This study set out to investigate how the use of a Smart Board impacts on the teaching and learning of algebraic functions. The research took place in a school equipped with Smart Boards in each Mathematics classroom. Data collection involved lesson observations in three classes over three lessons each. The teachers and learners were interviewed post observation and the data obtained were analysed according to Sfard‘s three-phase model framework to determine if the learners had a procedural or object view of a function after having been taught on a Smart Board. The findings show that by using a Smart Board learners had both procedural and object view of functions however, much of the teaching occurred in a way which would have been possible without the use of a Smart Board, indicating that teachers did not fully utilise the potential of such a technological tool. However, it emerged that visualisation played an important role in allowing learners to operate on functions as objects. So while the visualization that technology enables encouraged reification or allowed teachers and learners to operate on functions as a whole or even on families of functions, this appeared simply to 'speed up‘ the normal teaching-learning process rather than promote the explorative and investigative aspect of learning. Still, it must be acknowledged that this kind of practice is bound to strengthen these learners‘ function concepts as was evident in the ways they appeared to operate confidently on the objects as shown in the study. It must be acknowledged that teachers were extremely enthusiastic about the possibilities of the technology and were inspired to use technology more in their lessons to allow learners‘ visualisation of concepts. Positive comments made by learners showed that they too, were also motivated by the use of the Smart Board. / Thesis (M.Ed.)-University of KwaZulu-Natal, Pietermaritzburg, 2011.

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)