The 2009 intake of university students were the first to have received complete school education within the recently implemented Outcomes‐Based Education (OBE) system. A feature of the matriculation examination results of these students was the exceptionally high Grade 12 marks for Mathematics. This paper addresses the question of how the 2009‐ intake of students performed at university with respect to general performance, general attributes, mathematical attributes and content related attributes. It appears that these students are better prepared with respect to personal attributes such as confidence. However, in many instances they are weaker than their predecessors with respect to mathematical and content related attributes. Yet, there are positive indications that these students adapt and improve over a semester. We make some suggestions on how to make the transition from secondary to university mathematics somewhat smoother.
This paper presents a range of methods for computing the equilibrium configuration of shopping facility sizes. First, the presently available range of quasi-balancing factor methods is considered and built into a theoretical framework in which further algorithms may be defined. Then the use of the gradient method is considered, which is a general method of solution of nonlinear equations. Last, it is shown that a special case exists in which a closed form solution may be obtained.
In this paper, we present the New Modified Adomian Decomposition Method which is a modification of the Modified Adomian Decomposition Method. The new method incorporates the inverse linear operator theorem into the modified Adomian decomposition method for the calculation of u0. Six linear and nonlinear boundary value problems with Neumann conditions are solved in order to test the method. The results show that the method is effective.
Following the political changes of 1994 in South Africa, the decision was taken to replace the traditional skills-based education system at primary and secondary school level (Grades 1 - 12) with an outcomes-based education system (OBE). The OBE approach, referred to as Curriculum 2005, was introduced into schools in 1998. The implementation of the OBE system did not occur without problems, giving rise to revised initiatives and a fair amount of criticism. The 2009 intake of students at universities is the first group of students that had been subjected to the OBE approach for their entire school career. This is also the first group of students for whom some form of mathematics was compulsory up to Grade 12 level in the form of mathematics or mathematical literacy. These students were characterised by the fact that their mathematics marks for Grade 12 were exceptionally high and that many more students qualified for university entrance. This article reports on the impact of this new education system on the mathematics prepared-ness of students entering university. The study involves an empirical analysis of the students in the first-year mathematics course for engineering students at the University of Pretoria as well as an analysis of a questionnaire completed by experienced lecturers at this university. The question addressed in this article is how the 2009 intake of students cope with mathematics at university level with regard to Performance General attributes Mathematical attributes Content-related attributesResults indicate a decrease in mathematics performance of these students at university level and that the inflated matric marks result in unjustified expectations. However, it is not unusual for marks to decrease from school to university and there is still too little evidence for serious concern. The study also indicates that these students seem to be better equipped with regard to personal attributes such as self-confidence and the will to work. However, in many instances, their general mathematical attributes such as algebraic manipulation skills and their general mastery of mathematical writing are worse than those of students in the past. There are also areas where their content knowledge is either lacking or unexpectedly shallow. It therefore appears that these students have improved personal attributes but not necessarily the knowledge and mathematical skills to back them up. Some recommendations are made with regard to handling the situation. It is clear that the new school system necessitates changes at school level with a view to university level in order to ensure a transition that is surmountable.
The Modified Adomian Decomposition Method (MADM) is presented. A number of problems are solved to show the efficiency of the method. Further, a new solution scheme for solving boundary value problems with Neumann conditions is proposed. The scheme is based on the modified Adomian decomposition method and the inverse linear operator theorem. Several differential equations with Neumann boundary conditions are solved to demonstrate the high accuracy and efficiency of the proposed scheme.
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