Theories in the of teaching mathematics in foundation phase

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THEORIES IN THE OF TEACHING MATHEMATICS IN FOUNDATION PHASE

The intention of this section is to provide an overview of theories of learning suggested by theories in relation to the learning of mathematics. Theories help teachers to conceptualise learning communication, promote interpersonal relationships between teachers and children, help teachers to implement professional ethics and exert an impact on how teachers regard themselves. According to Illeris (2004) and Ormrod (1995), learning is generally explained as a process that involves the emotional, cognitive and environmental influences and experiences for gaining, enhancing, or making changes in a person’s values, skills, knowledge, and world views. A learning theory is an endeavour to explain how animals and human beings learn, thereby helping to understand the inherently complex process of learning. Learning theories have two main values, according to Hill (2002). On the one hand, they provide us with vocabulary and a conceptual framework to interpret the examples of learning that we observe. On the other hand, they suggest where to look for solutions to practical problems. Theories direct attention to the variables that are important in finding solutions, but do not themselves give the answers.

THEORETICAL FRAMEWORK

According to Henning, van Rensberg and Smit (2005:25) a theoretical framework is a lens on which the researcher positions his or her study. It helps with the formulation of the assumptions about the study and how it connects with the world. It is like a lens through which a researcher views the world and orients his or her study. It reflects the stance adopted by the researcher and thus frames the work, anchoring and facilitating dialogue between the literature and research. This research is framed within constructivism theory because the aim is to understand chow teachers teach children to actively construct new ideas and derives meaning from them. This also implies that the child should be able to explain what he has learnt or to be able to practically apply the knowledge gained. For instance, the child should be able to use the knowledge gained in a lesson on addition to count the number of marbles he has. The theories that influence the way mathematics should be taught are discussed below.

Constructivism and understanding of cognitive development in children

One of the scholars within the constructivism theory is Vygotsky (1978). Vygotsky has helped us to understand that the development of cognition in the young, and the social construction of knowledge itself are related processes. Both involve the construction and transmission of values, information, and ways of understanding through processes of social interaction (Donald et al., 2010:81). Vygotsky (1978) stresses the role of the mediator in the developmental construction of knowledge. His concept of the zone of proximal development (ZPD) incorporates the notion of active agency on the part of the child. He helps us to understand that knowledge in general is not passively received (Donald et al., 2010:80). Thus children provide feedback orally or through written work.

The influence of constructivism in foundation phase learning

Van de Walle (2007:28) alleges that the theory of constructivism suggests that teaching does not imply transferring information to children. Furthermore, he explains that learning is also not a process of passive imbibing of information from books or teachers. He alleges that children construct meaning themselves when the teaching and learning process is based on an interactive classroom situation in which children are actively engaged in learning (Van de Walle, 2007:39). In active learning, the children handle concrete objects to better understand and gain knowledge. The children will also use their own words to explain the information gained from their engagement with the milieu. In this manner children are afforded an opportunity to develop the acquired knowledge and understanding through active learning. By discussing their actions and how they solve the problems, their numerical knowledge is enhanced (DoE, 2003:65).

MATHEMATICS: A UNIVERSAL PROBLEM

The problem of poor mathematics performance is not only experienced in South Africa, it is universal (Reddy, 2003:17). In an attempt to address this problem in Australia, Van Kraayenoord and Elkins (1998:370-371) and Brown, Askew, Baker, Denvir and Millet (1998:375) identified certain factors that contribute to poor mathematics performance, namely: teaching method (whole class teaching); failure to use knowledge associated with mathematics; language; lack of flexibility; beliefs; and quality of educator–child interaction. Galton and Simon (Eds) (1980), Good, Grouws and Ebermeier (1983) and Brophy and Good (1986) also noted that poor performance in mathematics has always been associated with whole class teaching. The view of this researcher is in agreement with the above-mentioned authors.

TABLE OF CONTENTS :

• Page
• Declaration
• Acknowledgements
• List of abbreviations and acronyms
• Appendixes
• List of tables and figures
• Chapter 1 Orientation to the study
  • 1.1 Introduction and background
  • 1.2 Conceptualisation of the problem
  • 1.3 Awareness of the problem
  • 1.4 Statement of the problem
  • 1.5 The aim of the study
    • 1.5.1 Secondary aims
• 1.6 Research methodology
• 1.7 Research design
• 1.8. Methods of research
• 1.9 Research techniques
  • 1.9.1 Observations
  • 1.9.2 Interviews
  • 1.9.3 Document analysis
• 1.10 Significance of the study
• 1.11 Delimitation
• 1.12 Definitions of concepts
  • 1.12.1 Barriers/Difficulties
  • 1.12.3 Children
  • 1.12.4 Learning barrier
  • 1.12.5 Foundation phase
• 1.13 Chapter outline
  • 1.14 Conclusion
• Chapter 2 Literature review
  • 2.1 Introduction
  • 2.2 Theories in the of teaching mathematics in foundation phase
    • 2.2.1 Theoretical framework
    • 2.2.2 The influence of constructivism in foundation phase learning
    • 2.3 Identification of mathematics difficulties in children
  • 2.4 Mathematics: a universal problem
    • 2.4.1 Various misconceptions about mathematics teaching
    • 2.4.2 Language issues in the teaching of mathematics
    • 2.4.3 Teacher challenges in the teaching of mathematics
  • 2.5 Teacher development for addressing mathematics problems
    • 2.5.1 Teachers’ mathematics knowledge
  • 2.6 Mathematics teaching approaches
    • 2.6.1 The Mathematics Skills approach
    • 2.6.2 The Mathematics Conceptual approach
    • 2.6.3 The Mathematics Problem solving approach
    • 2.6.4 The Mathematics Investigative approach
    • 2.6.5 Mathematics: the enjoyable way
  • 2.7 Child related factors in the teaching and learning of mathematics
    • 2.7.1 Child’s conceptual knowledge
    • 2.7.2 Child led family
  • 2.8 The acquisition of early mathematics
    • 2.8.1 Children’ early mathematics–England
    • 2.8.2 Children’ early mathematics – People’s Republic of China
    • 2.8.3 Children’s early mathematics in France
  • 2.9 Grade 3: Mathematics curricular in South Africa
    • 2.9.1 Curriculum
    • 2.9.2 The Revised National Curriculum Statement (RNCS)
    • 2.9.3 National Curriculum Statement (NCS)
    • 2.9.4 Curriculum and Assessment Policy Statement (CAPS)
• 2.10 Chapter summary
• Chapter 3 Intervention strategies for supporting children who experience mathematics problems
  • 3.1 Introduction
  • 3.2. Principles of effective practice in mathematics teaching
  • 3.3 An early intervention strategy in literature and mathematics programme
  • 3.4 Oxford mathematical recovery scheme
  • 3.5 Intervention programme focusing on basic numerical knowledge and conceptual knowledge
  • 3.6 An early childhood intervention programme and the long– term outcomes for children
  • 3.7 Mathematics Recovery Programme (MRP)
    • 3.7.1 Findings of the programme (MRP)
  • 3.8 Strategies to improve mathematics
    • 3.8.1 Australia – National inquiry into the teaching of literacy
    • 3.8.2 England – National Numeracy Strategy (NNS)
  • 3.9 Intervention strategy at school level in the south african context in the classroom
  • 3.10 South Africa – The Foundation for Learning Campaign (FFLC)
  • 3.3 Conclusion
• Chapter 4 Research design and methodology
• Chapter 5 Data report, analysis and interpretation
• Chapter 6 Conclusions, limitations, recommendations and summary of the study

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TEACHER CHALLENGES IN THE TEACHING OF MATHEMATICS AT FOUNDATION PHASE