Wiskundige modellering : vanaf skool na universiteit

Abstract

The outcomes based education (OBE) system is characterised by controversy and the 2008 matric results that rendered admission to an unusually large number of students did nothing to silence critics. The first students who completed their full cycle of school education in the OBE system entered universities in 2009 and their preparedness for university mathematics as well as their performance at university level are important as indicaters for estimating the success or otherwise of the OBE system. In a previous study student performance in mathematics admission tests for 2005-2007 was investigated and it was found that students who had had partial exposure to OBE performed worse than had been the case with their predecessors in the categories of modelling and ratio problems. As a result, this study was conducted to investigate how the 2009 intake of students performed in a modelling course at university level. A report is presented which deals with student performance in the course, problems experienced, the effect of remedial intervention on performance and whether students of the OBE system are adequately prepared for mathematical modelling at university level. This study focuses on performance in a first year course in mathematical modelling at the University of Pretoria. The course is problem based and is technology intensive, requiring use of the software package Matlab. For investigative purposes the papers of semester tests 1 and 2 of 2005 were used unchanged for tests in 2009. Students of 2009 did not have access to the 2005 papers and the same lecturer taught students of both groups. The lecturer also noted personal experiences in respect of students and was able to draw reasonable comparisons between the 2009 students and previous groups because of her years of involvement with the course. The entrance requirement of 60% for matric mathematics in 2005 was increased to 70% in 2009. Results indicate that the pass percentage decreased in both semester tests from 2005 to 2009. The percentage of students with less than 40% also increased in both semester tests from 2005 to 2009. A surprising observation was that the percentage of students who excelled increased remarkably from 2005 to 2009 in both semester tests. Extra assistance was requested by students after the first semester test in 2009 and resulted in a week of intervention during which revision and extra problems were attended to. The results of the two semester tests of 2009 did not live up to expectations of the matric results of the group. Despite the exceptional matric results, performance in the modelling course was decidely poorer. Results indicate that most students were not adequately prepared for the course – as could be predicted from the previous study. The 2009 group was characterised by two aspects – excellent matric results on the one hand and full school education within the OBE system on the other. It is difficult to distinguish between the influence of the two aspects. It would be convenient to blame the substantial size of the “under 40” groups in both semester tests of 2009 on the better than average matric marks. Yet the increased admission requirements should have compensated for the high matric marks. If the matric results are considered to be reliable then the possibility cannot be excluded that the OBE system had had an influence on the underpreparedness of underperforming students in the course. By contrast, in the instance of top achievers if these students had been influenced by the OBE system it had a positive rather than a negative effect on their performance. It would appear that OBE may have had a polarising effect between good and poor students. Good students performed exceptionally well and poor students did worse than expected. It would, however, be unfair to summarily reject the OBE system. Personal impressions of the lecturer include that the OBE-generation asks for assistance when they need it, they are willing to try and use their resources to their own advantage.

Die uitkomsgerigte onderwysstelsel (UGO) word deur kontroversie gekenmerk en die 2008 matriekuitslae in wiskunde wat aan ongewoon baie studente toelating tot universiteit verleen het, het nie daartoe bygedra om kritici te stil nie. Die eerste studente wat hulle volle skoolopleiding in die UGO-stelsel beleef het, het universiteite in 2009 bereik en hulle gereedheid vir universiteitswiskunde en prestasie op universiteitsvlak is belangrik as sukseskriterium van die UGOstelsel. In ’n vorige studie is studenteprestasie in wiskunde-toelatingstoetse vir 2005-2007 ondersoek en bevind dat studente wat gedeeltelike blootstelling aan UGO gehad het, slegter vaar in die kategorie van modellering- en verhoudingsprobleme as wat hulle voorgangers gedoen het. Na aanleiding hiervan word hierdie studie onderneem om te ondersoek hoe die 2009-inname van studente in ’n modelleringskursus op universiteitsvlak vaar. Daar word verslag gedoen oor studenteprestasie in die kursus, probleme wat ondervind is, die effek van regstellende intervensie op prestasie en of die UGO-stelsel se studente voldoende vir modellering op universiteitsvlak voorberei is.