• The problem of perceived differences between school mathematics and mathematical literacy could be overcome or resolved by incorporating
ethnomathematical practices or ordinary everyday indigenous knowledge into school mathematics rather than to have split streams.
It is perhaps important at this stage (in the light of the foregoing) to consider what the implications of these results are, given that the new curriculum has already been introduced and has to be implemented. As the results have shown, most participating teachers viewed mathematical literacy as a subject, and as such have highlighted their concerns relating to its introduction and implementation. Furthermore, the results showed that many of the issues or factors that have been raised are related and interdependent in some ways. Hence, in the following sections I will discuss these findings in terms of their implications for policy and practice, as well as for further research.
South African high schools. This is particularly important given that almost all the present mathematics educators in South Africa were trained during the time when traditional approaches to teaching and learning were predominant; in which case then it is understandable that they may find it very difficult to use the novel teaching strategies that are in line with the spirit of OBE which forms the foundation for the curriculum in South Africa. There are two important areas of professional
development that need due attention. First, there is need to strengthen the current teacher education programs by structuring them so as to provide student-teachers opportunity to examine and reflect on their own beliefs and conceptions about mathematics, and also to learn more about the history of mathematics. Secondly, there is need for all mathematics educators to be formally retrained in line with the current curricular and pedagogical reforms especially in the light of the OBE
innovation which stresses the importance of constructivist perspective. Furthermore, there is need for an ongoing professional support that will help mathematics educators to experience for themselves how teaching for the development of mathematical literacy is like. Most of the participating teachers complained about not having been adequately trained for the teaching of mathematical literacy, and thus they did not have ideas on how to conduct such instruction in the context of the FET classrooms.
This, therefore, suggest that teachers need to undergo and experience (from the perspective of a learner) a training that brings together the content knowledge and the pedagogical knowledge, as well as the habits of mind, all of which should provide opportunity for them to reflect on such experiences from the perspective of
mathematics educators. It is also important, as a way of helping educators on the issue of providing relevant contexts, to train teachers on how they can use
ethnomathematics as a tool in the mathematics classroom to help learners make connections and develop deeper mathematical understanding (Masingila & King, 1997). This is, in fact, what mathematical literacy is all about.
The suggested professional development efforts, I believe, can help to address
specifically the issues of lack of adequate content knowledge of mathematics and lack of confidence to teach the subject, thereby helping teachers to be able to subsequently handle the issue of the interplay between content and context in their classrooms. It must be noted, however, that teachers’ beliefs and conceptions of mathematical literacy are invariably linked to mathematics subject, and in one way or the other, this
may have practical implications for their teaching practices (see Thompson, 1996).
For this reason, therefore, it should be expected that efforts to undo old practices through these kinds of professional development activities should be a major undertaking which will render the whole exercise to be costly both in terms of time and financial resources.
Furthermore, it is important to recognize that in the process of implementing mathematical literacy, teachers need help in understanding the concept of
‘mathematical literacy’ itself and what it entails in terms of how teachers should plan the mathematical activities for learners and how to reconcile the interplay between content and context within such activities and within their classroom diversities.
Teachers may, given the large class sizes that they are handling, also need support to reconcile the demands of introducing mathematical literacy activities with classroom management demands. Finally, it is also important to encourage mathematics educators, in the process, to conduct thorough and honest evaluation that will help them to confront their own practices, throughout the initial stages of the
implementation period (which should be at least the first five years). These efforts (and all that have been alluded to earlier), I believe, can make a difference in terms of helping teachers to appraise their professional thinking.
5.2.2 Curricular and Pedagogical issues/factors
The second category relates to curricular factors or elements, and includes macro- and micro elements. On the micro level, there is an immediate need to develop
instructional resources that are pertinent to proper development of mathematical literacy. As has been pointed out earlier, many of the participants were not involved in the teaching of the new subject (let alone in the acquisition of adequate
mathematics qualifications); and for those who were involved, they were not quite confident to handle it. And even as they were struggling to teach it, they simply could not do it satisfactorily due to (a) the high workloads resulting from the many classes and other different subjects that they were expected to teach, and (b) lack of adequate mathematical content knowledge. As a result it was very difficult for them to develop relevant instructional materials or even to prepare appropriate teaching aids. To address this, a crucial first step would be to have carefully constructed instructional materials readily available for teachers. These materials should have three major
characteristics: First, if they are to reflect a commitment to the widely held argument that mathematics provides tools to help us come to understand the world (and, more specifically, it prepares us for citizenship in an increasingly technological world), their primary thrust should be on mathematical activities that make use of
mathematical models to help learners understand realistic problems that they might conceivably encounter in everyday life or in the workplace, and that draw on and reinforce learning about mathematics concepts and topics (including abstractions) central to the required FET mathematics curriculum; secondly, they should integrate and sufficiently provide illustrations of appropriate pedagogical approaches so that teachers with the least modicum of confidence in the new teaching approaches feel that they can also use the materials in their classrooms to teach mathematics. (We should remember that many of the mathematics educators we have in South African schools have been trained in the traditional teaching and learning approaches; hence they are likely to find it difficult to embrace the new reforms); and thirdly, the materials must be designed in a student-centered approach (i.e. with more emphasis on project work) to the teaching and learning of mathematics. Implementing this curricular recommendation, of course, will entail cyclical developments and refinement, in addition to monitoring and investigating the extent to which the developed materials, as used by teachers, affect classroom instruction and student learning. This also suggests that, invariably, there will be no need for prescribed learners’ textbooks which are often recommended for schools.
On the macro level, there should be medium- and long-term mechanisms put in place and aimed at improving (making necessary changes to) the curriculum, as well as to ensure that materials do not easily fall out of favour and use. It was quite evident from the results of this study that almost all the participating teachers were unhappy with adequacy or supply of teaching and learning support materials, and also the professional support they expected from the department; and this should be seen as an indication of the need for a sustained micro curriculum development and macro curricular changes aimed at modifying overall curricular goals, priorities, and emphases directed towards helping teachers to cope with the overall aims and principles of the National Curriculum Statement for Mathematical Literacy.
5.2.3 Learners’ inadequacies to meet curricular demands
The third category (which is the last but not the least) of factors has to do with those that are related to learners. It has been revealed from the results of this study that many high schools in South Africa are facing financial problems resulting from learners’ failure to pay school fees. Consequently this leads to many of the schools not affording to buy appropriate and relevant prescribed textbooks and other related resource materials needed for instruction. To address this problem, there is need for the government to rethink its policy relating to school fees so as to make education accessible to all children, as well as enabling schools to facilitate the successful teaching and learning in mathematics education. The other two crucial factors here are learners’ difficulties with the language of instruction and their lack of adequate knowledge of mathematical concepts. The results of this study showed that some of the participants indicated/asserted that most learners (especially the black learners) in their classes had serious difficulties in understanding the mathematical concepts because of the English language problem. For this reason teachers also find it
difficult to present the mathematical ideas in the way that is intelligible to all learners, thereby making their attempts at providing relevant contexts almost impossible.
Furthermore, given the reality of the South African context, where learners taking the option of Mathematical Literacy are those who will have not passed Mathematics at Grade 9, the issue of English language (or mathematical language) problem in the teaching of mathematical literacy will remain as one of the greatest challenges to teachers. Although it seems like there is very little that can be done to address this language problem, given its association with larger cultural and political factors, Rowlands and Carson (2002) remind us that it would be a big mistake to “…assume that some pupils by virtue of their language use or the colour of their skin have an intrinsically different conceptual approach to maths…..’’ (p. 96) (see also Setati cited in Goba, 2004). In other words, they seem to suggest that language is not really the only problem when it comes to the learning of mathematical concepts (compare with Pillay, 2005). This is a challenge for educators to rethink their pedagogical
approaches to the teaching of mathematics or mathematical concepts if they are to succeed in producing mathematically literate learners.