72 research outputs found
An investigation into the impact of calculator usage on the mathematical skills of secondary school learners
No full textDissertation (MSc)--University of Pretoria, 2016.The aim of the study is to determine the extent to which secondary school learners are dependent on
using calculators for performing basic calculations and operations. The purpose of the study is to obtain
findings and conclusions that can be used to inform educators on the impact of learners' use of
calculators on their possible tertiary studies. The study also aims to add to the body of knowledge
regarding the use of calculators on secondary school level, in the South African situation in particular.
The study took place in Mpumalanga Province of South Africa. Three of the rural schools in
Thulamahashe circuit of Bohlabela district namely Orhovelani High School, Bombani High School and
Godide High School were selected to take part in the study. Grade 12 learners of these schools, a total of
183 learners, were involved in the study. A questionnaire was compiled from typical questions in Grade
8 to 10 school textbooks, chosen to cover a broad spectrum of basic calculations. These questions were
arranged in ten categories of four questions each, later reduced to three questions each after the pilot
study. The categories are: Addition and Subtraction, Multiplication, Fractions, Division, Mixed
calculations, Square roots, Substitution, Exponents, Trigonometry, and Powers of Primes.
Two groups of learners were selected at each school, one group allowed to use calculators (Group WC)
and the group (Group WO) not. The questionnaires were issued to both groups simultaneously during
the afternoon study period at each school to avoid disturbance of the normal running of the schools.
Data collected from the three schools were combined.
The analysis of the data is based on quantitative research methods. Student responses to the
questionnaire are analysed quantitatively using standard statistical techniques. Results of the two
groups are compared.
Results show that learners are dependent on calculators with respect to basic mathematical
calculations, and particularly so in the categories of Fractions, Division, Square Roots, Exponents and
Trigonometry. In the category of Addition and Subtraction and in the category of Multiplication traces of
dependency is evident in calculations with larger numbers. Learners lack knowledge and skills in the
categories of Exponents, Substitution and Powers of Primes. Even with calculators learners experience
problems in the categories of Fractions, Substitution, Exponents and Powers of Primes.Mathematics and Applied MathematicsMScUnrestricte
Mathematical modelling : from school to university
No full textThe 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
The impact of the transition to outcomes-based teaching on university preparedness in mathematics in South Africa
No full textFollowing 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 implementation of the OBE system did not come without problems, giving rise to revised initiatives. The OBE approach, referred to as Curriculum 2005, was introduced into schools in 1998, for all learners in Grades 1- 6 and progressively phased in after that. In 2002, the OBE system was put on hold for the two upper grades of these learners. Learners in these two grades reverted back to skills-based learning for their last three years of schooling, i.e. in Grades 10 – 12. The most senior of these learners that had been subjected to four years of OBE and another three years of the old system finished their schooling in 2005 and 2006 and entered university in 2006 and 2007. These groups are of interest. Students ahead of them had their full schooling in the old system and students two years younger were only subjected to OBE. These students are the “group in the middle”. This paper reports on what the impact is of the growing pains of such a new, inadequately planned education system on the mathematics preparedness of students entering university. This report will be extended in 2009 when the learners that have been fully subjected to the OBE system enter university
The use of personal response systems to renegotiate the didactical contract in tertiary mathematics education
No full textThesis (PhD (Mathematics Education))--University of Pretoria, 2020.Challenges experienced by first year students transitioning from secondary to tertiary mathematics education are examined through the lens of the didactical contract or agreement between the lecturer and students that is founded on beliefs about mutual obligations. First year students’ fundamental beliefs about the nature of mathematics and mathematics teaching/learning must be challenged to renegotiate the didactical contract at tertiary level. Through pedagogy aimed at self-directed learning personal response systems (PRS) are periodically used to make students aware of their own learning and their responsibility for learning. A Likert scale questionnaire is administered at the beginning of the students’ first year to gauge their beliefs about mathematics and mathematics teaching/learning and again at the end of the first semester (or term) to observe possible changes in beliefs and hence the didactical contract. The intervention consists of PRS sessions or so called Time-out sessions, regularly incorporated into the traditional transmission mode lecture to create a student-centred learning environment, aimed at influencing students’ beliefs. Questionnaire data is quantified and compared for the two surveys. There is evidence of a shift towards students taking ownership of their learning and a renegotiation of the didactical contract. Qualitative data generated by focus group interviews confirms the role of the PRS sessions in student beliefs.Mathematics and Applied MathematicsPhD (Mathematics Education)Unrestricte
Interventions to improve teaching and learning in first year mathematics courses
No full textIn keeping with the national mandate of increasing graduates in the sciences in South Africa, a
concerted effort in improving the first year experience becomes imperative. First year mathematics
courses commonly provide the base knowledge necessary for progression in different degree
programmes at university. Success in mathematics courses influences throughputs, retention and
graduation rates of various degree programmes. Due to the highly complex and integrated nature of
issues pertaining to improving teaching and learning in these courses, a multi-dimensional approach
was conceptualized and implemented at the University of Pretoria. This paper reports on the
development of a coherent framework, and the process and strategy for improving student success
through a number of teaching and learning interventions in the first year mathematics courses,
addressing the different dimensions of the framework. The process embarked upon resulted in a
coherent, resource-focused approach with a replicable model for similar contexts.University of Pretoria.http://www.tandfonline.com/loi/tmes202016-08-30hb201
Sibling curves and complex roots 1: looking back
No full textThis paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The concepts of the Cartesian and Argand planes prove to be central to the theme. We specifically pause to look at efforts of representing complex roots of a function on the real plane, first, by superimposing the Argand plane onto the Cartesian plane, and secondly, by keeping the planes side by side and moving between the two, and thirdly, by taking the modulus of the function value and hence eliminating one dimension to enable drawing of the complex function as a surface in three dimensions
Towards Alleviating the Post-Apartheid Education Crisis in South Africa
No full textPost-apartheid South Africa is witnessing an education crisis of significant proportions. The new outcomes-based education system has failed to deliver, and universities are suffering the consequences of under-preparation of learners for tertiary studies. The educator corps is lacking, and it has become common practice for universities to deploy augmented programmes in mathematics for secondary school learners in the surrounding area. This chapter describes a particular model of blended learning, devised for the Incubator School Project (ISP), an initiative of the Nelson Mandela Metropolitan University (NMMU) in the Eastern Cape of South Africa. The defining feature of this blended model is that it incorporates DVD technology, which offers an affordable and accessible option for the particular group of learners. DVD technology was used as an ingredient in this blended learning approach since it is easily available to the majority of learners and to the schools they attend. This chapter describes the particular blended model and reports both qualitatively and quantitatively on its success: qualitatively, based firstly on a questionnaire completed by learners and secondly on interviews of educators; quantitatively, based thirdly on learner performance before and after the intervention and fourthly on a single school case study where the mathematics performance of the learners who participated in the ISP is compared to those who did not participate in the ISP. Finally, the scope of blending of this model is evaluated by means of a radar chart, adapted from an existing radar measure. The findings of the study suggest that the use of DVD technology in the blended learning approach impacted favourably on the mathematics learning and enhanced the mathematics performance of these learners.</jats:p
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