This study provides a qualitative examination of the role of visualization through an understanding of the thought processes that occur during visualization when Grade 9 learners engage in data handling and spatial tasks. Data were gathered in a problem-centred context from learners' written responses in order to determine the students' visuality. Visuality is defined as how often learners used visualization. In addition interviews were conducted with the learners who described the thought processes that they engaged in during visualization while involved in problem solving. The role of visualization was highlighted through the processes that learners described during the interviews. The tasks which provided manipulative materials helped learners create visual images which promoted the process of visualization. Certain recommendations were made. Knowledge of the role of visualization enables the educator to encourage the use of visualization during the teaching of mathematics. / Educational Studies / M.Ed. (Mathematical Education)

This study provides a qualitative examination of the role of visualization through an understanding of the thought processes that occur during visualization when Grade 9 learners engage in data handling and spatial tasks. Data were gathered in a problem-centred context from learners' written responses in order to determine the students' visuality. Visuality is defined as how often learners used visualization. In addition interviews were conducted with the learners who described the thought processes that they engaged in during visualization while involved in problem solving. The role of visualization was highlighted through the processes that learners described during the interviews. The tasks which provided manipulative materials helped learners create visual images which promoted the process of visualization. Certain recommendations were made. Knowledge of the role of visualization enables the educator to encourage the use of visualization during the teaching of mathematics. / Educational Studies / M.Ed. (Mathematical 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)

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)