CHAPTER 1 INTRODUCTION
2.3 THEORETICAL FRAMEWORK
The first outcomes-based curriculum introduced in democratic South Africa was known as Curriculum 2005 (C2005) and was introduced into schools in 1998. (DoE, 2006, p. 12).
The curriculum introduced new perspectives and challenges for the teaching and learning of mathematics. Amongst the various challenges, there is also a shift to a problem centred or constructivist approach to the teaching and learning of mathematics as implied in the new curriculum documents.
Moll (2002) stated that the underlying theory of the C2005 is constructivism. He commented that the document Curriculum 2005: Towards a Theoretical Framework (DoE, 2000) looked explicitly towards constructivism to provide the teaching and learning solutions called for by OBE (Outcomes-Based Education) in South African schools. He contends that the Department takes a position and holds 'constructivism' to be the basis of the new teaching approach called for by OBE (p. 6).
What is Constructivism? According to Epstein (2002), constructivism, a theory of learning, emphasizes the importance of the knowledge, beliefs, and skills an individual brings to the experience of learning. It recognizes the construction of new understanding as a combination of prior learning, new information, and readiness to learn.
principles of learning that are derived from constructivism. Of these nine principles, four are directly related to this study:
• Learning involves language: the language that we use influences our learning.
• Learning is a social activity: our learning is intimately associated with our connection with other human beings, our teacher, our peers, our family, as well as casual acquaintances.
• Learning is contextual: we learn in relationship to what else we know, what we believe, our prejudices and our fears.
• One needs knowledge to learn: it is not possible to absorb new knowledge without having some structure developed from previous knowledge to build on. (p. 3)
I will briefly discuss how these four principles relate to this study. The focus of this study is on the CTA's in MLMMS, which are based on 'real- life' contexts. The language used in the CTA influences how learners respond to the CTA. The 'language' in this case is not only the written language of the CTA; the dialect of learners will also influence how they respond to the CTA. Secondly, over the years, learners have related to a number of individuals including parents, teachers, community and peers. These relations would have influenced the knowledge learners have developed. Thirdly, learning is contextual. The 'context' here has various interpretations.
The word 'context' is not as simplistic as it is assumed to be. Context on the one hand, could refer to contexts that learners are familiar with. Familiar contexts also create belief systems, prejudices and fears. Contexts such as HIV/Aids may be a sensitive context while contexts such as the seaside or Robben Island, may be unfamiliar. Contexts could also refer to the situation in which a problem is embedded. The context of the classroom also influences learning. As a result the learners are influenced by a number of factors when relating to context as a situation with a problem embedded in it or to the context of the classroom or examination. Lastly learners will respond to the CTA's on the basis of what they already know. When these learners attempt the CTA in the fourth term, they have already successfully completed 8 years of schooling and three terms of grade nine.
During my study, I could not escape the fact that language was an issue since the MLMMS CTA is language based. I was forced to search for literature that would help me understand the situation better. I found Au's (1998) study helpful and enlightening. Au uses social constructivism to address the literacy achievement gap of students of diverse backgrounds.
Au describes learners of diverse backgrounds as learners who are from low-income families; African American, Asian American, Latina/o, or Native American ancestry; and speakers of a home language other than the standard American English. In her study, to develop the argument for a diverse constructivist perspective, Au discusses social constructivism and its application to school literacy learning.
Au (1998) identified 5 explanations for the literacy achievement gap.
The 5 explanations are:
Linguistic differences: linguistic differences stem from the fact that many students of diverse backgrounds speak a home language other than Standard English.
Cultural differences: students have difficulty learning in school because school instruction does not follow their community'S cultural values and standards for behaviour.
Discrimination: the system of schooling is structured, so as to prevent equality of education and outcome.
Inferior education: students of diverse backgrounds are exposed to deteriorating buildings, outdated textbooks, and inexperienced teachers. Material circumstances in these schools led to inequalities in education.
Rationales for schooling: high school fees, schools' constitutions/rationale favour mainstream learners instead of learners from diverse backgrounds. In this case, mainstream learners refer to those whose home and school language is English.
Although Au's (1998) explanations relate to her study on literacy achievement, it is applicable to any study across the curriculum. It is particularly relevant to this study because the school that was used has learners from low-income families. The school fee of R750 per year, is an indication of which income group the school services. It is also particularly relevant to this study, which focussed on the eTA, which involved extensive use of language.
While Mathematics has its own 'language' and terminology, nevertheless learners in my study were taught through the medium of English. As a result language plays a significant role in how learners interpret and make meaning. Vygotsky (1934) stated, "it is not merely the content of a word that changes, but the way in which reality is generalized and
MLMMS has mathematiCal tasks embedded in a context.
Zevenbergen (2001), states that "providing a context for a problem means it has to be embedded in words" (p. 46). This brings me back to the statement by Vygotsky, which says, "reality is generalized and reflected in words". The CTA is embedded in words and reality is generalized in these words. By embedding the tasks within a context is generalizing reality and assuming that the reality is familiar to all learners.
With reference to the 2005 CTA, the theme is the Kruger National Park. The reality of Kruger National Park is generalized and assumed to be familiar to all learners. However it is compulsory for all grade 9 learners to undertake the CTAs. Consequently learners from diverse backgrounds as well as learners whose home language is not English are compelled to write the eTA. Learners who lack proficiency in English are suddenly faced with tasks for mathematics centred on language because the reality of the Kruger National Park is generalized and reflected in language in the form of mathematical tasks embedded in words.
Vygotsky (1934) complements his earlier statement by stating that words lead to thought processes.
The relation of thought to word is not a thing but a process; the relation of thought to word undergoes changes that themselves may be regarded as development in the functional sense.
Thought is not merely expressed in words; it comes into existence through them. Every thought tends to connect something with something else, to establish a relation between things. Every thought moves, grows and develops, fulfils a function, solves a problem. (p. 2 I 8)
This is relevant to this study because the CTA had many tasks that involved a large number of words. With learners whose home language is not English, each word forces the learners to connect the words to something they already know so as to 'make sense' of the words.
Each word in English has to be understood before applying the mathematics in the particular context. Zevenbergen (2001) substantiates this point by stating that there are specific examples of language that can cause a barrier to the access learners have to learning mathematics. Walkerdine (as cited in Zevenbergen, 2001) emphasizes the point of language being a barrier. The study showed that two words namely, 'more' and 'less' are used differently according to social background. The study also documented that working-
class families are less likely to use the word 'less' than middle class families. This study suggests that "many of the working- class students may not have the language, and hence concepts, to comprehend clearly and unambiguously what is meant" (p. 43).
The role of how learners experience mathematical tasks based on real-context is also a central focus of this study. In some cases the real-context has no relevance to mathematics and learners have to ignore the context and focus on the mathematics. Mathematical tasks presented in real-context have the potential to produce a variety of responses as well as multifaceted solutions for some learners.
This study embraces the basic view of constructivism. Central to this broader study is that constructivism is used in a descriptive position. Built on this descriptive position is the firm belief in the use of both language and real-contexts as important mediators in the process of knowledge construction.
2.4 CHAPTER SUMMARY
In this chapter, the literature review focused on real-life context in mathematics and Department of Education curriculum documents. The theoretical framework that underpins this study was presented.
RESEARCH METHODOLOGY AND DESIGN OF STUDY
This chapter will present the research methodology and the design of the study. Secondly, the qualitative approach that was adopted for this research project, together with the critical questions upon which this research was based, is discussed. Thirdly, this chapter examines the context of the study and provides an explanation of the process of the selection of the participants. Finally, the design of the study and the data collection instruments, which were used to investigate how learners experienced the Common Tasks for Assessment in Mathematical Literacy, Mathematics and Mathematical Sciences, is discussed.