Philosophiae Doctor - PhD (Mathematics and Science Education)

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Learning model (DAIBLM) in the vocational engineering mathematics classrooms at selected technical and vocational education and training colleges in South Africa
(University of the Western Cape, 2024) Goodman, Lynn
An investigation of the Dialogical Argumentation Instructional Blended Learning Model (DAIBLM) in the Vocational Engineering Mathematics classrooms at selected Technical and Vocational Education and Training colleges in South Africa. This thesis is part of a PhD study investigating the impact of a blended learning model on the understanding of functions in mathematics among first-year students enrolled in a Technical and Vocational Education and Training college in the Western Cape, South Africa. A mixed-methods approach was employed to examine the effectiveness of the blended learning model, which combined traditional face-to-face instruction with digital resources and online activities. The face-to-face component involves a dialogical argumentation instruction approach, while blended learning incorporates computer-mediated instruction. The DAIBLM replicated the combination of the Dialogical Argumentation Instructional Model (DAIM) from the master's study of the researcher and the blended learning approach via the usage of computers. The study focused on a group of students, exploring their understanding, problem-solving skills, and attitudes toward learning functions. The findings provide insights into the potential of blended learning to enhance mathematics teaching in vocational settings, highlighting implications for teaching practices and future research. This study was motivated by the low performance in passes, retention, and throughput rate, which continue into the Technical and Vocational Education and Training (TVET) band. According to Newman-Ford, Lloyd, and Thomas (2015), the annual graduation rate in engineering has decreased steadily while engineering jobs have gradually increased. Three questions informed this investigation: 1) What conceptions of functions did the selected students hold before DAIBLM, and how are these conceptions related to their everyday life experiences? 2) Is there a significant difference in the performances regarding the understanding of functions of the experimental group(E-group) after exposure to DAIBLM? 3) How does the E-group perceive the DAIBLM? The theoretical framework used in this study was constructivism theory, as espoused by Vygotsky (1978), and Connectivism as a learning theory (Siemens, 2005). The analytical tools that the study used were Toulmin’s (1958) Argumentation Pattern (TAP) and Ogunniyi's (2007a) Contiguity Argumentation Theory (CAT). The study was limited to three engineering campuses from one college and province out of the 50 TVET colleges in South Africa. Therefore, it could only represent some of the TVET colleges in the study area. The study adopted a case study approach where quantitative and qualitative data were analysed. The analysis revealed a positive attitude among the students who were exposed to the DAIBLM compared to those who were not exposed. Additionally, the findings revealed that the experimental group (E-group) enjoyed the idea of blended mathematics lessons because they could freely engage on functions with their peers via face-to-face and the TikTok social media platform. Furthermore, virtual collaborative tasks promoted effective student communication and collaboration, enhancing critical thinking and problem-solving skills. Interestingly, the female component in this study obtained much higher scores than the male. It is hoped that the investigation findings will contribute to raising awareness of DAIBLM, raise standards regarding mathematics teaching and learning at the college level, and simultaneously improve results and throughput rate.
Worldview presuppositions and conceptions of force held by junior secondary school science students.
(University of the Western Cape, 2003) Adams, Saleh; Ogunniyi, Meshach B.
The central concern of this study was to determine 12-13 year old students' worldview about force and how such worldview presuppositions affect their conceptions of force. The study accepted the constructivists' view, viz. that students bring ideas based on prior experience to the classroom, and these ideas or beliefs affect the ways they respond to and interpret instruction in science. A distinctive methodological feature of this study was the way the quantitative information obtained by structured observation and the class environment questionnaires were combined with qualitative data derived from obtained naturalist/interpretive procedures. The experimental design that was chosen for the pilot and main studies was the quasi-experimental model based on a modified Solomon-3-control group design. A battery of instruments was used to assess the cognitive, affective, psychomotor and observational aspects of the study. The main instrument, the Performance on Force Test (POFT), consisted of questions designed to elicit the students' qualitative understanding of the concept force. The POFT was constructed to capture both conceptual and alternative worldviews of the subjects regarding force. A sample of three comparable schools was used in the study. Two schools constituted the experimental (E) and true control (C1) groups and the third school served as the second control group (C2). The E and C2 groups received the experimental Curriculum on Force (COF) intervention; whereas group C1 received the tradition teaching approach. To minimise the effects of contamination, the treatment groups were chosen from different areas of metropolitan Cape Town. A total of three teachers and 91 students were involved in the study. To ameliorate the students' conceptions of force, the teachers were exposed to an exemplary instructional practice model for three weeks. Similarly, the students were exposed to exemplary instructional materials for six weeks. A pretest, post-test and delayed post-test evaluative instruments on the selected dependent variables were administered to the subjects to obtain the data needed for analysis. The collected data were analysed using descriptive statistics (mean, standard deviation, frequencies and percentages) and inferential statistics (analysis of covariance and t-test). Contrary to expectation, the induction programme that the teacher of group C2 went through with the teaching of the COF did not successfully crystalize in her class, unlike the teacher of the experimental class, E. Perhaps with more time, the teacher of group C2 could have implemented the teaching styles that the teacher of group E used successfully in teaching the COF emphasized during the induction programme. All the hypotheses were tested at the 0.05 level of significance. The major findings include: 1. The students involved in this study had already acquired some ideas about force before encountering the concept in the new science lessons. At the pretest level, the students in the experimental group (n = 30) had .x = 20.32, SD= 5.18 and the control group C1 (n = 26), x = 20.44 and SD = 4.63 with t = 0.37 at p = 0.05. 2. The post-test was administered after the students had been exposed to the exemplary instructional material known as the Curriculum on Force (COF) material. The achievement outcomes of the POFT at post-test level gave x = 26.19 and SD = 5.41 for the experimental group and for the control group C1, x = 24.54, SD = 3.71 and control group C2, .x = 23.42 and SD = 5.03 respectively. These mean scores were relatively close to the grand mean score of 24.72. However the mean of C2, where the students also received the treatment, was somewhat lower than C1, where the students were not exposed to the COF treatment. 3. Pairwise comparisons of the post-test scores of the experimental and control groups showed that the difference between E and C1 was not statistically significant (t = 1.34, at p = 0.18). On the other hand, the post-test scores of E and C2 were statistically different (t = 2.18, at p = 0.03), whereas C1 and C2 were not statistically different (t = 0.89, at p = 0.37). 4. The outcomes of the performance on the POFT at the delayed post-test level gave the combined mean score for the three groups of 24.60 and a SD = 4.54. For the Experimental (E) group the mean score was 26.15 and SD = 3.87, whereas for the control groups C1 and C2, the means were 24.54 and 23.11 and the SD's = 3.72 and 5.14, respectively. Although the mean achievement scores of E and C1 were not statistically different (i.e., t = 1.43, p = 0.16 and t = 1.21, p = 0.23, respectively), those for E and C2 were statistically different (t = 2.31 and p = 0.02). 5. a) As regards gender on the subjects' conceptions about force, the females obtained a slightly higher mean than their male counterparts, although the difference was not statistically significant. 5. b) A one way t-test for comparing performance of 12 and 13 year olds on the POFT showed a significant difference in their performance (t = 3.50 at p < 0.05). 5. c) As regards the effect of language, there appeared to be a significant difference between the English and Xhosa speakers when their pretests and post tests were compared (t = 7.74 and p < 0.05). 5. d) The achievement differences between the two religious groups were not statistically significant in the pretest (t = 0.79 at p = 0.05), nor in the posttest (t = 1.29, p = 0.05). 6. As in many earlier studies, it is worth noting that alternative conceptions held by the students about force persisted despite the spirited effort made in the study to attain conceptual change. No doubt, the instructional exemplary model used by the two teachers in both the experimental and control groups contributed to an overall increase in performance of the students on the POFT. The approach did not prove superior to the traditional approach used by the true control group (C1) teacher. The students in C2 obtained the lowest mean score. However, all three groups maintained their relative positions even at the delayed post-test. This probably indicates the retention of what had been learned by the students. Different instruments were used to study classroom dynamics with the experimental and control groups. This was followed by interviews with teachers and their students about various aspects of force. The aim was to obtain a robust picture of classroom transactions during the study period. An analysis of both the quantitative and qualitative data indicates an increased understanding of force by the subjects. However, it was evident that the instructional model would perhaps need to be refined and implemented over a longer period than has been done in this study before any significant impact is achieved. Whether other outcomes might have occurred, the failure to achieve significant conceptual change has once more demonstrated the complexity of the teaching-learning process. By the same token, it has generated a greater respect on the part of the investigator for the work of science teachers and an appreciation for their onerous tasks. Finally, the implications of the findings for teacher training, curriculum and instructional practice, as well as areas warranting further investigations, were highlighted.
Learning mathematics through parental support during Covid-19 pandemic: Teaching of junior primary learners in Namibia
(Universty of the Western Cape, 2024) Shikwaya ,Renate Olga; Khuzwayo, Bhekumusa
The COVID-19 pandemic has caused unexpected and sudden educational changes for everyone involved, including learners, students, teachers, education officers, policymakers, guardians and parents. Global associations have focused on their reactions in emergencies by using elective methods of instruction. The usual face-to-face teaching and learning techniques were supplanted by homeschooling and e-learning. Everyone involved in education had to adjust to creative strategies. Most studies focused on teachers' and students' difficulties, barriers and new challenges. However, parents were also given a new role, especially in the junior primary phase (Pre-primary to Grade 3), as they were expected to assist by supporting their children's school subjects, including mathematics. The critical problem explored was the backlog in learners' understanding of mathematics concepts caused by learning inequalities during the COVID-19 lockdown. During the COVID-19 lockdown, parents had to support their children throughout the learning process—the current study aimed to investigate how parents have been crucial in supporting their children's mathematics learningat home.
The impact of intergrating the history of science into the teaching and learning of life sciences in the further education and training curriculum
(University of the Western Cape, 2024) Buthelezi, Penelope Zamashenge Gugulethu; Langenhoven, Keith
This study examined the impact of incorporating the History of Science (HoS) into the teaching and learning of Life Sciences in the FET curriculum. A sample of ten (10) Grade 11 Life Sciences teacher respondents from 2 (two) public secondary schools were chosen at random for the study's qualitative component. These schools were drawn from sixteen public schools in the Thabo-Mofutsanyane district, in the Free State Province of South Africa. A selected sample of fifty (50) Grade 11 learners was further drawn from these 2 (two) selected schools for the quantitative part of the study. The study developed History of Science Integrated Instruction (HoSII) experimental unit model as a teaching strategy and assessment tools. The study employed a sequential exploratory mixed methodological research design, where qualitative and quantitative data were collected sequentially. Qualitative data was collected through open-ended questionnaires and was analyzed a week prior to the implementation of the treatment. This served to inform the implementation of the HoSII experimental unit model. Quantitative data from learners was collected by one test instrument that was administered at varying periods, a preliminary test first, a day before the treatment, and as a post-test immediately after the intervention. The learners’ scores obtained from pre and post-tests were analysed using SPSS statistical analysis. The study findings indicated that historically based instruction impacted on Grade 11 learners’ educational achievement.
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.

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