This study investigates the effect of using Van Hiele’s instructional model in the teaching of congruent triangles in grade 10 in Gauteng high schools. Three randomly selected high schools in Gauteng formed the research fields, while intact groups of grade 10 learners in these schools formed the study participants (136 learners) for the study. A mixed method approach which was adopted for the study, using pre-test/post-test matching control group design and classroom observation. The pre-test/post-test was used to collect quantitative data, while classroom observation was used to glean qualitative data. Some of the findings from the quantitative data analysis suggested that the intervention improve the achievement scores in the experimental groups while the qualitative data was revealed that the intervention facilitated the learning of the concepts of congruent. It was recommended that Van Hiele learning and instructional model be adopted and applied in the teaching of other areas of mathematics / Mathematics Education / M. Sc. (Mathematics Education)

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)