MATHEMATICAL LITERACY IN SOUTH AFRICA
8.3 Definitions, statements of intention and curricular agendas for the subject Mathematical Literacy 70
8.3.1 Definitions, statements of purpose and dominant intention(s) and agenda(s) in the NCS conception of the subject Mathematical
8.3.1.5 Category 5 − Dominant orientation in the NCS conception of the subject- matter domain of Mathematical Literacy in South Africa
The discussion so far has highlighted a degree of incongruence between the definition and statement of purpose for the subject Mathematical Literacy provided in the NCS curriculum and the structure of legitimate participation promoted and prioritised in other supporting documents. I have suggested that this provides a possible reason for the wide variation in opinion on the purpose and areas of focus in the subject amongst various role- players, including curriculum writers, textbook authors, examiners and teachers, and, hence, for the spectrum of pedagogic agendas identified by Venkatakrishnan and Graven (2007). This difference in opinion revolves primarily around the prioritising of mathematical content, contextual entities or competencies as the basis for legitimate participation in the subject.
Despite this variation in opinion and the sometimes contradictory messages espoused in the various curriculum and supporting documents, it is still possible to identify the dominant agendas and intentions that are prioritised in the South African conception of Mathematical Literacy. To do this I draw once again on the two-dimensional framework of Agendas and Intentions introduced in sub-section 5.2.2.3 on page 47 above (and represented in Figure 7). Also note that, as part of the discussion of the dominant agendas and intentions in the subject-matter domain of Mathematical Literacy, I make reference to the dominant agendas as intentions in international conceptions of mathematical literacy, numeracy and/or quantitative literacy. These dominant agendas and intentions are categorised in the framework of agendas and intentions in Section 6.5 on page 82 above. As a reminder, this categorisation also includes the documentation that relates and refers to the South African subject-matter domain of Mathematical Literacy (formatted in italics in the framework). As such, the reader may wish to refer back to that utilised framework to contextualise the discussions in the sub-sections below that make comparisons of the categorisation of the literature on the subject-matter domain of Mathematical Literacy and the literature on more general conceptions of mathematically literate, numerate and/or quantitatively literate behaviour.
8.3.1.5.1 Dominant Intention(s) for the NCS conception of Mathematical Literacy As regards the dominant Intention that is promoted through and for the South African conception of Mathematical Literacy, various statements in the NCS and supporting documents reference several of the categories of intentions shown in the framework. To begin with, an analysis of Chapter 1 in the NCS (DoE, 2003a, pp. 1-7) – a generic chapter that appears in the NCS documents for all subjects and which provides an introduction to the components of the entire National Curriculum Statement curriculum framework – reveals reference to at least four of the categories:
the inclusion of words such as “high knowledge and high skills” suggest an intention for the development of Human Capital;
the inclusion of words such as “valuing indigenous knowledge systems” hint at an intention for the promotion of Cultural Identity;
the inclusion of words such as “social transformation”, “human rights”, “inclusivity”,
“social justice” suggest an intention for Social Change; and
words such as “environmental justice” suggest that the curriculum is presented as an avenue for Environmental Awareness.
Despite reference to four of the categories, the inclusion of the following statement in Chapter 1 – under the heading “The kind of learner that is envisioned” (DoE, 2003a, p.
5) − suggests the dominance of an intention for Social Change in the broader NCS framework:
Of vital importance to our development as people are the values that give meaning to our personal spiritual and intellectual journeys. The Manifesto on Values, Education and Democracy (Department of Education, 2001:9-10) states the following about education and values:
Values and morality give meaning to our individual and social
relationships. They are the common currencies that help make life more meaningful than might otherwise have been. An education system does not exist to simply serve a market, important as that may be for economic growth and material prosperity. Its primary purpose must be to enrich the individual and, by extension, the broader society.
The kind of learner that is envisaged is one who will be imbued with the values and act in the interests of a society based on respect for democracy, equality, human dignity and social justice as promoted in the Constitution.
Shifting to the chapters in the NCS document that deal specifically with the components of the subject Mathematical Literacy, there are, similarly, statements that make reference to a variety of differing intentions for the subject. Numerous statements in the NCS prioritise the mathematical literacy for Human Capital intention and the conception that by engaging in the subject Mathematical Literacy learners are better prepared to cope with the demands of daily life and the workplace and, so, increase their value and worth in the economy:
The inclusion of Mathematical Literacy as a fundamental subject in the Further Education and Training curriculum will ensure that our citizens of the future are highly numerate consumers of mathematics. (DoE, 2003a, p. 9)
The Further Education and Training subject, Mathematical Literacy, should enable the learner to become a self-managing person, a contributing worker and a
participating citizen in a developing democracy. (DoE, 2003a, p. 10)
Mathematical Literacy will ensure a broadening of the education of the learner which is suited to the modern world. (DoE, 2003a, p. 10)
... realise that mathematical literacy contributes to entrepreneurial success.
(DoE, 2003a, p. 10)
Students proceeding to Higher Education institutions will have acquired a
mathematical literacy that will enable them to deal effectively with mathematically related requirements in disciplines such as the social and life sciences.
(DoE, 2003a, p. 11)
These statements are, however, intertwined with statements of intention for Social Change and for Evaluating Structures:
To be a participating citizen in a developing democracy, it is essential that the adolescent and adult have acquired a critical stance with regard to mathematical arguments presented in the media and other platforms. (DoE, 2003a, p. 11)
The concerned citizen needs to be aware that statistics can often be used to support opposing arguments … (DoE, 2003a, p. 11)
In the information age, the power of numbers and mathematical ways of thinking often shape policy. Unless citizens appreciate this, they will not be in a position to use their vote appropriately. (DoE, 2003a, p. 11)
Being mathematically literate implies an awareness of the manner in which Mathematics is used to format society and enables astuteness in the user of the products of Mathematics (DoE, 2003a, p. 43)
An explicit statement of intention for the promotion and development of Cultural Identify is also included, specifically in reference to the promotion of ethnomathematical principles in the teaching of Mathematical Literacy:
Another aspect of providing access and affirmation for learners of Mathematics is to look at examples of Mathematics in the variety of cultures and societal practices that exist in our country. (DoE, 2003a, p. 43)
Ethnomathematics provides a wealth of more recently developed materials,
sensitive to the sacredness of culture, for use in the classroom. (DoE, 2003a, p. 43) ... use the concepts of rotation, symmetry and reflection in describing decorative Ndebele and Sotho mural designs. (DoE, 2003a, p. 29)
Finally, references are also made to an intention for the development of mathematically literate behaviour to facilitate Environmental Awareness. Many of these references are contained in listings of specific contexts for investigation or examples of fields of application that are embedded in the assessment standards in the curriculum component of the NCS rather than in the statement of purpose for the subject (which, perhaps, hints at the secondary importance placed on this intention). For example:
... use mathematical literacy in a critical and effective manner to ensure that science and technology are applied responsibly to the environment and to the health of others (DoE, 2003a, p. 10)
... investigate the rate of depletion of natural resources (DoE, 2003a, p. 21)
... interpret graphs of temperature against time of day during winter over a number of years to investigate claims of global warming (DoE, 2003a, p. 23)
Despite the varied reference to several statements of intention in the Mathematical Literacy component of the NCS, and despite the dominant intention for Social Change in the broader NCS framework, my reading of the NCS leads me to contend that the dominant intention promoted for Mathematical Literacy is for the development of Human Capital. Engagement with the NCS presents the reader with an image that a mathematically literate learner is a learner who is empowered to use mathematics to solve problems and inform decisions relating to their daily-life experiences. A mathematically literate person is financially savvy, economically productive, and engaged critically on economic, social and political issues. In short, a mathematically literate individual is a (more?) desirable commodity. This conception of mathematical literacy is consistent with the dominant intention identified within the international literature read for this study.
8.3.1.5.2 Dominant Agenda(s) for the NCS conception of the subject-matter domain of Mathematical Literacy
The second dimension in unpacking the dominant orientation prioritised in the subject- matter domain of Mathematical Literacy involves the issue of Agenda, which relates specifically to the extent to which the learning of mathematical content, techniques and
mathematised forms of participation are prioritised over contextual sense-making practices (or vice versa). In previous discussion above I have highlighted issues relating to the dual emphasis on content and context in the NCS curriculum and the, sometimes, ambiguous statements in supporting documents regarding the form of legitimate participation – and the structure of knowledge according to which legitimate participation is determined − in the practices of the subject. Drawing from this discussion, it is my contention that at the level of intended purpose the NCS promotes a form of participation in the subject that reflects, primarily, an agenda associated with the second category:
namely, developing the ability to perform calculations in real-world contexts. More specifically, the NCS promotes the dimension of Agenda 2 that is characterised by Application (i.e. Agenda 2 [a]) (as opposed to mere Numeracy-in-Context − Agenda 2 [b]). Furthermore, the NCS posits as a key component of legitimate participation in the subject the utility of a variety of forms of mathematical content (both complex and elementary, and including esoteric contents such as trigonometry) in engagement with real-world problem-solving contexts. The NCS document does also include rhetoric that alludes to modelling processes (Agenda 3); however, the dominance of explicit statements of mathematical contents and structures in the Assessment Standards in the curriculum document ensures that the direction of movement is always from the mathematics to the extra-mathematical.
It is my opinion that the NCS curriculum has never prioritised a form of participation that has as a primary objective the development of mathematical competence (Agenda 1 in the framework). Rather, the NCS curriculum is built on the assumption that learners entering the subject already have an understanding of some level of mathematical content (having completed Grades 8 and 9 level mathematics) and, so, focus in the subject should be on contextualised applications of the already learned mathematics. Similarly, although the NCS hints at the development of mathematically literate behaviour for contextual sense-making practices (Agenda 4 in the framework), the specific body of content listed for the subject clearly prioritises mathematical agendas over the contextual terrain.
Importantly, however, not all of the documents that accompany and/or support the NCS curriculum prioritise the same agenda or the same component of an agenda. Specifically (and as is discussed in more detail immediately below), all of the documents that specify the structure and focus of assessment-related practices in the subject prioritise forms of participation consistent with the Numeracy-in-Context (and not the Application) component of Agenda 2. By contrast, the Teacher Guide document (DoE, 2006) that provides examples of the types of pedagogic practice expected in the subject prioritises a form of participation that reflects an agenda for modelling processes (Agenda 3). This inconsistency in the dominant agenda prioritised in the different documents made available to teachers is a likely explanation for the spectrum of pedagogic agendas that Venkatakrishnan and Graven (2007) have identified in classroom practices in the subject.
As mentioned directly above, at the level of implementation it is, I contend, the Numeracy-in-Context dimension of Agenda 2 that dominates in national assessment practices (and also in the documents that elaborate on the structure of these assessment practices, such as the Subject Assessment Guidelines (DoE, 2005b, 2007, 2008d) and Examination Guidelines (DoE, 2008c, 2009c)) and, so, also at the level of classroom practice. A quick reading of any of the Grade 12 Mathematical Literacy national examinations since 2008 provides clear evidence of this predominantly mathematical agenda, with each and every question driven by a particular mathematical concept or calculation, and with the structure and organisation of the examination papers around mathematical content topics rather than around contexts or real-world problem situations.
Participation in the examinations is legitimated according to mathematical knowledge and structures, and successful participation in the examinations is determined to a large extent by the ability of the participants to generate mathematically accurate narratives.
Contextual sense-making practices (Agenda 4) are largely absent and reference to contextually relevant knowledge and forms of participation and communication are considered inappropriate for use in the examinations. Furthermore, any included contexts serve simply to provide settings in which calculations can be performed, and understanding of contextual elements is neither necessary for successful engagement with the questions or for the generation of endorsable narratives to the problem scenarios. The extract shown in Figure 16 on the page below, taken from the 2009 National Mathematical Literacy Paper 1 examination paper, illustrates clearly and explicitly the irrelevance of the contextual domain and the dominance of mathematical calculations, knowledge structures and considerations as the basis of legitimate participation in the subject (DoE, 2009a, p. 4).
While the dominant agenda in the NCS curriculum for mathematical forms of application shares similarity to trends in the dominant agenda prioritised in international perspectives on mathematical literacy, numeracy and/or quantitative literacy, the same cannot be said for implemented practice in the subject-matter domain of Mathematical Literacy. While much of past and current practice in the subject is characterised by a dominant agenda that promotes and prioritises a structure of participation involving contextualised numeracy-type calculations with elementary mathematical content (i.e. Agenda 2 [b]), only a small number of perspectives on general conceptions of mathematical literacy, numeracy and/or quantitative literacy prioritise the same agenda. Instead, most other perspectives promote an agenda for mathematical literacy that involves more complex and intricate problem-solving processes, characterised either by application of more complex mathematics (i.e. Agenda 2 [a]), or by modelled engagement with more complex contextual environments (i.e. Agenda 3). The implemented reality of Mathematical Literacy in South Africa, thus, promotes a form and agenda of or for mathematically literate behaviour that is largely not prioritised in other parts of the world.
Figure 16: Extract from the 2009 National Mathematical Literacy Paper 1 Examination