NATURE AND STRUCTURE OF MATHEMATICS

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In this chapter, literature related to mathematics confidence, reflection and problem- solving are reviewed. The chapter begins with an introduction to mathematics and the occurrence of educational changes and concerns in South Africa. It examines the metacognitive activity reflection and its various facets along with affective issues in mathematics. Then, differentiating between past and current research, the focus will be on how mathematics confidence and reflective thinking relates to the level of achievement and performance in mathematics problem-solving processes. Concluding description will follow, illustrating the relationship between reflection and mathematics confidence during problem-solving processes.

2.1 Mathematics, its nature and structure

Mathematics can be seen as a combination of calculation skill and reasoning (Hannula, Maijala & Pehkonen, 2004:17) and can further be classified as an individual’s mathematical understanding. Mathematics is a process, fixed to a certain person, a topic, an environment or an idea (Hiebert & Carpenter, 1992).

Mathematics originated as a necessity for societal, technological and cultural growth or leisure (Ebrahim, 2010:1). This desire led to the advancement of concepts and theories in order to meet the needs of various cultures throughout time. With its imprint in nature, architecture, medicine, telecommunications and information technology, the use of mathematics has overcome centuries of problems and continues to fulfil the needs of problem-solvers to solve everyday problems. Although mathematics has changed throughout time, in its progress and influences there are interwoven connections between the cognitive, connotative and affective psychological domains. The increasing demand to process and apply information in a South African society, a society characterised by increasing unemployment and immense demands on schools, still awaits recovery and substance from these cognitive and metacognitive challenges (Maree & Crafford, 2010: 84). From a socio-constructivists perspective, developing, adapting and evolving more complex systems should be the aim and goal of mathematics education (Lesh & Sriraman, 2005). According to Thijsse (2002:34) mathematics is an emotionally charged subject, evoking feelings of dislike, fear and failure. Mathematics involves cognitive and affective factors that form part of the epistemological assumptions, regarding mathematical learning (Thijsse, 2002:7 & that will be discussed in the following section.

2.1.2 Epistemological assumptions regarding mathematics learning