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,0\wIb+0vIACF0F[AK?1^K$AKA!--r13.\.L!-!-!-WFWF1"!-!-!-F////b+b+T 6V*T~6Mathematical Literacy as a school subject in the new South Africa:Big ideas, superficial engagement
Iben Maj Christiansen
School of Education and Development, Faculty of Education, University of KwaZulu-Natal
HYPERLINK "mailto:christianseni@ukzn.ac.za" christianseni@ukzn.ac.za
Abstract
As the first country in the world, South Africa is introducing Mathematical Literacy as a school subject. The South African National Curriculum Statement (NCS) for Mathematical Literacy is part of a progressive agenda for transformation towards increased democracy and social justice. It claims that the new school subject Mathematical Literacy (ML) will provide learners with awareness and understanding of the role that mathematics plays in the modern world. However, the analysis developed in this paper indicates that the superficial engagement with complex applications of mathematics implied by the ML NCS is not likely to live up to its claim its vision is saturated by the myth of mathematics utility to everyday practices, while the curriculum is largely organised around mathematics which is often not of utility in everyday practices. As a result, the NCS renders invisible to the learners the organising principles of the content, and thus is dis-empowering. In addition, we do not understand enough about the connections between mathematical, technological and reflective knowledge/knowing/competencies to know how to facilitate the awareness and understanding that is part of the vision of the ML NCS. Furthermore, the NCS assumes simple transfer, which has been challenged by substantial bodies of research, and which refutes learners agency in determining similarities between activities or practices.
The Notion of Mathematical Literacy
Different views on ML as a competency. ML as a school subject the visions behind the NCS.
A Curriculum driven by Applications viewed through Dowlings Myths of Reference, Participation and Emancipation
It proved rather difficult to code the assessment standards to see if they were relevant to everyday practices or ordered by mathematics. A single assessment standard could contain a range of statements and examples that had to be considered together. Furthermore, I found that many of the standards were not obviously everyday or mathematics driven. Thus, I had to include a category for assessment standards that would signify experiences with the potential to lead to exemplary insights. For instance, comparing different data sets using statistical descriptors (12.4.3) would not be something the learners would be likely to engage in, in their adult lives, but it has the potential to lead to an increased understanding of descriptors appearing in the media, for instance.
Coding the 18 assessment standards for grade 11 in this manner, I found that 5 referred to competencies with some potential everyday use, 10 had the potential to offer exemplary insights as described above, 7 were strictly ordered by mathematics, and 1 referred to generic skill which I would think most learners develop in practice anyway.
This indicates that the NCL for ML is less driven by everyday applications than implied by its stated purpose. In my view, the exemplary competencies are much more relevant to the progressive agenda since they have the potential to develop insights which are not likely to be encouraged in everyday practices, and I would consider this the strength of the curriculum. Nonetheless, the formulation of the assessment standards are clearly written with a focus on learning the skill, with the contexts as illustrators of the use of mathematics, rather than mathematics being used as a tool to solve a specific problem. Thus, they are mostly a result of looking at the world with a mathematical gaze.
From a mathematics perspective, we can say that significant recontextualisation takes place of the everyday practices in order for us to apply mathematics to them. However, even this is belying the nature of the everyday activities mentioned here. These activities are not mathematical; disciplinary knowledge and everyday knowledge are not organised in the same way ADDIN EN.CITE Muller2002181cf. also 7181Muller, Johan2002Progressivism redux: Ethos, policy, pathosKraak, A.Young, M.Education in Retrospect: Policy and Implementation since 1990Pretoria & LondonHuman Sciences Research Council (SA) & Institute of Educationhttp://web.uct.ac.za/depts/educate/staff/progressivismredux.pdf(cf. also Muller, 2002). Thus, were the curriculum organised around applications, it may well teach the learners relevant competencies and knowledge, but it would not be mathematics.
The myth of participation also assumes that it is possible to separate skills from their goals, and thus not only assumes mathematics to be decontextualised (general knowledge), but also that transfer of skills is likely to happen.
The Transfer Assumption
It is therefore relevant to investigate the assumptions about transfer reflected in the NCS for ML. Using N-Vivo, I have coded the statements of the curriculum into Paul Dowlings four domains of practice (see Dowling, 1998, p. 135 or Parker, 2006, pp. 67-70 for a brief discussion). Since the assessment standards vary in format, sometimes consisting of a list of bulleted points, sometimes containing only one sentence containing a list of items, I often had to code parts of a standard as belonging to different domains. Furthermore, some standards are open to interpretation, and therefore I coded them as belonging to more than one domain. The table below shows how many of the 18 assessment standards for grade 11 contained coding belonging to each domain.
Esoteric domainDescriptive domainPublic domainExpressive domainGrade 11710 + 5 open to interpretation61
Most of the statements in the NCS for ML were coded as belonging to the descriptive domain, which is characterised by the recontextualisation of a non-specialised setting but describes the contents of this setting in mathematical forms of expression. One example is Work with numerical data and formulae in a variety of real-life situations, in order to establish relationships between variables by: o finding break-even points; o finding optimal ranges. (11.2.1) This type of statement was often combined with statements coded as belonging to the esoteric domain such as Types of relationships to be dealt with include two simultaneous linear functions in two unknowns, inverse proportion, compound growth [only positive integer exponents] and quadratic functions. (11.2.1) Or they were open to interpretation as belonging to the public domain, with its appearance as non-specialised practices. Statements only coded as belonging to the public domain did, however, dominate the assessment standards for the fourth outcome, as in Investigate a problem on issues such as those related to: social, environmental and political factors; (11.4.1)
To me, this dominance of the descriptive domain implies that the curriculum is intended to teach the learners something they either can apply in the original settings or which will inform them more generally in those same or similar settings. In that sense, transfer is implied. Likewise, the purpose of the NCS appears to rest on an assumption of direct transfer. It says:
International studies have shown that South African learners fare very poorly in mathematical literacy tests when compared to counterparts in other developed and developing countries. Learners who could not do well mathematically in General Education and Training usually stopped studying Mathematics, thus contributing to a perpetuation of high levels of innumeracy.
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.
Differences in context and relevance of various test items may contribute to the low test scores of South African learners together with language difficulties (cf. Dempster, 2007). The first paragraph remains silent about this, and thus reflects an assumption that numeracy is testable away from its context of use, also ignoring the research showing how differently people perform in different contexts. It makes the mistake of assuming that numeracy/mathematical literacy is closely linked to the level of mathematics studied in a school context, which not only assumes fairly straight-forward transfer, but also ignores that people learn other/additional knowledge and competencies in the contexts where they need them. This assumption is also reflected in the expectations put on the ML subject, namely that it will make the citizens of the future highly numerate.
The NCS for ML falls into the same trap as some of the transfer researchers, namely to assume that the similarities which the researchers/curriculum authors recognise are those worth considering. Thereby, it is assuming that the mathematical gaze of the mathematicians and ML curriculum designers is a relevant gaze in at least some everyday life contexts.
The Role of Mathematics in Society
The National Curriculum Statement for Mathematical Literacy writes about the role played by mathematics as if it can be assumed that this role is well known, not the least to the educators. But what do we know about this role? Some general philosophical considerations have been given to it, but the literature still only contains sketches of an understanding.
We know that mathematics can be a powerful modelling tool. It is in modelling complex phenomena that mathematics assists us in developing insights we otherwise could not have had. Some of the examples listed in the NCS belong in this category. For instance, a dialogue between medical sciences (including community health science) and mathematics can lead to the development of a model for AIDS. Complex mathematical models, based on natural geography and geo-physics, have been developed for the interplay between our impact on the environment, global warming and the depletion of the ozone layer. Statistical models can be used to indicate the extent to which two factors can be said to be correlated. On the other hand, this also means that mathematics can change the discourses around these issues.
I refer to the transformation of a fundamentally political problem into a question which can be addressed through technical means as the technocratic transformation (Christiansen, 1996a).
Perhaps it is these roles of mathematics to which the NCS refers, when it states that Mathematical Literacy provides learners with an awareness and understanding of the role that mathematics plays in the modern world? If so, we are lacking analyses of the ways in which mathematics influences decisions and political debates in South Africa. It may be that the expert ideology is less prevalent here than in the European countries from which the philosophical considerations above arise.
However, let me, for the purpose of this paper, assume that mathematics does indeed play the same role in South Africa as in Denmark, where the analyses of Skovsmose and myself originate.
Paradoxically, some of the examples given in the NCS refer to fairly advanced mathematical models, but the learners are not expected to engage with the models on a level which would lead to substantial insights neither in the phenomena modelled nor in the technocratic transformations and other alterations of discourses generated through the use of mathematics and science.
Facilitating learners awareness of the role of mathematics in society
The NCS for ML is, naturally for an outcomesbased curriculum, mostly concerned with the competencies which learners should be able to demonstrate at the end of their education. There is mention of what learners should or could engage with to become more aware of the role of mathematics in society. All fourteen of these examples (excerpts of the 57 outcomes statements and assessment criteria) are about critical investigation or discussion of the use of mathematics.
Reflecting on experiences from elsewhere in the world with facilitating learners awareness of the role of maths in society.
Though most of these experiences are from other political, social and cultural contexts, they do illustrate that learners awareness of the role of mathematics in society is not straight forward to facilitate. Through engagement with authentic problems, classroom practices may still eventually come to frame a reflective practice within which the relation between science, technology, mathematics and society can be addressed in a way which is not possible in the work-related or disciplinary practices. But we do not understand enough about how these practices, with their recontextualised critical mathematics discourse, are developed and sustained, to know how to ensure the vision of the NCS.
Epistemological Access with an non-transparent curriculum
The introduction of ML as a school subject was in part driven by a vision of a non-esoteric mathematics with real use value, which could still provide reasonable access to further education, etc. This obviously raises the important question: Is it possible to combine access to existing areas of privilege (epistemological access) and at the same time further social empowerment of learners?
A curriculum mostly organised around the myths of reference and participation belies the differences in organisation of mathematical knowledge and everyday knowledge. By claiming that it is about life-related topics, the curriculum renders the underlying (mathematical) organising principles of the content invisible to the learners (and possibly to some teachers, too), who therefore will not learn mathematics, unless the teacher is in a position to ensure coherence and progression of mathematical concepts. The learner who thinks that AIDS is the topic, when it really is about reading graphs, will get it wrong, yet the curriculum does not encourage that the learner is given the necessary guidance to develop the mathematical concepts of graphs.
If learners learn neither mathematical knowledge nor competencies of relevance to their lives, neither mathematical gaze nor livelihood gaze, what do they learn? Perhaps to submit to a practice ordered by principles invisible to them, thus in a strong yet subtle way disciplining them away from subjectivity and control over their lives?
The selection of knowledge considered worthwhile in the constitution of the ML curriculum is reflecting a continuation of existing relationships of power and social control, and thus is far from its proclaimed transformation goals.
Conclusion and Discussion
Acknowledgements
References
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