Philosophiae Doctor - PhD (Mathematics and Science Education)

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An ethnomethodological analysis of students’ ways of working with algebraic fractions in high-stakes examinations: the case of level 3 mathematics students at technical and vocational education and training (tvet) colleges
(University of the Western Cape, 2023) Mbeki, Nwabisa Vivian; Simons, Marius
The study investigates the National Certificate Vocational (NCV) Level 3 students’ ways of working with rational algebraic fractions in a high-stakes examination. An ethnomethodological analysis was used to reveal the textures of examinees’ work. Ways of working in this study refer to how examinees deal with algebraic fractions when simplifying them, including even those elements of their work, which are rough work in the sit-down examination. Ethnomethodology is the study of ordinary actions by ordinary members of society. Ordinary action means that members regularly and recurrently do it with such automaticity that it is given little thought. Ethnomethodology is the study of how people use common sense, procedures, and considerations to gain an understanding of everyday situations (Garfinkel, 1967). In the context of mathematics education, ethnomethodology seeks to understand how examinees construe, construct and orient themselves to these norms that are usually seen but unnoticed (Garfinkel 1967). The study is premised on a qualitative research paradigm that focuses on studying situations in their natural settings and applying an interpretive perspective. Data were collected from two colleges using students’ examination scripts for the end-of-year NCV L3 mathematics exams. Guba and Lincoln’s (1985) concepts of trustworthiness, credibility, transferability, dependability, and confirmability were used. The study sought to ensure ethical principles were followed by applying to each college for permission to conduct research and collect data. Permission was granted. Ethical clearance from the University of the Western Cape was obtained before conducting any data collection. The researcher ensured confidentiality and the anonymity of the participants’ scripts. The examination guidelines require that the examination scripts and mark sheets be kept at an institution for verification and cases of appeal. The institution keeps examinees’ examination scripts, which are confidential. The researcher ensured that scripts did not leave the college and ensured the confidentiality of their information by making copies of the scripts and keeping the copies safe. The study poses no harm to the participants or the colleges.
Effects of Dialogical Argumentation – Assessment for Learning Instructional Model on Grade 10 Learners’ Conceptions and Performance on Static Electricity
(University of the Western Cape, 2021) Hlazo, Noluthando; Fakudze, Cynthia
This study examined the effects of using Dialogical Argumentation and Assessment for Learning as an Instructional Method (DAAFLIM) in teaching static electricity focussing on lightning as an example of static electricity to Grade 10 learners. Three groups of learners from two township schools were used as a sample for the study. The Solomon three-group design was employed in collecting data. One class was used as the experimental group and the other two were the control groups: control 1 group and control 2 group. The study drew on theoretical frameworks associated with prior knowledge of learners such as the constructivist viewpoint. The frameworks that were applied in the analysis of the data were Toulmin’s Argumentation Pattern (TAP) and Ogunniyi’s Contiguity Argumentation Theory (CAT). The experimental group and control group 2 were exposed to DAAFLIM as a teaching method and AFL as the assessment strategy. The control 1 group was taught in the traditional chalk- talk method and assessment was mostly summative. The experimental and control 1 groups received pre-tests and also wrote a post-test whereas the control 2 group only wrote the post test.
An Evaluation of a Science and Indigenous Knowledge Systems Project at a Western Cape University
(University of the Western Cape, 2021) A. Anga’ama, Daniel; Fakudze, Cynthia
This study was an evaluative case study of a Science and Indigenous Knowledge Systems Project on the Project (SIKSP) at a Western Cape University, South Africa. It was an internal evaluation from the perspectives of the project participants, with the aim of assessing (1) the opportunities and challenges faced by the participants (in-service teachers), (2) the effectiveness of an argumentationbased strategy (DAIM) used by some of the in-service teachers to integrate science and IKS, (3) the manner in which the trained teachers actually taught using the DAIM, and (4) the impact of SIKSP on the participants’ professional development and research capacities. I used a hybridised version of Stufflebeam’s (2003) context, input, process, product (CIPP) as well as Guba and Lincoln’s (1989) Constructivist evaluation models to guide the study, within a constructivist-pragmatist paradigm. I used a questionnaire, semi-structured interviews, reflective diaries, and document analyses to collate the data from 22 in-service participants, as well as from the project director. The analyses were done using mixed methods, though largely dominated by qualitative approaches. The results suggest that: through the use of multiple sources of engagement in conceptual, practical, and discursive activities, SIKSP enabled the participants to change their views about science and IKS – from a largely positivist to a more dualistic worldview that considered IKS as a source of valid knowledge in science classrooms. SIKSP activities also enabled the participants to acquire the largely student-centred, discursive, interactive DAIM approach of teaching and learning to effect an inclusive science-IK curriculum. The teachers used DAIM to teach science, mathematics as well as socio-scientific topics, each teacher applying it differently. SIKSP had many positive impacts on the participants – psychological, social, intellectual, pedagogical and professional. Through SIKSP, many participants obtained higher degrees, advanced professionally, and some have become researchers in science and IKS; with two of the postdoctoral fellows now carrying on similar research at other universities in South Africa and beyond. An unanticipated outcome of SIKSP was the creation of the African Association for the Study of Indigenous Knowledge Systems (AASIKS) which is now pursuing an inclusive science-IKS vision at a much larger scale. Overall, in the view of the participants, SIKSP was very successful project, and its DAIM approach, though difficult to master, has many advantages that could be explored in-and-out of science classrooms.
Pre-service mathematics teachers’ engagement with the evaluation and construction of alternative mathematical models for the same phenomena
(University of Western Cape, 2020) Cornelissen, Belinda m.; Julie, C.
The overarching purpose of this research study was to ascertain the deliberations preservice mathematics teachers engage with when they construct alternative mathematical models for social phenomena. The study is situated within the mathematical competencies and, in particular, on the evaluation competency with the possibility of developing alternative models flowing from the evaluation. Twenty fourth-year pre-service mathematics teachers participated in the completion of three different mathematical modelling tasks on which the analysis was based. The data collected was analysed qualitatively. The researcher exploited a thematic analysis design to investigate how pre-service mathematics teachers build alternative models.
The influence of an in-service training Programme on Libyan biology teachers' Pedagogical content knowledge (pck)
(University of Western Cape, 2020) Tarek Abdalla; Ogunniyi, Meshach
Libya, as one of the third world countries, is struggling to address the issue of transformation and various institutional reforms (including the education system). For example, it has been observed that many biology teachers are faced with challenges relating to both subject matter knowledge (SMK) and pedagogical content knowledge (PCK) yet the expectation of the new curriculum is that biology teachers demonstrate professional efficacy in their work regardless of the challenges they face. In light of this, a group of Libyan secondary school biology teachers was investigated in Tripoli through a participatory action research process. The study was underpinned by the Shulman theory of PCK using a mixed-methods design to generate an understanding of the theory of basic knowledge of teaching.
The influence of an in-service training programme on Libyan Biology teachers' pedagogical content knowledge (PCK)
(University of the Western Cape, 2020) Abdalla, Tarek; Ogunniyi, Meshach
Libya, as one of the third world countries, is struggling to address the issue of transformation and various institutional reforms (including the education system). For example, it has been observed that many biology teachers are faced with challenges relating to both subject matter knowledge (SMK) and pedagogical content knowledge (PCK) yet the expectation of the new curriculum is that biology teachers demonstrate professional efficacy in their work regardless of the challenges they face. In light of this, a group of Libyan secondary school biology teachers was investigated in Tripoli through a participatory action research process. The study was underpinned by the Shulman theory of PCK using a mixed-methods design to generate an understanding of the theory of basic knowledge of teaching. This investigation examined the influence of an in-service training programme consisting of three components of PCK namely: teachers‘ subject matter knowledge (SMK); use of instructional strategies; and understanding of learners on a group of Libyan biology teachers‘ instructional practices. On the one hand, the investigation considered their theoretical knowledge, and their experiences during the professional development programme aimed at designing new teaching and learning activities and materials while on the other hand, it considered their practical knowledge in terms of their professional skills or their practical use of what has been learned during their pre-service training as well as what they learned during the professional development programme. Specifically, the study focused on biology teachers from the Hai Alandalus District (Libya). This representation enabled me to unveil the PCK components held to some extent by the Libyan teachers in general. Moreover, the PCK representation has also enabled me to clarify the category of the teachers‘ PCK in the Libyan context especially as their PCK was unknown at the commencement of the study. The findings have shown that the professional development used in the study facilitated the biology teachers‘ ability in several ways such as increased their PCK and SMK; improved their ability to organize activity-based lessons; increased their desire to use a variety of instructional strategies; increased the understanding of their learners‘ needs; improved their awareness that their learners‘ performance is not unrelated to their socio-economic background; and so on. Overall, the findings suggest that designing and implementing new teaching and learning activities and materials based on the teachers‘ knowledge, experiences, and needs, in a workshop context could provide an enabling learning environment for them as well as facilitate their potential to provide a powerful means for increasing their PCK, SMK and understanding their learners. The study also reveals that there is a great necessity for designers to mount professional development programmes that take into consideration the teachers‘ PCK to meaningfully promote their professional development and instructional practices.
The Effectiveness of peer instruction (PI) in enhancing pre-service teachers’ understanding of electromagnetism I in a Nigerian college of education
(University of the Western Cape, 2020) Kola, Aina Jacob; Langenhoven, Keith Roy; Kizito, Rita
This research study investigated the effectiveness of Peer Instruction (PI) in enhancing preservice teachers’ understanding of Electromagnetism I in a Nigerian college of education. PI as a research-based pedagogy was invented for the teaching of introductory science courses to large classes. Lectures in PI is made of short presentations on the main points, each followed by short conceptual questions known as ConcepTest, posed in a multiple-choice format, on the subject under discussion. Electromagnetism is a branch of Physics where students perform poorly at Colleges of Education in Nigeria. Electromagnetism I covers electrostatics, magnetostatics, current electricity, electrolysis, and capacitance. Each of these themes has different topics under it. Most students studying Electromagnetism I, cannot relate or connect what they learned in the classroom to real-world situations because they often learn by memorization (rote learning).
Social and cultural relevance of aspects of Indigenous Knowledge Systems (IKS), meteorological literacy and meteorological science conceptions
(University of the Western Cape, 2020) Riffel, Alvin Daniel; Luckay, Melanie B.
This research study examines those aspects of Indigenous Knowledge (IK) that could be socially and culturally relevant in the Western Cape Province, South Africa, for teaching meteorological science concepts in a grade 9 Social Science (Geography) classroom using dialogical argumentation as an instructional model (DAIM). The literature reviewed in this study explains the use of argumentation as an instructional method of classroom teaching in particular dialogical argumentation, combined with IKS (Indigenous Knowledge Systems), which in this study is seen as a powerful tool both in enhancing learners’ views and positively identifying indigenous knowledge systems within their own cultures and communities, and as tool that facilitates the learning of (meteorological) literacy and science concepts. With the development of the New Curriculum Statements (NCS) and the Curriculum and Assessment Policy Statements (CAPS) for schools, the Department of Basic Education (DBE) of South Africa acknowledges a strong drive towards recognising and affirming the critical role of IK, especially with respect to science and technology education. The policy suggests that the Department of Education take steps to begin the phased integration of IK into curricula and relevant accreditation frameworks. Using a quasi-experimental research design model, the study employed both quantitative and qualitative methods (mixed-methods) to collect data in two public secondary schools in Cape Town, in the Western Cape Province, South Africa. A survey questionnaire on attitudes towards, and perceptions of high school, of a group of grade 9 learners, as well as their conceptions of weather, was administered before the main study to give the researcher baseline information and to develop pilot instruments to use in the main study. An experimental group (E-group) of learners were exposed to an intervention - the results were recorded against a control group (C-group) that were exposed to no intervention. Both the E-group and C-group were exposed to a Meteorological Literacy Test (MLT) evaluation before and after the DAIM intervention. The results from the two groups were then compared and analysed according to the two theoretical frameworks underpinning the study, namely, Toulmin’s Argumentation Pattern - TAP (Toulmin, 1958) and Contiguity Argumentation Theory - CAT (Ogunniyi, 1997). The findings of this study revealed that: Firstly, the socio-cultural background of learners has an influence on their conceptions of weather prediction and there was a significant difference between boy’s and girls’ pre-test conceptions about the existence of indigenous knowledge systems within the community they live in. For instance, from the learners’ excerpts, it emerged that the girls presented predominantly rural experiences as opposed to those of the boys which were predominantly from urban settings. Secondly, those E-group learners exposed to the DAIM intervention shifted from being predominantly equipollent to the school science to emergent stances and they found a way of connecting their IK to the school science. The DAIM model which allowed argumentation to occur amongst learners seemed to have enhanced their understanding of the relevance of IK and how its underlying scientific claims relate to that of school science. Thirdly, the argumentation-based instructional model was found to be effective to a certain extent in equipping the in-service teachers with the necessary argumentation skills that could enable them to take part in a meaningful discourse. The study drew on the personal experiences and encounters from a variety of sources. These included storytelling-and sharing, academic talks with local community members recorded during the research journey, formal round table discussion and talks at international and local conferences, conference presentations, informal interviews, indigenous chats at social event-meetings, and shared experiences at IKS training workshops as a facilitator. These encounters lead to the formulation of the research study and occurred throughout the country in various parts of the Southern African continent including: Namibia, Zimbabwe, Malawi, Botswana, Tanzania and Mozambique.
Exploring the Incorporation of mental Arithmetic into primary school mathematics: A case of Oshana Region, Namibia
(University of the Western Cape, 2019) HAIMBODI, FRANS NDEMUPONDAKA; KHUZWAYO, HERBERT BHEKUMUSA
This study, “Exploring the incorporation of mental arithmetic into primary school mathematics: A case of Oshana region, Namibia”, explored the execution of mental arithmetic strategies in senior primary schools in the northern Namibia. Informed by the Critical Mathematics Education theory, the study explored the state of mathematics education in primary schools by looking at the computation strategies used by teachers and learners during classroom mathematics sessions at senior primary grades. Mathematics at the senior primary school level is expected to develop learners’ functional numeracy and logical thinking in order to be able to apply mathematics in their everyday lives. However, learners recorded low academic achievements in mathematics over the years despite numeral reforms that attempted to address the situation. This study was guided by the research question: How is the senior primary mathematics curriculum incorporating mental arithmetic? The study sampled 10 schools in the Oshana region in northern Namibia. Senior primary school teachers and learners at these schools were observed during mathematics lessons. The computation procedures used by both teachers and learners were recorded. The study utilised a mixed methods approach in two phases. The first phase consisted of classroom observations, individual teacher interviews and a psychometric mathematics test (pre-test) for the Grade 7 learners. The second phase consisted of a critical intervention for teachers and learners. The intervention involved series of workshops that trained teachers on mental computation strategies. The workshops were followed by a focused group interview for teachers. Out of the 10 schools, four were sampled (two experimental and two control) and the learners in the experimental schools were exposed to mental arithmetic strategies. A mathematics post-test was then administered to all the four schools. The study evaluated the effectiveness of the mental arithmetic approaches on learners’ performance.
Evaluation of an in-service degree programme at a Nigerian University
(University of the Western Cape, 2019) Fatoba, Abiodun Folakemi; Mbekwa, Monde
The Sandwich degree programme is an in-service training programme run by Nigerian Universities for primary and secondary school teachers who either do not have a first degree or those who do not have professional teaching qualifications. The main aim of this study was to evaluate the Sandwich degree programme at Fountain State University in Nigeria, and determine its impact on improving the subject content knowledge of teachers. This study was spurred by the poor performance of some learners in both external and internal examinations despite several efforts made by the government to improve the quality of education in Nigeria. The poor performance of learners has often been blamed on teachers who have no teaching qualifications and hence lacked pedagogical knowledge. The study therefore investigated the Sandwich degree programme at Fountain State University which was specifically designed to upgrade the qualifications of teachers. The study investigated the Sandwich degree programme to determine whether it adequately enhanced teachers’ content and pedagogical knowledge. The evaluation of the Sandwich degree programme was carried out using Kirkpatrick's Four-Level Training Evaluation Model. The study employed a qualitative research paradigm. The research sample comprised of three university lecturers (Sandwich degree lecturers), the director of the Sandwich degree programme and eight high school teachers purposively sampled who are graduates of the Sandwich degree programme. Data collection was achieved by means of questionnaires, semi-structured interviews and documentary analysis.
A teaching strategy to enhance mathematical competency of pre-service teachers at UWC
(University of the Western Cape, 2017) May, Bruce Mathew; Julie, Cyril; Holtman, Lorna
In this study a mixed methods approach was employed to investigate how exposure to a teaching strategy based on spiral revision, productive practice and a mainly direct expository instructional method would influence the mathematical competencies of procedural fluency and conceptual understanding of pre-service mathematics teachers at a South African university. A secondary concern of the study was how retention and transfer abilities of participants would be influenced if they experience mathematics through a teaching strategy underpinned by spiral revision and productive practice. A revised version of the taxonomy table of Anderson et al (2001) was utilized to classify learning and instructional activities in the study in terms of mathematical reasoning and knowledge requirements. In this revised taxonomy the cognitive processes are understood to operate on knowledge structures during the process of cognition (i.e. reasoning categories based on knowledge categories.). The categories of the revised taxonomy table were the main measuring instrument for the study. The findings of the study indicate that the competencies of procedural fluency and conceptual understanding were positively enhanced by the teaching strategy. Some categories however did not show the same level of positive enhancement. Arguments are presented as to why this might be the case and possible solutions are mooted. Findings also indicate that retention and near transfer abilities of participants were positively enhanced. Far transfer abilities were unchanged post intervention. Explanations are offered for this finding and possible resolutions are suggested.
Continuous professional learning community of mathematics teachers in the Western Cape: developing a professional learning community through a school-university partnership
(University of the Western Cape, 2015-11) Smith, Charles Raymond; Julie, C; Holtman, L; Smith, J
Ways of enacting effective professional development (PD) and professional learning (PL) of teachers are diverse and often contested and therefore needs sustained inquiry (Schuck, Aubussona, Kearney, & Burden, 2013). The “quick fix” mentality that is endemic to most including those aimed at educational systems leads to very superficial implementation of improvement strategies, including teacher development. These strategies are usually bureaucratically mandated and superficially implemented in a top-down manner. One of the critical drawbacks of such superficial implementation of top-down improvement strategies is that it fails to appeal to teachers because of their historical experiences of such short term and intermittent improvement interventions. This study focussed on the development of a Professional Learning Community (PLC) as a possible continuous professional teacher development (CPTD) model with a promise to deliver effective CPTD. Literature in this regard indicates this model of CPTD as highly effective to support sustained teacher development. The efficacy a PLC is predicated on a collaborative and relational approach to teacher development and professional learning underpinned by a microclimate of commonality. The initiation of PLCs is a complex task. It requires a deep understanding of the processes involved in orientating teachers to processes that involve reflective dialogue and collaborative inquiry. Hence this study sought to investigate experiences of teachers in a PLC established through an alliance involving teachers, didacticians and education officials. This study found that the PLC signifier conveys significant meaning for teachers in terms of their engagement in the PLC. Moreover, teachers’ experiences of the PLC model confirmed the generally accepted features of a PLC. The importance of having a common vision, norms and standards was shown to be an important dimension of the PLC. Besides the fact that the active promotion of this shared vision by the PLC leadership and other education administrators was highlighted, teachers in general accepted the importance of being reflective practitioners. Despite this belief in the value of collaborative reflection, this study found that it does not take place as often as one would expect. This is, to some extent, due to the timetabling arrangements at most schools in the sample. Findings of this investigation provided evidence that it is possible in a PLC to effect a shift from professional development to professional learning. This is consistent with literature in this regard, for example, Benken & Brown (2010) support this argument by indicating that CPTD should be viewed as professional learning that is sustained over time. However, the issue of sustainability is an important challenge. This study revealed that teachers see sustainability as a function of three important variables, namely, recognition by school leadership and administrators, support from the organised teacher movements and subject organisations, and teacher commitment. Important affordances of a PLC identified through this study are relational agency, epistemic agency and a micro-climate of commonality. These affordances are viewed as important enablers of collaborative inquiry and reflective dialogue and underscores the community aspect of a PLC.
The effectiveness of an argumentation instructional model in enhancing pre-service science teachers’ efficacy to implement a relevant science indigenous knowledge curriculum in Western Cape classrooms
(University of the Western Cape, 2014) Langenhoven, Keith Roy; Ogunniyi, Meshach B.; Fakudze, C.
The study investigated the impact of a dialogical argumentation instructional model (DAIM) as an intervention teaching strategy to assist pre-service science teachers to implement integrated science-indigenous knowledge (IK) lessons during their seven week block teaching practice at schools in the Western Cape. This imperative is found in Specific Aim 3 of the Curriculum and Assessment Policy Statement (CAPS) of the South African School Curriculum (Department of Basics Education, 2011). The study focussed on the pre-post conceptions of pre-service science teachers’ conceptions of the nature of science and the nature of indigenous knowledge. In addition the study examined pre-service teachers’ sense of self-efficacy in deploying a dialogical argumentation instructional model to implement an integrated science-IK lesson. The sample consisted of a cohort of thirty (30) Post-graduate Certificate of Education (PGCE) students training to teach at the Further Education and Training (FET) phase of school. They were a combined class enrolled for method in Natural Sciences, Life Sciences and Physical Sciences. A mixed methods approach was used to generate quantitative and qualitative data using a series of questionnaires, reflective diaries, journals and focus group interviews. Transcripts provided a rich bank of data of which only exemplars were used to highlight trends and to illustrate how theoretical constructs were used as analytical tools. The theoretical constructs used were Toulmin’s (1958/2003) Argumentation Pattern (TAP), Ogunniyi’s (1997) Contiguity Argumentation Theory (CAT) and Banduras’ Social Cognitive Theory (1986). The findings showed that the pre-service teachers appeared to overestimate their sense of self-efficacy (i.e. the ease and comfort) in using DAIM to implement a science- IK curriculum at the pre-test than at the post-test. The study also identified important implications for policy, teacher training programmes, teaching practice, pre-service science teachers, learners and further research. Furthermore, the pre-service reflective experiences indicated their increased awareness of the challenges and successes related to using dialogical argumentation to integrate a science-IK lesson. The most important contribution of this study to an argumentation paradigm was the emergence of a visual model called the Pyramid Argumentation Model that succinctly connected the apparent disparate module units in a holistic way (To be discussed in follow-up reports). The findings revealed numerous complexities as the participants navigated their own cosmologies of a scientific worldview and that of their indigenous knowledge worldview. Finally, the findings have not only corroborated the findings in earlier studies with respect to the merits and demerits of argumentation instruction but also identified various challenges that prospective and even practicing teachers might encounter in an attempt to make school science relevant to the sociocultural environment of learners especially those living in indigenous or traditional societies like the participants in this study.
The effect of an argumentation-based training programme on pre-service science teachers’ ability to implement a learner-centred curriculum in selected Eritrean Middle Schools
(University of the Western Cape, 2014) Berhe, Senait Ghebru; Ogunniyi, Meshach B.
This study is part of a larger school-based research project aimed at training science teachers to integrate argumentation into K-12 science instruction. The current study examined the effect of an argumentation-based training programme on pre-service science teachers’ ability to use an argumentation-based instructional model (ABIM) to implement a learner-centred curriculum in selected Eritrean middle school science classrooms. The study was situated within the social constructivist and argumentation theoretical frameworks. A predominately qualitative research approach was utilized to address the purpose and the research questions of this study. The research design was primarily a case study of a cohort of 25 undergraduate middle school pre-service science teachers, enrolled in a teaching practice course in January, 2013 under the auspices of the Department of Science, College of Education at Eritrea Institute of Technology (EIT). None of the pre-service teachers involved in the study had taken a formal course work, workshops or seminars on argumentation instruction. Six of the 25 pre-service teachers were selected for an in-depth qualitative analysis using purposive sampling technique (Groenewald, 2004; Flyvbjerg, 2006). This study utilized multiple data collection instruments including, questionnaire, argument-based tasks, classroom observation, interview, reflective questionnaire, video-tape class lessons and field notes. Argumentation framework as espoused in the work of Toulmin (1958) and Ogunniyi (2004) were utilized as the units of analysis for the data collected in the study. Furthermore, the study considered a variety of validity and ethical protocols to ensure the findings and interpretation generated from the data were valid.
Relevance of science education in Zimbabwe from the perspective of secondary school children - the voice of the learner about science and technology in a developing country
(2011) Mavhunga, Francis Zvidzai; Sjøberg, Svein; Mikalsen, Øyvind; Julie, Cyril
In all countries, regardless of culture and level of development, science and technology(S&T) are seen as key areas for further material development and welfare. A certain proportion of the population needs to develop S&T-related skills and competences at a high level. But also for the majority, who will not enter such careers, S&T are key subjects to master the challenges in everyday life and for full participation in democracy. In our efforts to make S&T attractive as careers and as a key subject for mastering challenges in everyday life, we need to know more about the interests, concerns and values of the learners.The study of Zimbabwean learners sought to find what students like to learn in science, their interest in science lessons, use of science principles in everyday life and what attitudes they have about the environment. Learners’ attitudes to S&T were also measured by an open ended question that sought their ideas on what they would like to research on if they were scientists.The empirical basis for this thesis is data collected with the ROSE instrument, developed by a team of international scholars in S&T education. Data used in this thesis is from twenty one secondary schools in Zimbabwe (N=734) targeting sixteen year old learners.Comparisons are made with twenty eight other countries.Factor analysis and descriptive statistics has been used to make comparisons of Zimbabwean and international trends.The Zimbabwean sample generally showed a mismatch between their expectations and realities of the science education curriculum. Results suggested that Science education was largely irrelevant to their needs and interests. Many out-of-class experiences were not explored in science classes. However, the sensitivity of learners to significant issues around their lives, such as AIDS and other diseases showed in their wish to research to cure those infected.The newly found voice of the learners will provide new insights on how to improve science education in Zimbabwe in such a way that it is able to meet the hopes, aspirations and the perceived interests, needs and priorities of the learners. Rapid developments in mundane applications of science and technology require that the curriculum negotiates a level that empowers learners to cope with a technologically driven world.For the development of capabilities to understand and use science and technology, either in daily life or study at higher levels the science education debate must periodically consider needs, views and concerns of the learners themselves among other stakeholders.
Fitted numerical methods to solve differential models describing unsteady magneto-hydrodynamic flow
(2011) Buzuzi, George; Patidar, Kailash C.
In this thesis, we consider some nonlinear differential models that govern unsteady magneto-hydrodynamic convective flow and mass transfer of viscous, incompressible,electrically conducting fluid past a porous plate with/without heat sources. The study focusses on the effect of a combination of a number of physical parameters (e.g., chemical reaction, suction, radiation, soret effect,thermophoresis and radiation absorption) which play vital role in these models.Non dimensionalization of these models gives us sets of differential equations. Reliable solutions of such differential equations can-not be obtained by standard numerical techniques. We therefore resorted to the use of the singular perturbation approaches. To proceed, each of these model problems is discretized in time by using a suitable time-stepping method and then by using a fitted operator finite difference method in spatial direction. The combined methods are then analyzed for stability and convergence. Aiming to study the robustness of the proposed numerical schemes with respect to change in the values of the key parame- ters, we present extensive numerical simulations for each of these models. Finally, we confirm theoretical results through a set of specificc numerical experiments.
Fitted numerical methods for delay differential equations arising in biology
(2009) Bashier, Eihab Bashier Mohammed; Patidar, Kailash C.
Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.
Recent transformations in West-Coast Renosterveld: patterns, processes and ecological significance
(University of the Western Cape, 2008) Newton, Ian Paul; Faculty of Science
Malawian secondary school students' learning of science: historical background, performance and beliefs
(University of the Western Cape, 2006) Dzama, Emmanuel Nafe Novel; Kolstoe, Stein Dankert; Holtman, Lorna; Mikalsen, Oyvind; School of Science and Mathematics Education; Faculty of Education
This study explored the problem of poor performance in science among students who are provided secondary school places on merit in Malawi. Existing studies of the problem are inconsistent suggesting that these studies may have shed light on some parts of a complex problem. Questionnaires, interviews and analysis of documents were used to obtain information concerning students’ conceptions of science, science learning and events that eventuated into the problem in the past. The population for this study was 89 government and governmentassisted secondary schools. From that population eighteen schools were randomly selected from each of the six education divisions in the country. One thousand five hundred secondary class 3 students drawn from randomly selected schools participated. The participating students completed a 31item learning beliefs and practices questionnaire with items drawn from the science education literature and adapted to the local situation and a selfefficacy and attribution of failure questionnaire. Forty students were interviewed about their concepts of science and science learning. Relevant documents found in the Malawi National Archives were analyzed to determine the origin of the problem.
Prospective Zimbabwean "A" level mathematics teacher's knowledge of the concept of a function
(University of the Western Cape, 2006) Nyikahadzoyi, Maroni Runesu; Mtetwa, David K.; Julie, Cyril; Torkildsen, Ole Einar; School of Science and Mathematics Education; Faculty of Education
The purpose of the study was to investigate prospective 'A' level mathematics teachers’ knowledge of the concept of a function. The study was a case study of six prospective Zimbabwean teachers who were majoring in mathematics with the intention of completing a programme leading to certification as secondary mathematics teachers. At the time of the study the six prospective teachers were in their final year of study. Prospective teachers' knowledge of the concept of a function was assessed through task-based interviews and reflective interviews. These interviews, which were done over a period of three months, were structured to capture the prospective teachers' subject matter knowledge and pedagogical content knowledge for teaching the concept of a function. The interviews were also meant to capture the prospective teachers' underlining pedagogical reasons for their choices of the examples, representations and teaching approaches when planning to teach the concept. As part of the study a theoretical framework for understanding prospective teachers' knowledge of the concept of a function was developed. The framework, which was developed, was used as an analytical tool in analyzing prospective teacher’s knowledge of the concept of a function. The results of the study indicated that the prospective teachers had a process conception of a function although some of them had given a set-theoretic definition of a function in which a function is perceived as a mathematical object. They also confined the notion of a function to sets of real numbers. Functions defined on other mathematical objects (for example, the differential operator and the determinant function) were not considered as functions by five of the six prospective teachers.

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