEVELOPMENT OF A ‘LANGUAGE OF DESCRIPTION’
Internal and external languages of description .1 General theory on languages of description
The structure and orientation of the internal description language is largely driven by a response to a critical analysis of existing. As such, to facilitate the use of the internal language in interpretation and analysis of specific empirical practices related to the subject area of Mathematical Literacy, an external language of description is needed.
The claims and concepts of the language of description
- Claim
- Concepts
Thus, it is in an attempt to address these issues that the impetus for an alternative language for describing the structure of knowledge for the domain of mathematical literacy arises. As such, effective pedagogical practices associated with the Mathematical Literacy topic format aligned with the knowledge structure outlined in the description language developed in this study should give recognition, exposure, and credibility to informal and non-mathematical techniques. structures and considerations that influence and reflect the reality of participating in real-world problem scenarios.
POSITIONING THIS STUDY IN THE FIELD OF KNOWLEDGE PRODUCTION
This process is also located in the field of recontextualization, although this time in the pedagogical recontextualization subfield. As for the area of reproduction: this is the area where teachers make use of.
CONCEPTUALISING AND CLARIFYING THE NOTIONS OF A
LIFE-PREPAREDNESS ORIENTATION’ AND ‘PRACTICE’
4.1 ‘Life-preparedness orientation’
The notion of ‘practice’ as employed in this study
However, the empirical analysis component of this study is focused specifically on the analysis of textual resources and of the practices legitimized in these resources for successful participation in the subject Mathematical Literacy. This contributes to a key limitation of this study – namely that the conclusions presented regarding practice in the subject of Mathematical Literacy are limited to those involving engagement with specific textual resources.
WHERE TO FROM HERE
5 See Part 5 starting on page 253 for a discussion of the external description language for this study. The collective of these domains includes the components of the developed internal language of description of a knowledge structure for the.
REVIEW OF THE LITERATURE
In Chapter 7 I outline the different meanings attached to the terms mathematical literacy, numeracy and/or quantitative literacy within the literature and provide a justification and motivation for my privileging of the term 'mathematics literacy'. A brief history of the secondary school subject Mathematics Education in South Africa Introduction: the unique situation of South Africa.
A FRAMEWORK FOR ORGANISING THE LITERATURE ON MATHEMATICALLY LITERATE, NUMERATE AND/OR
QUANTITATIVELY LITERATE BEHAVIOUR 14 5.1 Justifying the need for a framework
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’: dominant agendas and intentions
- Dominant agendas in mathematical literacy and numeracy 17
- A proposed structure for identifying dominant agendas and statements of intention in the literature relating to mathematical literacy, numeracy and
- Summary of the categories and sub-categories to be used for organising, categorising and comparing the literature on
- Rationalising the intended use of these categories and sub-categories in the analysis of the literature
The current use of the term mathematics in much of the literature on mathematical literacy, numeracy and/or. Critical evaluation of real-world problems and the use of mathematics in those problems). That is, these components provide an indication of the function or purpose toward which a particular account of mathematical, numerical, and/or quantitative literacy is oriented and.
AREAS OF COMMONALITY AND DIVERGENCE IN THE LITERATURE
Category 1 − Considerations of mathematics
All quotes also hint at a further element of shared agreement regarding mathematical literacy, mathematical and/or quantitative literacy. Consideration of (iii) sets of mathematical content highlighted in the literature is the next sub-category for discussion. Descriptions (iv) of the range of mathematical content41 that is appropriate for mathematical literacy, mathematical and/or quantitative literacy, is an area where the literature varies considerably.
Category 2 − Interplay of content, contexts and/or competencies
This is especially true for many concepts of mathematical literacy, numeracy literacy, and/or quantitative literacy, in which the responsibility for developing these kinds of behaviors lies within the domain of the mathematics classroom. This dual emphasis on the interplay of content and context is a common feature of much of the literature. This demonstrates the dominance of mathematical terrain and mathematical goals in many conceptions of mathematical literacy, mathematical and/or quantitative literacy.
Category 3 - Arena of application
These types of contexts offer a simulation of reality (by incorporating real names, photos, and other localization resources) by presenting contexts (and the problem-solving activities associated with those contexts) as a reflection of a collaborative structure that is legitimate and validated in the real world. Unfortunately, there is no definition of "realistic" in ALL, so it is impossible to determine whether realistic problems include only "real" ones. At the same time, the responsibility for the development of such behavior should not fall exclusively on the shoulders of the mathematics teacher.
Category 4 – Components (and/or features) associated with courses, assessments and/or pedagogic practice
Despite these sentiments, there is still an underlying assumption in all notions of mathematical literacy, numeracy and/or quantitative literacy that it is mathematical knowledge that is positioned as the primary organizing principle of such behaviour. An assessment adapted to these conditions would prioritize mathematical competence and modeling as primary components of mathematical literacy, numeracy and/or quantitatively literate behaviour. The discussion in this section has served to highlight issues relating in particular to the assessment of mathematically literate, numerically and/or quantitatively literate behaviour.
Category 5 – Dominant orientations in international perspectives of mathematical literacy, numeracy and/or quantitative literacy
53 See page 120 below for a detailed discussion of the comparison of the dominant orientation in the field of Mathematical Literacy with the orientations that characterize international perspectives on mathematical literacy, numeracy and/or quantitative literacy. I refer to this figure to emphasize the dominant orientation in the topic compared to the dominant orientations that characterize international views on mathematical literacy, numeracy and/or quantitative literacy. Interestingly, note the wide variation in the dominant agenda prioritized in South African documentation and literature relating to the subject domain of mathematical literacy.
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
While privileging the term mathematical literacy, he often uses the terms mathematical literacy and numeracy interchangeably and argues that the term numeracy is the British equivalent of mathematical literacy.58. Niss (2003, p. 216), on the other hand, deliberately privileges the term mathematical literacy, arguing that “The main reason I prefer mathematical literacy is that the breadth of the term. In summary, the above discussion has highlighted the differential usage and meanings attached to the terms mathematical literacy, numeracy and quantitative literacy across the literature.
My privileging of the term ‘mathematical literacy’
The final literacy that should be considered an essential component of mathematical literacy—what I have called real-world literacy. The diagram in Figure 12 below – as an adapted version of de Lange's (2006) schematic 'The Tree Structure of Mathematical Literacy' – illustrates my view of the relationship between the different literacies that make up the overarching category of literacy mathematical. As a final comment, it is essential to emphasize the 'education' component of the conceptualization of mathematical literacy as described above.
MATHEMATICAL LITERACY IN SOUTH AFRICA
Introduction: the unique South African situation
In contrast, in the African context, the primary responsibility for the development of mathematically literate behavior rests with the teachers of the mathematical literacy subject. Moreover, the curriculum and contexts to which students are exposed in South African schools are not determined by the requirements, relevance and applicability of specific subject areas, but rather by the authors of subject curriculum documents and then by the textbook authors and assessment professionals who interpret these curriculum documents. Mathematical literacy in South Africa is therefore a school subject with its own curriculum and is assessed as a full-fledged discipline.
A brief history of the secondary school subject Mathematical Literacy in South Africa
67 For the sake of transparency, I should emphasize that I was the main author of the CAPS document for mathematical literacy. Importantly, and based on the guidance I received in the development process of the CAPS document on mathematical literacy, the curriculum described in the CAPS documents is not a new curriculum. This concludes a short journey into the history of the field of mathematical literacy.
Definitions, statements of intention and curricular agendas for the subject Mathematical Literacy 70
- Definitions, statements of purpose and dominant intention(s) and agenda(s) in the NCS conception of the subject Mathematical
- Category 1 − Considerations of mathematics
- Category 2 − Interplay of content, context and/or competencies
- Category 3 − Arena of application
- Category 4 – Components (and/or features associated with courses, assessments and/or pedagogic practice)
- Category 5 − Dominant orientation in the NCS conception of the subject- matter domain of Mathematical Literacy in South Africa
- A comparative analysis of the South African NCS conception of
- Dominant Agenda(s) and Intention(s) in the CAPS conception of the subject Mathematical Literacy 87 & 88
- NCS vs. CAPS: from Learning Outcomes to Topics
- Consideration of non-mathematical techniques and considerations
- Content, context and skills
- Sense-making of contexts
- Emphasis on a form of problem-solving characterised by modelling processes
- Communication
- Dominant intentions and agendas in the CAPS document
Mathematical literacy, by its very nature, requires that the subject matter be rooted in students' lives. Mathematical literacy, by its very nature, requires that the subject matter be rooted in students' lives. 88 As previously mentioned, I was directly involved in the development of the CAPS curriculum document for the field of Mathematical Literacy.
THEORY-INFORMED ANALYSIS OF CURRENT PRACTICES IN THE SUBJECT MATHEMATICAL
LITERACY
A BROAD OVERVIEW OF KEY ASPECTS OF DOWLING’S LANGUAGE OF DESCRIPTION
9.1 ‘Road Map’ and broad overview of Dowling’s language
- Mathematics as an ‘Activity’
- The Structural Level of Dowling’s language of description − Domains of Practice and Positions
- Domains of Practice
- Positions
- Brief discussion of components of the ‘Textual’ and ‘Resources’
- Considerations of (successful) apprenticeship in mathematics
The everyday world that students are presented with in the math classroom is not a copy of the real thing; it is virtual. The remaining two domains - the Expressive and Descriptive Domains - are also the result of the imposition of a 'mathematical gaze' by the Esoteric Domain on the everyday world, and both represent an alternative form of recontextualisation to that which occurs in the Public Domain. This position is primarily related to Public Domain practices that have been re-contextualized - through a 'mathematical view' - according to the principles of the Esoteric Domain.
THE RELATIONSHIP BETWEEN ACADEMIC AND MATHEMATICAL KNOWLEDGE AND EVERYDAY NON-
MATHEMATICAL ACTIVITIES
- The incommensurability of academic and everyday knowledge .1 Academic and everyday activities as fundamentally different domains
- Vertical and Horizontal Discourses
- The subordination of the everyday to the academic
- Summary (of the discussion on the incommensurability of academic and everyday knowledge and practices)
- The relationship between mathematical and non-mathematical knowledge and/or practices
- The distinctive nature of mathematics and everyday activities
- The ‘Mathematical Gaze’ and associated mathematical myths
- The ‘production of ability’: considerations of educational disadvantage
- The ‘best’ way forward (according to Dowling)
153 activity rather than an accurate or realistic representation of the structure of legitimate participation and communication in the activity. The dilemma with this imposed mathematical view is that the image of everyday practice that is presented in the public domain of the math classroom is not true;. As such, the image of everyday activity recontextualized in the mathematics classroom is not authentic or realistic.
