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)

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / O estudo realizado nesta dissertaÃÃo, busca apresentar as seccÃes cÃnicas, dando Ãnfase a uma abordagem por meio de uma geometria sintÃtica e elementar, onde o trabalho à desenvolvido da seguinte forma: inicia-se com uma abordagem histÃrica, assim como a sua relaÃÃo com o cone circular; em seguida, à feito um estudo sintÃtico sobre as cÃnicas, exclusivamente, no plano; apresenta-se algumas superfÃcies quÃdricas; a equaÃÃo geral do segundo grau à apresentada como uma representaÃÃo algÃbrica de uma cÃnica e sÃo mostradas diversas situaÃÃes, onde as cÃnicas surgem de forma, curiosamente, natural, alÃm das inÃmeras aplicaÃÃes prÃticas em diversas Ãreas do conhecimento. / The study in this dissertation, seeks to present the conic sections, emphasizing an approach by means of a synthetic and elementary geometry, where the work is carried out as follows: begins with a historical approach, as well as their relationship with the circular cone; then itâs done a synthetic study on the conical exclusively on the plan; It presents some quadric surfaces; the general equation of the second degree is presented as an algebraic representation of a conic and are shown several situations where the conical arise so, curiously, natural, in addition to numerous practical applications in various fields of knowledge.

No description available.