The nature of geometry instruction and observed learning-outcomes opportunities in Nigerian and South African high schools:
- Authors: Atebe, Humphrey U , Schäfer, Marc
- Date: 2013
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140919 , vital:37929 , DOI: 10.1080/10288457.2011.10740712
- Description: The purpose of this qualitative case study involving six secondary school teachers was to obtain insight into how geometry is taught in selected Nigerian and South African high schools. It also aimed, by making use of the van Hiele model of geometry instruction, to elucidate what possible learning opportunities observed instructional methods could offer learners in the subject. The sample comprised three mathematics teachers from Nigeria and three mathematics teachers from South Africa, all of whom were selected using purposive sampling techniques. Instructional activities in six geometry classrooms were recorded on videotape. The van Hiele learning phases provided the framework for data analysis. The findings of this study indicate that observed teaching methods in geometry classrooms in the participating schools offer learners scant opportunity to learn geometry.
- Full Text:
- Date Issued: 2013
Students’ understanding of geometry terminology through the lens of Van Hiele theory
- Authors: Jogymol Alex , Kuttikkattu J. Mammen
- Date: 2018
- Language: English
- Type: Journal Article
- Identifier: http://hdl.handle.net/11260/4703 , vital:44164
- Full Text:
Beyond teaching language: towards terminological primacy in learners' geometric conceptualisation
- Authors: Atebe, Humphrey U , Schäfer, Marc
- Date: 2010
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140960 , vital:37932 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20922
- Description: This paper reports on a specific aspect of a broader geometry conceptualisation study that sought to explore and explicate learners' knowledge of basic geometric terminology in selected Nigerian and South African high schools. It is framed by the notion that students' acquisition of the correct terminology in school geometry is important for their success in the subject. The original study further aimed to determine the relationship that might exist between a learner's ability in verbal geometry terminology tasks and his/her ability in visual geometry terminology tasks. A total of 144 learners (72 each from South Africa and Nigeria) were selected for the study, using both the stratified and the fish-bowl sampling techniques. A questionnaire consisting of a sixty-item multiple-choice objective test provided the data for the study. An overall percentage mean score of 44,17% obtained in the test indicated that learners in this study had only a limited knowledge of basic geometric terminology. The Nigerian subsample in the study had a weaker understanding of basic geometric terminology than their South African counterparts. Importantly, there were high positive correlations between participants' ability in verbal geometry terminology tasks and their ability in visual geometry terminology tasks. These results are consistent with those of several earlier studies, and provide a reasonably firm basis for certain recommendations to be made.
- Full Text:
- Date Issued: 2010
“As soon as the four sides are all equal, then the angles must be 90° each”: children's misconceptions in geometry
- Authors: Atebe, Humphrey U , Schäfer, Marc
- Date: 2013
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140983 , vital:37934 , DOI: 10.1080/10288457.2008.10740634
- Description: This study describes Nigerian and South African students' conceptual understanding in high school geometry based on the van Hiele model of geometric thinking levels. The study further highlights students' misconceptions in school geometry. Concepts of triangles and quadrilaterals were investigated among 36 mathematics learners drawn from grades 10 through 12 who participated in this study. The tasks included identifying and naming shapes, sorting of shapes, stating the properties of shapes, defining of shapes and establishing class inclusions of shapes. The results indicated that many Nigerian and South African high school learners in Grade 10, 11 and 12 hold a number of misconceptions about geometric concepts of triangles and quadrilaterals.
- Full Text:
- Date Issued: 2013
Mathematics teachers' experiences of designing and implementing a circle geometry teaching programme using the van Hiele phases of instruction as a conceptual framework: a Namibian case study
- Authors: Dongwi, Beata Lididimikeni
- Date: 2013
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1412 , http://hdl.handle.net/10962/d1003133
- Description: The aim of this case study was to examine, analyze and report on the findings of the experiences of selected mathematics teachers when they used the van Hiele phases of instruction in designing and implementing a Grade 11 circle geometry teaching programme. The sample consisted of three selected mathematics teachers from the school where the researcher teaches. This school is located in the Oshikoto Education Region in Namibia. The school serves a multicultural group of 759 learners from a middle-class economic background. The site and participants were selected conveniently as the researcher had unrestricted access to both the facilities and the participants. This research takes the form of a case study and is underpinned by the interpretive paradigm. Data for this research was collected using a variety of techniques such as interviews, classroom observation and document analysis. This facilitated easy triangulation of the data. The findings of this research make four claims with regard to the experiences of the mathematics teachers with designing and implementing the circle geometry teaching programme using the five van Hiele phases of instruction as a conceptual framework. The findings revealed that firstly, all three participating mathematics teachers used and implemented all the five van Hiele phases of instruction in their lessons I observed. Secondly, the teachers navigated quite freely from one phase of instruction to the next, but also returned to the earlier phases for clarification and reinforcement in their teaching. Thirdly, the teachers saw the phases of instruction as a good pedagogical tool or template for planning and presenting lessons. Fourthly, the majority of the learners followed the instructions and seemed to obtain the answers faster than expected. The lesson presentations were lively and both teachers and learners communicated at length to discover angle properties of circles while developing and nurturing the technical language of geometry.
- Full Text:
- Date Issued: 2013
Rhodes University Research Report 2010
- Authors: Rhodes University , Roberts, Jaine
- Date: 2010
- Language: English
- Type: Text
- Identifier: vital:565 , http://hdl.handle.net/10962/d1011968
- Description: From Introduction: In 2010, the total subsidy earning accredited research output count for Rhodes University of 615.3 units represents an increase of 9% on the previous year. By far the major contributor to this growth was the significant increase in both PhD (37.5% up on 2009) and Masters by thesis students (34.5% up on 2009). Rhodes contributed 3.3% of all accredited research output in the public higher education sector in 2010 (0.1% up on 2009). With 1.9% of academic staff in the system, Rhodes retained its place amongst the top three most productive universities as measured by accredited publications per academic. Rhodes exceeds the DHET research output norm for universities by 53%. In 2010, the total accredited publication output count for Rhodes University of 325.33 units represented a decline over 2009 of 7.3 percent. This followed two years of steep growth during which accredited research publication output grew by 28%. Accredited publication output for 2010 consisted mainly of journals at 89.9%, with conference proceedings at 7.2% and books and book chapters at 2.9% making far smaller contributions. This mix is roughly in line with the sector as a whole. It has been recognised that books and book chapters are underappreciated in relation to journals, and recommendations to increase the weighted points that they attract as proposed by ASSAf1 are awaiting approval by the DHET. and book chapters submitted, because the hurdle of independent reviewing is not always met by the publishing avenues chosen by authors. The University has become increasingly reliant on research funding in recent years as a larger proportion of its budget, and attention at university council level is being given to ensuring that appropriate systems and support structures for researchers are in place. I add my warm thanks and congratulations to all of our researchers, funders, collaborators and partners who contributed to the excellent research results of 2010. , A Publication of the Rhodes Research Office,compiled and edited by Jaine Roberts
- Full Text:
- Date Issued: 2010
Mechanistic studies of unusual Miruta-Baylis-Hillman reactions
- Authors: Nyoni, Dubekile
- Date: 2012
- Subjects: Chemical reactions Benzaldehyde Acrylonitrile Methyl acrylate Coumarins
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:4400 , http://hdl.handle.net/10962/d1006692
- Description: This study has focussed on the application of synthetic, kinetic and exploratory theoretical methods in elucidating the reaction mechanisms of four Morita-Baylis-Hillman (MBH) type reactions, viz, i) the reactions of the disulfide 2,2'-dithiodibenzaldehyde with various activated alkenes in the presence of DBU and Ph₃P, ii) the reactions of chromone-3-carbaldehydes with MVK, iii) the reactions of chromone-2-carbaldehydes with acrylonitrile and iv) with methyl acrylate. Attention has also been given to the origin of the observed regioselectivity in Michaelis-Arbuzov reactions of 3-(halomethyl)coumarins. Cleavage of the sulfur-sulfur bond of aryl and heteroaryl disulfides by the nitrogen nucleophile DBU has been demonstrated, and a dramatic increase in the rate of tandem MBH and disulfide cleavage reactions of 2,2'-dithiodibenzaldehyde with the activated alkenes, MVK, EVK, acrylonitrile, methyl acrylate and tert-butyl acrylate has been achieved through the use of the dual organo-catalyst system, DBU-Ph₃P – an improvement accompanied by an increase in the yields of the isolated products. Detailed NMR-based kinetic studies have been conducted on the DBU-catalysed reactions of 2,2'-dithiodibenzaldehyde with MVK and methyl acrylate, and a theoretical kinetic model has been developed and complementary computational studies using Gaussian 03, at the DFT-B3LYP/6-31G(d) level of theory have provided valuable insights into the mechanism of these complex transformations. Reactions of chromone-3-carbaldehydes with MVK to afford chromone dimers and tricyclic products have been repeated, and a novel, intermediate MBH adduct has been isolated. The mechanisms of the competing pathways have been elucidated by DFT calculations and the development of a detailed theoretical kinetic model has ensued. Unusual transformations in MBH-type reactions of chromone-2-carbaldehydes with acrylonitrile and methyl acrylate have been explored and the structures of the unexpected products have been established using 1- and 2-D NMR, HRMS and X-ray crystallographic techniques. Attention has also been given to the synthesis of 3-(halomethyl)coumarins via the MBH reaction, and their subsequent Michaelis-Arbuzov reactions with triethyl phosphite. An exploratory study of the kinetics of the phosphonation reaction has been undertaken and the regio-selectivity of nucleophilic attack at the 4- and 1'-positions in the 3-chloro- and 3-(iodomethyl)coumarins has been investigated by calculating Mulliken charges, LUMO surfaces and Fukui condensed local softness functions.
- Full Text:
- Date Issued: 2012
Using the van Hiele theory to analyse geometrical conceptualisation in grade 12 students: a Namibian perspective
- Authors: Mateya, Muhongo
- Date: 2009
- Subjects: Hiele, Pierre M. van Hiele-Geldof, Dina van Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching (Secondary) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1820 , http://hdl.handle.net/10962/d1003706
- Description: The study reported here utilised a theory of levels of geometric thinking. This theory was proposed and developed by two Dutch mathematics educators, Pierre van Hiele and his wife, Dina van Hiele-Geldof. The van Hiele theory enables investigations into why many students experience difficulties in learning geometry. In many nations, such as the UK, the USA, Netherlands, the USSR and to a certain extent, Nigeria and South Africa, research evidence has indicated that the overall students’ mathematical competencies are linked to their geometric thinking levels. This study is the first of its kind to apply the van Hiele theory of geometric thinking in the Namibian context to analyse geometrical conceptualisation in Grade 12 mathematics students. In all, 50 Grade 12 students (20 from School A and 30 from School B) were involved in this study. These students wrote a van Hiele Geometry Test adapted from the Cognitive Development and Achievement in Secondary School Geometry test items. Thereafter, a clinical interview with the aid of manipulatives was conducted. The results from this study indicated that many of the School A and School B students who participated in the research have a weak conceptual understanding of geometric concepts: 35% of the School A and 40% of the School B subsamples were at the prerecognition level. 25% and 30% of the School A, and 20% and 23.3% of the School B students were at van Hiele levels 1 and 2 respectively. An equal number of students but different in percentages, 2 (10%) in School A and 2 (6.7%) in School B, were at van Hiele level 3. Only one student from School B attained van Hiele level 4. These results were found to be consistent with those of previous similar studies in UK, USA, Nigeria and South Africa. The findings of this study also highlight issues of how the Namibian Grade 12 geometry syllabus should be aligned with the van Hiele levels of geometric thinking as well as the use of appropriate and correct language in geometrical thinking and problem solving.
- Full Text:
- Date Issued: 2009
Linkage in extra-sensory perception
- Authors: Marsh, Maurice Clement
- Date: 1959
- Subjects: Telepathy , Extrasensory perception
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:3215 , http://hdl.handle.net/10962/d1012840
- Description: The aims of this investigation were firstly to find whether 371 subjects, mainly students at Rhodes University, would be able to reproduce target drawings made 470 miles away by an agent in Cape Town, by means of General Extra-Sensory Perception; secondly, to find whether any association existed between any such hit scoring ability shown and personality ratings derived from a battery of personality test material; and thirdly, to find whether providing the subjects with material designed to link them more closely with the agent would increase their scoring rate. The 17,440 drawings returned by the subjects were randomised, and scored against a randomised set of 100 drawings consisting of 50 which had actually been used as targets, intermixed with 50 that were equal in difficulty but which had not been used as targets, and which were inserted merely as controls. Three independent judges assessed the subjects' drawings, and awarded hits in terms of title, shape and association. In the crucial title hits highly significant deviations in favour of the experimental target drawings were found, the control series of drawings showing no such effects. It was found that the subjects' hits were distributed evenly throughout the whole 25 day period of the experiment for each target, and showed no tendency to occur more frequently in the week a particular drawing was being used as a target than in the other weeks when it was not. When the subjects were divided into a high scoring and low-scoring group in terms of their E.S. P. abiility, the high- scoring group proved to be significantly more extraverted (as measured by the Bernreuter B3I scale) than the low- scoring group, confirming a relationship previously reported by Humphrey. In addition the data showed several other relationships, predicted by the work of previous experimenters, although these did not reach the .01 level of statistical significance. To assess the effect of the Linkage Material the subjects were divided into an experimental and a control group. The Experimental Group was supplied with correct Linkage Material, the Control Group with incorrect Linkage Material, which they were led to believe was correct . The two sets of Linkage Material were equated in all other respects. The Experimental Group showed significant improvements in scoring rate when supplied with a photograph and description of the agent, and a probably significant improvement when supplied with squares of handkerchief which had previously belonged to him. When supplied with squares of colour, also appearing on the agent's target sheets, no significant increase in scoring rate took place on the target drawings, but a significant decrease occurred in hits scored on the control targets. By contrast no consistent significant fluctuations were shown by Control Group Subjects, leading to the conclusion that the correctness of the Linkage Material was a factor contributing to its effectiveness. A qualitative examination of the hits scored by the subjects revealed that they tended to reproduce the concepts depicted by the target drawings, rather than the actual shapes drawn by the agent, suggesting that the hits were being produced by a telepathic process rather than a clairvoyant one. The results of the experiment suggest that the subjects were assisted by the Linkage Material to gain access to the agent's mind as a whole, and not to particular items in it. This throws doubt on the correctness of Whately Carington's Association Theory of Telepathy, which the experiment was designed to test.
- Full Text:
- Date Issued: 1959
The evaluation of an instructional framework using the Van Hiele levels for learning and teaching geometry: a study in five rural senior secondary schools
- Authors: Alex, Jogymol Kalariparampil
- Date: 2012
- Subjects: Teaching and learning -- Geometry -- Education (Secondary)
- Language: English
- Type: Thesis , Doctoral , D Ed
- Identifier: vital:18470 , http://hdl.handle.net/11260/d1011278
- Description: The Constitution (1996) of the Republic of South Africa forms the basis for social transformation in our new society. The Constitution (Act 108 of 1996) and the amendments that followed provided a basis for curriculum transformation and development in South Africa. The Department of Education introduced the present curriculum known as the National Curriculum Statement, which is modern and internationally benchmarked, in grade 10 in 2006. It required the learners to do seven subjects in grades 10 to 12 of which mathematics or mathematical literacy was prescribed as compulsory subjects. To attain social transformation, the South African Government attached a great deal of importance to the learning and teaching of mathematics and sciences in the South African schools. This study was undertaken in an effort to improve the understanding of geometry and, consequently, the performance and achievement of senior secondary school learners in geometry. The study was inspired by the van Hiele theory. The study made use of the different levels of the van Hiele theory for the development of an instructional framework for geometry in senior secondary schools. The research was conducted in a previously disadvantaged area in South Africa. Given the setting of this study and the wider application of it, the use of ‘hands-on’ and practical approach to use manipulatives and worksheets to improve the geometric understanding was tried and tested in this study. The assumption was that such experiences would make the learning of geometry more relevant and enjoyable for learners from limited financial and underprivileged circumstances. A quasi-experimental design was chosen. A total of 359 learners from five purposively selected schools in Mthatha district in the Eastern Cape Province participated in this study. Qualitative data through interviews were gathered. The data were analysed using IBM SPSS Version 19 and Microsoft Excel. Findings indicated that there was a notable improvement in the performance of learners who were taught by the application of the van Hiele theory. The results revealed that most of the learners were not ready for the application of deductive principles of geometry in terms of formal proof in senior secondary school geometry. Based on the results, some recommendations are made to enhance the teaching and learning of geometry in senior secondary schools.
- Full Text:
- Date Issued: 2012
The synthesis and analysis of (2R,3R)-1,1,4,4- tetraphenylbutane-1,2,3,4-tetraol (tetrol) and derivatives, and a study of their host potential
- Authors: Weitz, Selwyn Herbert
- Date: 2015
- Subjects: Chemistry, Organic
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10948/3735 , vital:20459
- Description: This investigation focussed on the inclusion and resolution ability of (2R,3R)-1,1,4,4-tetraphenylbutane-1,2,3,4-tetraol (TETROL), studies on the stoichiometry of its derivatives and the formation of inclusion compounds for single crystal analysis. The guest compounds that featured in the main study were cyclohexanone, 2-methylcyclohexanone, 3-methylcyclohexanone and 4-methylcyclohexanone. It was found that 3- and 4-methylcyclohexanone were trapped in their energetically unfavourable axial conformations in the inclusion crystal. Resolution experiments proved that (2R,3R)-1,1,4,4-tetraphenylbutane-1,2,3,4-tetraol can be used as a resolving agent for 2- and 3-methylcyclohexanone, with ee values of 13% and 22%, respectively (according to the method of Hiemstra), in favour of the R-enantiomer. Single crystal X-ray diffraction (SCXRD) studies, however, showed that 2-methylcyclohexanone was resolved with an ee of 30% in R. An ee of 56% in R was obtained for 3-methylcyclohexanone. Enantiomer enrichment of 2-methylcyclohexanone was achieved in basic medium (ee of 18% according to the method of Hiemstra) and showed that by using the host in either half or double the molar ratio of the guest, a higher ee was obtained than for a 1:1 ratio. The following TETROL derivatives were also synthesized and their stoichiometries with various guest compounds were determined: (2R,3R)-1,1,4,4-tetra(naphthalen-1-yl)butane-1,2,3,4-tetraol; (2R,3R)-1,1,4,4-tetra(naphthalen-2-yl)butane-1,2,3,4-tetraol; (2R,3R)-1,1,4,4-tetra(p-anisyl)butane-1,2,3,4-tetraol; (2R,3R)-1,1,4,4-tetra(p-tolyl)butane-1,2,3,4-tetraol; (2R,3R)-1,1,4,4-tetra(m-tolyl)butane-1,2,3,4-tetraol and; (2R,3R)-1,1,4,4-tetra(o-tolyl)butane-1,2,3,4-tetraol.
- Full Text:
- Date Issued: 2015
Application of lie group analysis to mathematical models in epidemiology
- Authors: Otieno, Andrew Alex Omondi
- Date: 2013
- Subjects: Epidemiology -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:18486 , http://hdl.handle.net/11260/100
- Description: Lie group analysis is arguably the most systematic vehicle for finding exact solutions of differential equations. Using this approach one has at one's disposal a variety of algorithms that make the solution process of many differential equations algorithmic. Vital properties of a given differential equation can often be inferred from the symmetries admitted by the equation. However, Lie group analysis has not enjoyed wide-spread application to systems of first-order ordinary differential equations. This is because such systems typically admit an infinite number of Lie point symmetries, and there is no systematic way to find even a single nontrivial one-dimensional Lie symmetry algebra. In the few applications available, the approach has been to circumvent the problem by transforming a given system of first-order ordinary differential equations into one in which at least one of the equations is of order two or greater. It is therefore fair to say that the full power of Lie group analysis has not been sufficiently harnessed in the solution of systems of first-order ordinary differential equations. In this dissertation we review some applications of Lie group analysis to systems of first order ordinary differential equations. We shed light on the integration procedure for first-order systems of ordinary differential equations admitting a solvable Lie algebra. We do this via instructive examples drawn from mathematical epidemiology models. In particular we revisit the work of Nucci and Torrisi [54] and improve the exposition of the Lie-symmetry-inspired solution of a mathematical model which describes a HIV transmission. To aid implementation of the integration strategy for systems of ordinary differential equations, we have developed ad-hoc routines for finding particular types of admitted symmetries and checking if a given symmetry is indeed admitted by a system of ordinary differential equations.
- Full Text:
- Date Issued: 2013
How important is green infrastructure in small and medium-sized towns? Lessons from South Africa
- Authors: Shackleton, Charlie M , Blair, Andrew , De Lacy, Peter , Kaoma, Humphrey , Mugwagwa, Noster , Dalu, Mwazvita , Walton, Wesley
- Date: 2018
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/398321 , vital:69400 , xlink:href="https://doi.org/10.1016/j.landurbplan.2016.12.007"
- Description: The current nature and challenges of urbanisation in sub-Saharan Africa display several unique features only weakly evident on other continents. Key ones include the current high rates of population growth, inadequate planning and governance systems, concentration in small and medium-sized towns, and increasing urban poverty. These shape the extent, nature and use of ecosystem services provided by urban green infrastructure. This paper first examines the location of green infrastructure across nine towns, showing that it is unequal between suburbs and that the bulk is located under private tenure (74%) rather than in public spaces. We then consider the extent and patterns of use of selected provisioning and cultural ecosystem services from green infrastructure in different locations within towns, including private gardens, public parks and street trees. The results show significant use of green infrastructure for a range of provisioning and cultural services as well as its contribution to spiritual and mental wellbeing. Provisioning contributions are both in regular support of livelihood needs as well as increased use after a covariate shock (a flood), both of which help reduce household vulnerability. Lastly, our results show the expressed level of support and willingness-to-pay or work amongst urban residents for green infrastructure and the services it provides. Whilst the composite results indicate marked variation between and within towns, they show that there is widespread use of green infrastructure for both basic needs as well as for more aesthetic and psycho-spiritual appreciation and recreation, in small and medium-sized towns in a developing country such as South Africa.
- Full Text:
- Date Issued: 2018
How important is green infrastructure in small and medium-sized towns? Lessons from South Africa
- Authors: Shackleton, Charlie M , Blair, Andrew , De Lacy, Peter , Kaoma, Humphrey , Mugwagwa, Noster , Dalu, Mwazvita , Walton, Wesley
- Date: 2018
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/398307 , vital:69399 , xlink:href="https://doi.org/10.1016/j.landurbplan.2016.12.007"
- Description: The current nature and challenges of urbanisation in sub-Saharan Africa display several unique features only weakly evident on other continents. Key ones include the current high rates of population growth, inadequate planning and governance systems, concentration in small and medium-sized towns, and increasing urban poverty. These shape the extent, nature and use of ecosystem services provided by urban green infrastructure. This paper first examines the location of green infrastructure across nine towns, showing that it is unequal between suburbs and that the bulk is located under private tenure (74%) rather than in public spaces. We then consider the extent and patterns of use of selected provisioning and cultural ecosystem services from green infrastructure in different locations within towns, including private gardens, public parks and street trees. The results show significant use of green infrastructure for a range of provisioning and cultural services as well as its contribution to spiritual and mental wellbeing. Provisioning contributions are both in regular support of livelihood needs as well as increased use after a covariate shock (a flood), both of which help reduce household vulnerability. Lastly, our results show the expressed level of support and willingness-to-pay or work amongst urban residents for green infrastructure and the services it provides. Whilst the composite results indicate marked variation between and within towns, they show that there is widespread use of green infrastructure for both basic needs as well as for more aesthetic and psycho-spiritual appreciation and recreation, in small and medium-sized towns in a developing country such as South Africa.
- Full Text:
- Date Issued: 2018
Factors Influencing Enrolment In Rural Primary Schools In One Circuit, Port St. Johns Cmc, Or Tambo Coastal Education District
- Authors: Lungu, Simlindile Humphrey
- Date: 2020
- Subjects: Collaboration, school culture, school merger, rationalisation, educator attrition, enrolment, rural, educators, learners.
- Language: English
- Type: Masters , Master of Education (M. Ed)
- Identifier: http://hdl.handle.net/11260/6244 , vital:45343
- Description: The purpose of this study was to investigate the factors influencing enrolment in rural primary schools in one Circuit in Port St. Johns CMC in OR Tambo Coastal Education District. The literature review looked into each of the following aspects of factors influencing enrolment in rural primary schools: challenges resulting in policy issues, the challenge of infrastructure, other factors that influence enrolment in rural school and strategies to overcome enrolment challenges in rural schools. The study was qualitative in nature and employed case study research design. Convenient sampling was used to select four rural primary schools in one Circuit in Port St. Johns Circuit Management Centre (CMC) in OR Tambo Education District. The principal, one (1) educator, one (1) parent and one (1) learner were purposively selected from each school and this made a total of sixteen (16) participants. Face-to-face individual interviews were conducted to gather data about the views and opinions of the participants. Data were analysed using the interpretational analytical strategies. Themes were drawn from the responses of the participants. The major findings were:When the number of learners decreases, the number of educators is also reduced proportionately as a results educators have to take more subjects.There was a negative effect of the relocation of parents, there was poor quality of teaching and learning, the effect of instability crippled normal functioning of the school, there was poor school management as the schools were hit by having no principals due to internal disputes, there were disruptions of teaching and learning due to instability in rural primary schools. The main recommendations are: Rural primary schools should gradually improve the quality of teaching and learning provisioning and arrest the decline in enrolment;At least each class should have an educator, so that discipline can be maintained in all classes; Given the highly technical nature of the process involved in determining the PPN of schools, the DBE, the Provincial Education Departments as well as educator unions should as a matter of priority engage in a massive campaign to capacitate principals on the application of the PPN and its related formula; An audit into the schools' physical infrastructure be conducted to redress the meaningful pedagogical environment of teaching and learning.
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Historical biogeography of the tribe Platypleurini Schmidt, 1918 (Hemiptera: Cicadidae) with a focus on Southern Africa
- Authors: Price, Benjamin Wills
- Date: 2010
- Subjects: Biogeography -- History -- Africa, Southern Cicadas -- Africa, Southern Cicada (Genus) -- Africa, Southern Biodiversity -- Africa, Southern Cicadas -- Variation -- Africa, Southern
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5708 , http://hdl.handle.net/10962/d1005394
- Description: With our contemporary biota under increasing threat of extinction, it is of interest to understand where, why and how biological diversity is generated. If focussed on appropriate taxa, phylogeographic and phylogenetic studies can assist in the identification of both places and processes central to the origin and maintenance of biological diversity. It is explained why southern Africa presents a perfect test-bed for exploring such mechanisms of diversification and why cicadas (Hemiptera: Cicadidae) have proved very suitable tools for studies of historical biogeography. This study then exemplifies these points by providing the first large-scale investigation of the historical biogeography of the tribe Platypleurini Schmidt, 1918, with emphasis on the genus Platypleura Amyot & Seville, 1843 in southern Africa. Standard methods of DNA sequencing provided data from portions of the mitochondrial small subunit ribosomal 16S RNA (16S) and cytochrome oxidase subunits I (COI) and II (COII); and the nuclear elongation factor 1 alpha (EF-1α) from 400 ethanol-preserved specimens. These data were analysed using standard phylogenetic methods and a time scale of diversification was estimated using a Bayesian framework and both fossil data and DNA substitution rates. The results showed that the tribe is too recent to be of Gondwanan origin. The lack of monophyly of the genera represented in both Asia and Africa showed that the tribe needs formal taxonomic revision. Diversification of the African platypleurine genera coincides with aridification in the early Oligocene. Dispersal of Asian platypleurine taxa coincides with the meeting of Africa and Eurasia in the mid-Oligocene. Two radiations within African Platypleura are hypothesised; one distributed over most of sub-Saharan Africa and the second restricted to southern Africa, with clades restricted within regional biomes. Within each of the three focal biomes, cryptic taxonomic diversity was confirmed, suggesting that, even in relatively well understood groups such as the southern African platypleurine cicadas, molecular data can identify further diversity. Although each focal taxon was restricted to non-overlapping biomes, comparison of the three biomes highlighted interactions between palaeoclimates and fixed landscape features (coastal topography, river catchments and escarpments) as causative agents of vicariance, dispersal, extinction and diversification of these volant insects. The results of using co-distributed species for comparative study cautions against making inferences based on single-taxon datasets and highlights the need to use many, evolutionarily independent taxa when identifying mechanisms of diversification. The dating analyses imply that within-species lineage diversification occurred overwhelmingly within the Pleistocene, a trend that is being increasingly recognised in print for other biota. Some caveats about using phylogenetic approaches to estimate ancestral areas are illustrated. Several recommendations are made regarding additional taxa and data sources for understanding the origin and maintenance of biological diversity.
- Full Text:
- Date Issued: 2010
The geochemical stratigraphy of the volcanic rocks of the Witwatersrand triad in the Klerksdorp area, Transvaal
- Authors: Bowen, Teral Barbara
- Date: 1985 , 2013-03-14
- Subjects: Lava -- South Africa -- Transvaal , Igneous rocks -- South Africa -- Transvaal , Geochemistry -- South Africa -- Transvaal
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4932 , http://hdl.handle.net/10962/d1004932 , Lava -- South Africa -- Transvaal , Igneous rocks -- South Africa -- Transvaal , Geochemistry -- South Africa -- Transvaal
- Description: This study lias initiated with the aim of identifying the existence of any geochemical criteria which may be used to distinguish between the various volcanic formations within the Witwatersrand triad. The Witwatersrand triad comprises three sequences: the Dominion Group at the base, the Witwatersrand Supergroup in the middle, and the Ventersdorp Supergroup at the top. It is underlain by Archaean basement rocks, and covered by rocks of the Transvaal sequence. The Dominion Group consists of the sedimentary Rhenosterspruit quartzite Formation at the base, overlain by a bimodal component of the Syferfontein Porphyry succession of lavas. Basaltic lavas are the major component of the Rhenosterhoek Formation, while the overlying Formation consists primarily of dacitic porphyries. Intercalations of one lava type within the other are common, however, so each formation is not the exclusive domain of only one lava type. The Witwatersrand Supergroup, a predominantly argillaceous and arenaceous sequence, contains two narrow volcanic horizons, one of wbich, the Jeppestown Amygdaloid (now Crown Formation), consisting of tholeiitic andesites, occurs in the study area. The overlying Ventersdorp Supergroup has, at its base, the basaltic Klipriviersberg Group, of which four out of six formations are present in the study area, namely, the Alberton, Orkney, Loraine and Edenville Formations. This group is succeeded unconformably by the PIatberg Group, consisting of the sedimentary Kameel doorns Formation, followed by the (informal) Goedgenoeg, Makwassie Quartz Porphyry and Rietgat Formations. The Goedgenoeg and Rietgat Formations are basaltic, whil e the Mawassie rocks range from basaltic to dacitic, the majority being tholeiitic andesites and andesites . The Pniel sequence at the top of the Ventersdorp Supergroup consists of the sedimentary Bothaville Formation, and the Allarridge Formation, the lavas of which are basaltic with some andesitic tendencies. A well-defined geochemical stratigraphy was found to exist. From the eleven volcanic formations examined, nine distinct geochemical units emerged, as the Loraine and Edenville Formations were found to have the same geochemical characteristics, as did the Goedgenoeg and Rietgat Formations. Despite having undergone law-grade greenschist facies metamorphism, very clear variation patterns with height are displayed by the immobile elements Ti, P, Kb, Zr and Y, and the light rare earth elements La, Ce and Nd. In contrast, much scatter was observed in the variation patterns of Na, K, Mn, Ba and Rb. Three techniques were employed to effect discrimination between formations - orthosonal discrimination, interelement and ratio vs ratio plots, and discriminant analysis. Confidence limits placed on normal probability plots served to isolate outlier samples for further examination by the various discrimination techniques. A successful test of the efficacy of the discrimination techniques was afforded when fourteen samples from an unknown succession were positively identified as representative of the Klipriviersberg Group
- Full Text:
- Date Issued: 1985
The geology and geochemistry of the north-western portion of the Usushwana Complex, South-Eastern Transvaal
- Authors: Riganti, Angela
- Date: 1992
- Subjects: Geology -- South Africa -- Transvaal , Geochemistry -- South Africa -- Transvaal
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4958 , http://hdl.handle.net/10962/d1005570 , Geology -- South Africa -- Transvaal , Geochemistry -- South Africa -- Transvaal
- Description: The 2.9 Ga old Usushwana Complex in the Piet Retief-Amsterdam area (south-eastern Transvaal) represents an exposed segment of a layered intrusion. It has the form of a dyke-like body elongated in a northwesterly direction, and extends to an estimated depth of 3000 -5500 m. Lithologically, the Complex consists of a cumulate succession of mafic rocks capped by granitoids and has intruded along the contact between the basement and the supracrustal sequences of the Kaapvaal Craton. Differentiation of an already contaminated gabbroic magma resulted in an ordered stratigraphic sequence comprising progressively more evolved lithotypes, with at least two imperfect cyclic units developed over a stratigraphic thickness of about 700 metres (Hlelo River Section). Meso- to orthocumulate textured gabbros and quartz gabbros grade upwards into magnetite- and apatite-bearing quartz gabbros, interlayered with discontinuous magnetitite horizons. The gabbros in turn grade into hornblende-rich, granophyric granodiorites. The differentiation process is regarded as having been considerably enhanced by the assimilation of acidic material, derived by partial melting of the felsic country rocks at the roof of the magma chamber. Recrystallisation of these rocks gave rise to the microgranites that locally overlie the granodiorites. Mineralogical, textural and geochemical features indicate a relatively advanced fractionation stage, suggesting that the exposed sequence of the Usushwana Complex in the study area represents the upper portion of the intrusion. No significant mineralised occurrences were identified. However, on the basis of similarities between the Usushwana Complex and other mafic layered intrusions which host significant ore deposits, it is suggested that economic concentrations of base metal(Cu-Ni) sulphides, PGE and chromitites are likely to be developed at lower stratigraphic levels.
- Full Text:
- Date Issued: 1992
Optical nonlinearities in non-peripherally substituted pyridyloxy phthalocyanines
- Authors: Sanusi, Kayode , Antunes, Edith M , Nyokong, Tebello
- Date: 2014
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/241618 , vital:50955 , xlink:href="https://doi.org/10.1039/C3DT52462K"
- Description: The optical nonlinearities of six non-peripherally-substituted pyridyloxy phthalocyanines have been studied at 532 nm using a nanosecond Z-scan technique in a dimethyl sulphoxide solution. Ring-strain effects and the absence of a metal center were found to greatly reduce the inherent high nonlinearities expected of some of these phthalocyanine complexes. Of the six molecules investigated, 1(4),8(11),15(18),22(25)-tetrakis-(2-pyridyloxy)phthalocyaninato lead(II) 3, 1(4),8(11),15(18),22(25)-tetrakis-(2-pyridyloxy)phthalocyanine 5, and 1(4),8(11),15(18),22(25)-tetrakis-(4-pyridyloxy)phthalocyanine 6 were found to exhibit negligible nonlinear optical behavior, due to either the absence of asymmetry or central metal and/or the presence of a ring-strain effect. A two-photon absorption process was found to be the major contributor to the observed reverse saturable absorption (RSA) in 1(4),8(11),15(18),22(25)-tetrakis-(4-pyridyloxy)phthalocyaninato lead(II) 4, 1(4)-mono-(2-pyridyloxy)phthalocyaninato lead(II) 7, and 1(4)-mono-(4-pyridyloxy)phthalocyaninato lead(II) 8, with large two-photon absorption cross-section, high hyperpolarizability and high third-order susceptibility values in the range of 4.53 × 10−43–5.33 × 10−42 cm4 s per photon, 1.61 × 10−28–1.89 × 10−27 esu and 9.73 × 10−12–7.05 × 10−11 esu respectively.
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- Date Issued: 2014
A study of a class of invariant optimal control problems on the Euclidean group SE(2)
- Authors: Adams, Ross Montague
- Date: 2011
- Subjects: Matrix groups Lie groups Extremal problems (Mathematics) Maximum principles (Mathematics) Hamilton-Jacobi equations Lyapunov stability
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5420 , http://hdl.handle.net/10962/d1006060
- Description: The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
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- Date Issued: 2011