Science and Technology Education

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Exploring pre-service mathematics teachers' knowledge and use of mathematical modelling as a strategy for solving real-world problems.
(2008) Dowlath, Eshara.
Mathematical modelling is an area in mathematics education that has been much researched but conspicuously absent from the South African curriculum. The last few years have seen a move towards re-inclusion of mathematical modelling in the South African school curriculum. According to the National Curriculum Statement (2003a), “mathematical modelling provides learners with the means to analyse and describe their world mathematically, and so allows learners to deepen their understanding of Mathematics while adding to their mathematical tools for solving real-world problems”. The purpose of this study was to explore pre-service mathematics teachers’ conception of mathematical modelling and the different strategies that pre-service mathematics teachers use when solving real-world mathematics problems. This study further investigated pre-service mathematics teachers’ ability to facilitate the understanding of specific mathematical modelling problems. Twenty-one fourth year Further Education and Training students from the Faculty of Education, University of KwaZulu-Natal participated in this study. In order to obtain appropriate data to answer the research questions, the researcher designed three different research instruments. The open-ended questionnaire and the task-based questionnaire were administered to all the participants, whilst ten participants were chosen to be interviewed. The data that was collected was analysed qualitatively. The research findings emanating from this study suggested that pre-service mathematics teachers did not have a suitable working knowledge of mathematical modelling, but were nonetheless able to use their mathematical competencies to solve the three real-world problems that formed part of the task-based questionnaire. It was found that although the participants were aware of different strategies to solve these real-world mathematics problems, they choose to use the ones that they were most familiar with. It is hoped that this study would prompt more universities to include mathematical modelling courses in the curriculum for prospective mathematics teachers.
Promotion of critical thinking in school physical science.
(2008) Stott, Angela Elizabeth.; Hobden, Paul Anthony.
This dissertation describes an action research study aimed at promoting critical thinking in learners while learning physical science within the South African national curriculum. The data were primarily qualitative in nature, and were collected primarily through participant observation, composed of audio- and video- recorded lessons, interviews, questionnaires, journal entries and written material. Data collection, analysis and interpretation were done in the inductive, cyclic manner of action research. This process was guided by research questions about task characteristics, their position in the teaching sequence, the role of the learning environment, and the need to adjust tasks to fit the needs of different learners, so as to effectively promote critical thinking. A pragmatic approach was used. It was found that it is possible, using particular strategies and tasks, to promote critical thinking while meeting the curriculum outcomes, although the intense syllabus pressure of the curriculum makes this challenging. Task design characteristics and positioning in the teaching sequence, and conditions of the learning environment, were found to affect a task’s effectiveness at promoting critical thinking. Various teaching strategies can improve attainability by a wider range of learners. An instructional model, The Ladder Approach, emerged as being most likely to promote success. This was found to be successful when evaluated against criteria of active engagement and interest by learners, attainability with effort, display of critical thinking traits, and compatibility with the South African curriculum. In this model, an interesting problem is posed at the start of a section, after which direct instruction and learner engagement with the problem run parallel to one another, linked by scaffolding tools which are engaged in individually and collaboratively.
Post-graduate physical science teachers' knowledge of and classroom practice in the nature of science in KwaZulu-Natal.
(2008) Naidoo, Kumarasen Kristnasamy.
The introduction of the new Physical Science curriculum in South Africa in 2006 has created challenges for physical science teachers and curriculum developers, including tertiary science educators. The curriculum recommends that the Nature of Science (NOS) has to be taught in an integrated manner in physical science lessons. In addition approximately one-third of all questions in class tests and examinations should be on NOS. Studies that were conducted nationally and internationally have shown that most science teachers‟ have inadequate views of NOS. This study, in particular, looks at post- graduate physical science teachers‟ knowledge and classroom practice of the Nature of Science in KwaZulu-Natal. Data was collected using a NOS questionnaire by a group of 38 FET physical science and life science teachers who had completed an honours module in NOS. Part of this module included the history and philosophy of science in classroom lessons, indigenous knowledge, and science and culture. Four physical science volunteers were then selected for in-depth classroom observations and interviews. This formed the main data for the study with fieldwork carried out in teachers‟ classrooms. Results indicated that postgraduate science teachers have an adequate understanding of NOS, mainly as a result of having completed modules covering NOS objectives, history of science and philosophy of science. Furthermore, evidence confirms that these teachers made positive attempts to plan and teach for the achievement of the NOS objectives during physical science class lessons and used materials and references from their post-graduate programmes.
The role of visual literacy on grade 11 learners' conceptual understanding of graphical functional relationships.
(2009) Rampersad, Rajesh.
This study intends to foreground visual literacy within the wider context of visualisation and visual thinking in mathematics teaching and learning. Visualisation in general has been receiving attention in mathematics education research. I distinguish visual literacy from visualisation by referring to visual literacy as the combination of visualisation and logical thought. Visual literacy emphasises construction of meaning through the process of decomposition, comprehension and analysis of visual representations. The section on functional relationships is located in the National Curriculum Statement (NCS) for mathematics in the Further Education and Training (FET) phase for Grades 10-12 (Department of Education, 2003). Graphical functional relationships, which form an integral part of functions and algebra in the FET phase for Grades 10-12, demand visual literacy, which includes graphical interpretation and comprehension skills. Therefore, the conceptual understanding associated with graphs is dependent on the way graphs are presented. This study examines learners‟ and educators‟ procedural and conceptual understanding of the graphs they sketch and interpret in the FET curriculum. The data analysis contributes towards the fast growing body of knowledge on visualisation in mathematics with the significant impact visual literacy has on the conceptual understanding of mathematical graphs. The analysis reveals that the overarching theoretical framework of constructivism embracing the Process-Object, Visualizer-Analyzer and Semiotic models are useful in illustrating and justifying the link between visual literacy and the conceptual understanding of learners. In examining the visual understanding of graphical representations of ten Grade 11 learners and the two mathematics educators that teach them, the data reveals that learners display a somewhat skewed understanding of the nature of the Cartesian plane, the characteristics of graphs, functional notation and graphical terminology. In fact their educators, in some instances, displayed similar understandings. Learners display procedural understanding of graphical representations to a large extent. The educators‟ visual understanding does suggest that learners‟ interpretation of graphs is in some way influenced by the way they teach. The overriding contribution of the research study is that visual literacy plays a significant role in the conceptual understanding of functional graphical relationships. The relationship between graphical representations and logical thought is central to visual literacy. Key concepts: visual literacy, conceptual understanding, graphical representations, visualisation, analytical thinking, constructivism, process-object, Visualizer / Analyzer, semiotics and vehicles of reasoning.
Teachers' interpretation and implementation of the policy on indigenous knowledge in the science national curriculum statement.
(2010) Naidoo, Premella Devie.
In the new National Curriculum Statement in South Africa, there has been a strong drive towards recognizing and affirming the critical role of indigenous knowledge (IK), especially with respect to science and technology education. The Natural Sciences, Physical Sciences and Life Sciences curricula statements form the basis of this research. This study strove to establish how science teachers responded to the inclusion of indigenous knowledge systems (IKS) in their science classrooms. My study began with 23 science teachers who completed a university module ―Issues in Science Education, which included an IKS component. The study investigated firstly, what currently informed teachers‘ thinking, knowledge and action of IKS. Secondly, the research questioned how teachers interpreted and implemented IKS in the science classroom. A sample of three teachers were followed into their classrooms to investigate how they specifically implemented Learning Outcome Three related to IK in the Science Curricula Statements, and what approaches pertinent to the inclusion of IK were developed. That is, the study explored how shifts were being made from a theoretical phase at the university where teachers engaged IK to an actual phase of implementation in their school science classrooms. Finally I attempt to explain why the teachers interpreted and implemented IK in the way they did. Production of data took place from 2006 to 2007, and used surveys, telephonic interviews, written assignments, face-to face interviews, classroom observations and reflective interviews. The three case studies involved three science teachers at three secondary schools in the province of Kwa-Zulu Natal, South Africa. The study found that the three teachers used three very different approaches through which IKS was brought in the science curriculum: an incorporationist approach, that brings IKS into science by seeking how ―best IKS fits into science; a separatist approach that holds IKS ―side-by-side with scientific knowledge; and an integrationist approach that ―links and makes ―connections between IKS and science. The approaches developed by the teachers were found to be informed by their biographies, values, cultural backgrounds and worldviews.
Science foundation students' experiences at a tertiary institution.
(2008) Keke, Bulelwa.; Stears, Michele.
Abstract not available.
A description of mathematical proficiency in number skills of grade ten learners in both the mathematics and mathematics literacy cohorts at a north Durban school.
(2008) Moodley, Vivendren Govindarajaloo.; Hobden, Sally Diane.
The main objective of this study was to determine the progress made in the development of mathematical proficiency, in the domain of number skills, by learners in the two cohorts (namely: Mathematics and Mathematical Literacy) during Grade ten. The research was conducted at Temple Valley Secondary School, which is situated at Verulam, north of Durban in KwaZulu-Natal. Furthermore, this research study was questionnaire-based employing basic descriptive statistics as well as qualitative analyses. Data was collected through numeracy (number) skill tests, a questionnaire and focus group interview responses of grade ten mathematics learners. A total of two skill tests were administered and 3 focused group interviews were conducted with six grade ten learners each. The first test and first attitudinal questionnaire was administered in May 2006 when learners had branched off into the two paths of mathematics. Thereafter, a second test and second attitudinal questionnaire was administered, during October 2006; when learners had completed most of the school year. The October-test was followed by the focus group interviews. A convenient sample was used in selecting the learners for this research study and a purposeful sampling technique was used for the focus group interviews. All grade ten learners at Temple Valley Secondary School were selected as the sample. The results showed that the mathematics learners slightly outperformed the mathematical literacy learners in the development of mathematical proficiency for number skills. The findings from this research could inform: Teachers of grade ten learners with an interest in improving the mathematical proficiency, in number skills, of learners and; curriculum developers and materials development specialists who prepare mathematical material for grade ten classrooms. The results showed that none of the grade ten learners, from either cohort, were mathematically proficient in May or October. From the study, it was noted that the female grade ten learners generally outperformed their male counterparts. The focus group interviews revealed that learners had a positive attitude to the learning of the subject mathematics, despite the poor test results of this study.
An investigation into learner perceptions of mathematics : a means to understanding the challenges of learning mathematics
(2007) Moodley, Mogasuri.
The purpose of this study was to investigate the experiences and perceptions that learners have in the maths class with the aim of determining learners’ attitude to maths. It also intended to identify and understand the challenges that maths learners face in the maths class. The findings from this investigation would be used in the development of strategies to (a) improve the attitude of learners in the maths class, (b) develop healthier self-efficacy beliefs in learners and (c) create a positive learning environment for maths learners. To this end, a poster activity and group interview were used as the data collection instruments for the qualitative part of the research. The poster activity entailed the development of a poster by learners in which they recorded information on their experiences and perceptions of maths. This highlighted emerging themes that were further explored in the group interview and used in the development of the questionnaire. A group interview was conducted with a select group of learners with the intention of confirming the themes that had emerged from the poster activity. The quantitative phase of the study included a questionnaire, the design of which was based on the findings from the poster activity and was administered to all grade eleven learners of maths in order to determine whether the findings from the poster activity were representative of all the grade eleven maths learners. These data collection instruments generated data that was used to answer the main research questions. Analysis and interpretation of the findings lead to the following conclusions being reached: (a) Learner attitude to maths is in part a product of the accumulated experiences and perceptions of learners in the maths class, (b) The teacher, peers and learners’ self-efficacy beliefs affect maths learning and (c) The learning environment is an important factor in maths learning. The final part of the write-up includes the implications that this research has for the practising maths teacher with suggestions for further research in the area of affect.
Perceptions of the notion of mathematical literacy as a competence and as a subject.
(2007) Madongo, Phineas Sponsor.; Hobden, Sally Diane.
Given the controversy surrounding the theoretical concept of mathematical literacy within mathematics education community around the world and, in particular, its introduction as a new subject of study in the South Africa’s FET curriculum as part of a social transformation process, it seemed necessary and appropriate that a study of this nature had to be undertaken. Thus the study explored perceptions of the notion of ‘mathematical literacy’ as a competence and as a subject of study. It focused on a group of first-year in-service teachers who were part-time students in the faculty of education at Edgewood Campus in the University of KwaZulu-Natal, as well as the documentary analysis of some of the South African curriculum policy documents. The guiding research questions for this study were: (a) what understandings or notions of mathematical literacy are evident in the South African curriculum documents? (b) What are mathematics educators’ perceptions of the competencies of a mathematically literate person? (c) What are their perceptions of, beliefs and views, and initial experiences about mathematical literacy as a subject of study? (d) How do these perceptions and/or understandings play out in the implementation of the new Mathematical Literacy curriculum? In an attempt to answer these questions, I began by, first, exploring the wider theoretical perspectives (both locally and internationally) in extant literature within the domain of mathematics education, and which underpins the debate about mathematical literacy and its related terms as well as informing the recent curriculum change, particularly in South Africa. In the process I discussed the different connotations that were used to describe mathematical literacy and its related terms, as well as the arguments in favour of and against its introduction as a subject of study. Secondly, I explored teachers’ understandings of the concept of mathematical literacy both as a competence and as a subject of study in relation to the NCS documents, as well as the problems associated with its implementation and the importance of understanding the interplay between content and context used for its development. It is argued, however, that re-framing of ‘mathematical literacy’ as a subject of study rather than a competence proves to be problematic in terms of the distinction that could be drawn between epistemology and pedagogy. Finally I have discussed the implications which the findings of this study have for policy and practice, and for further research. Data on the understandings and teachers’ perceptions about mathematical literacy as a competence and a subject of study were obtained using both qualitative and quantitative styles of research as a mixed-mode approach. The major findings of this study are that (1) teachers generally perceived mathematical literacy as a subject of study (2) the South African curriculum documents portray ML as a subject, and therefore framed as such; (3) teachers generally consider a person mathematically literate if that person could do basic arithmetical calculations in everyday life (4) from the international perspective, there are variations on the interpretation of ML, and finally (5) the study has revealed that teachers had difficulties pertaining to their own pedagogical content knowledge of the new subject. Based on these findings it can be concluded that there is need for a sustained monitoring of the implementation process, reviewing of policy documents, and professional development of teachers involved with the teaching of mathematical literacy.
Links between content knowledge and practice in a mathematics teacher education course.
(2009) Isaac, Vilvanayagie.; Brijlall, Deonarain.
The link between content knowledge and how this influences classroom practice has been prominent in educational research in recent years. Shulman was the forerunner of research on this topic and his research dates back to 1986. Shulman’s views on content knowledge were contrary to the views of his time. In South Africa, however, the Presidential Education Initiative Report which was published in 1999 initiated research on content knowledge and brought this topic into the forefront of educational research. This study examined the link between content knowledge and practice from the perceptions of two university lecturers. The study was contextualized at a tertiary institution in South Africa where the two university lecturers were lecturing to a second year undergraduate teacher trainee class. The topic under discussion was calculus-rates of change. The research was located in the interpretivist paradigm since it focuses on the individual and tries to understand the phenomenon that is being investigated from the individual’s perspective. The research was also conceptualised in terms of Vygotsky’s educational theory and the process of scaffolding. A qualitative case study research methodology was employed. The data was gathered through semi-structured interviews with the two university lecturers and through the observation of video-recorded lessons that the lecturers conducted. The study revealed that the two university lecturers saw a link between a teachers’ content knowledge and his classroom practice. This study is by no means exhaustive, and is a case study of two university lecturers and their perception of the link between content knowledge and practice. This topic can be explored further, and suggestions for further research have been made.
A critical review of postgraduate environmental education research from selected South African universities, 1995-2004.
(2009) Madiya, Nomanesi.; Moletsane, Relebohile.; James, Angela Antoinette.
This study focuses on reviewing Environmental Education (EE) research that has been conducted by M. Ed and PhD postgraduates from selected South African universities during the period 1995 to 2004. This period 1995-2004 has been characterized by transformation, restructuring, and change in different educational areas of South Africa. This research is premised on the notion that such transformation, restructuring and change may have had an impact on research. The research questions were on the focus, methodologies and, gaps and silences in postgraduate Environmental Education research during the period 1995 to 2004. The study was informed by Homer-Dixon‘s (1994) theory of Resource Capture and Ecological Marginalisation which claims that environmental problems that exist in South Africa today emanated from apartheid and other marginalisation policies. Firstly, the study has argued that knowledge produced through postgraduate research can be useful in addressing these problems if it includes issues in all the environmental dimensions, biophysical, social, economic and political, as understood by O‘Donoghue (1995). Secondly, it further argued that the methodologies that are used to research on these issues can be useful in addressing these problems if they involve the participation of affected people so that they are empowered with appropriate attitudes, skills and knowledge to deal with these. Thirdly, the study argued that unless new knowledge is produced that will address issues of marginalisation as were created by the past, environmental problems experienced in South Africa will persist. Because of its reliance on documents as the source of data, I describe the design of this study as unobtrusive documentary small scale study. Masters and PhD theses and dissertations that were produced at the University of Johannesburg and Rhodes University during the period 1995-2004 were reviewed, using both quantitative and qualitative approaches. The study identified some gaps in the reviewed postgraduate Environmental Education research. For example, more focus on schooling issues resulted in the overlooking of problems that emanated from marginalisation in the contexts where the sampled institutions are located. Little was done to empower people with skills and knowledge that would be useful in addressing environmental problems. Keywords: Environmental Education research, Education for Sustainable Development, marginalisation, Transformation,
The integration of indigenous knowledge systems (IKS) in the teaching of conservation of biodiversity and natural resources : a critical case study of grade 10 life sciences educators in the Pinetown district.
(2009) Nnadozie, Ijeoma Jacinta.; Alant, Busisiwe Precious.
This is a qualitative case study which sought to explore the integration of indigenous knowledge systems (IKS) in the teaching of conservation of biodiversity and natural resources by Grade 10 Life Sciences Educators in the Pinetown district. The study was done in two parts. Part one explored the Grade 10 Life Sciences educators’ understanding of the integration of indigenous knowledge in Life Sciences and the extent to which the educators integrated indigenous knowledge in their teaching of conservation of biodiversity and natural resources. The data analysed was collected through questionnaires with open ended questions. Part two interrogated how the two educators who were purposively selected from part one of the study integrated indigenous knowledge in their teaching; as well as what informed the way they integrated indigenous knowledge in their teaching. The data analysed was collected through a pre-observation interview, a lesson observation and a post-observation interview with each of the two participants. The data was analysed within the conceptual framework of teachers as cultural brokers. The National Curriculum Statement (NCS) policy document for Life Sciences explains indigenous knowledge as another way of knowing and as an alternative way of explaining concepts that are usually explained using scientific knowledge. Hence it encourages the interaction of different ways of knowing in formal schooling. The analysis of part one of the study showed that 90% of the educators that participated in the study said that they integrated indigenous knowledge in their teaching of conservation of biodiversity and natural resources. The analysis of how the educators integrated indigenous knowledge in their teaching and what they did when they integrated indigenous knowledge showed that, even though the educators verbally asserted that they integrated indigenous knowledge in their teaching, there was in fact no evidence of a proper understanding and integration of indigenous knowledge in their teaching. Instead, the educators’ integration of indigenous knowledge point to the educators using indigenous knowledge to foster and strengthen the learning of scientific knowledge and to promote the interest of their learners in the learning of science knowledge. At the core of the educators’ integration of indigenous knowledge is their concern with their learners’ learning of scientific knowledge. In this regard, the educators couldn’t be seen to function as cultural brokers in helping learners move between their indigenous knowledge and the science knowledge of the concept of the conservation of biodiversity and natural resources. The analysis showed a limited understanding of the principles and ideas upon which indigenous knowledge can be integrated into the Life Sciences curriculum.
Readiness of learners to study space, shape and measurement in mathematical literacy : case studies at two Durban schools.
(2006) Pillay, Krubagaran Subramoney.; Hobden, Sally Diane.
This dissertation reports case studies conducted at two secondary schools in Durban. With the introduction of the Further Education and Training (FET) curriculum in 2006, learners who terminate their study of Mathematics at the end of grade nine will have to study Mathematical Literacy, an applications-based mathematics course. In South Africa the Mathematics results at the grade twelve exit examination are generally poor and learners are known to underachieve in the field of geometry. This study was aimed at determining the readiness of learners in studying geometry under the Learning Outcome, Space, Shape and Measurement in the Mathematical Literacy curriculum. Questionnaires were administered to grade nine learners who had elected not to study, or were excluded from studying, Mathematics from grade ten onwards. Data was sought to determine what factors influence the decision to discontinue mathematics, and to gauge attitudes to the study of mathematics. Learners were given a test to measure geometry skills and knowledge that they ought to have acquired by the end of the senior phase in geometry. Data was also obtained from focus group interviews with both of learners and educators. This study indicates that learners do not continue mathematics because of the difficulties they experience. Furthermore they do not have the requisite skills and knowledge in Space, Shape and Measurement to cope with the Mathematical Literacy curriculum. Nevertheless, the attitudes of learners to the study of this new subject are positive. It is suggested that educators need to conduct baseline assessments to determine learners' abilities so as to plan appropriate revision measures before continuing with the teaching of Mathematical Literacy.
A context-based problem solving approach in grade 8 natural sciences teaching and learning.
(2009) Khumalo, Leonora Thandeka Nontsikelelo.; Alant, Busisiwe Precious.
The demands of the new curriculum are such that problem solving is foregrounded as one of the core skills in the learning of the Natural Sciences. However teachers in general have difficulties in conceptualizing how this core skill should be incorporated into their everyday teaching of the Natural Sciences. Furthermore there seems to be some confusion in the literature on how the concept of problem solving should or ought to be understood. This is a qualitative case study to explore a grade 8 Natural Sciences educator who involves the learner's context when developing the curriculum, during teaching and learning and assessment. The educator allows the learners to use their context to negotiate during teaching and learning. The learners discuss the context-based activities in their groups and solve problems in their context, produce the portfolio boards by using the resources from their context and present their portfolio board to the class. The educator assesses the learners' activities in context and the portfolio boards. The educator and classroom activities are explored by using semi-structured interview as the main source of the data, unstructured interviews semi-structured obs~rvation schedule and classroom observation. The educator's understanding is explored by using a multifaceted methodology which targets the following key aspects namely, curriculum development, teaching and learning and assessment. In the activity theory the context is the unit of analysis. Activity theory is used as the lens and the conceptual framework in this study to understand how the educator develops the curriculum, teach learners Matter and Materials in their context and assess their context-based activities and the portfolio boards. The findings show that according to this educator he sees himself as the curriculum implementer rather than developer. The curriculum changes are at theoretical level rather than classroom level. Contextual teaching involves construction of knowledge from learners pre-knowledge and interests. Teaching within an Outcomes Based Education is transformative and educator as a mediator of learning. Problem solving needs more time but maximise non-routine thinking. Assessment is for learning, it is continuous and it contributes towards assessment for grading.
OBE in action.
(2000) James, Angela.; Vithal, Renuka.
Abstract not available.
A study of learners conceptual development in mathematics in a grade eight class using concept mapping.
(2009) Moodley, Urmilla.; Mudaly, Vimolan.
This study encompasses the use of concept maps to investigate learners' conceptual understanding of mathematics of a grade eight class in the predominantly Indian suburb of Shallcross. The grade eight learners that were the participants of this study were in the secondary school for the first time. They were in the middle of the Senior Phase within the General Education and Training Phase of their schooling career. This study is embedded in an action research methodology and is conducted from an interpretivist paradigm. Operating on a mixed methods theory, concept maps constructed by learners were analysed through the duration of the study. Towards the end of the study learners completed a questionnaire. Based on certain responses in the questionnaire and the analysis of the concept maps, six learners were then selected and interviewed to probe learners' conceptual understanding of concept maps. The results of the study reveal that most learners find concept maps enjoyable, fun and a creative way to learn mathematics. Further analysis of the questionnaire indicates that learners enjoy the social dynamics that group work provides and they found that working together also enhances their understanding. Further analysis of individual and group concept maps reveals that group work is effective in the use of concept mapping. The results of the study suggest that concept maps might be successfully used in assessing learners' declarative knowledge. An important implication of this study is that concept maps can be practically and effectively applied to a variety of outcomes within the constraints of the classroom.
An investigation of grade 9 learners educational conceptions in two secondary schools : a case study.
(2004) Makhathini, Thamsanqa Emmanuel.; Brijlall, Deonarain.
This research considers specific strategies that would enhance teaching and learning of fractional concepts in mathematics at a secondary school. The notion of the Zone of Proximal Development (ZPD) ~ Vygotskian view, is invoked as one of the fundamental frameworks for explaining fractional knowledge. This view is contested on the bases of that "human thinking is inherently social in its origin" (Goos, 2004: 259). Another theory that bears testimony to mathematics education especially abstract concepts like fractions is that of constructivism, drawn from the works of, Lave (1996), Steffe (1990) and others. Learners' informal knowledge is investigated for the purposes of highlighting what learners know and can do. Therefore, the study examined the development of learners' understanding of fractions during instruction with respect to the ways their prior knowledge of whole numbers influenced the meanings and representations they construct for fractions as they build on their informal knowledge. There were 30 participants (15 School A and 15 from School B) that were engaged in worksheets. Thereafter, 6 cases of the participants were carefully selected for clinical interview purposes. The overall methodology of this study is participatory action research (Kemmis & Mctaggart, 2000).
Grade 9 learners experiences of the common tasks for assessment in mathematics literacy, mathematics and mathematical sciences.
(2008) Khan, Mumtaz Begum.; Bansilal, Sarah.
This was a qualitative study carried out with one Grade 9 MMLMS class. The purpose of the study was to explore the experiences of the learners with respect to the CTA that they completed for their summative assessment. The methods of data collection were classroom observation, document analysis and interviews. Data was gathered from 4 classroom observations, a document analysis of the 2005 CTA instrument, the detailed responses of 3 learners to the CTA as well as a focus group interview with the 3 learners. The document analysis was done against a framework of moderating criteria identified by the moderating board of the eTA. The 4 lessons were video taped while the researcher was a participant observer in the classroom. The transcription of the tapes, the field notes and observation schedules were analysed with the intention of providing answers to the main research question. Similarly the interviews were video taped, transcribed and then analysed to provide further insight into the research question. Finally the learners' responses to certain items were scrutinized for further details. The findings revealed that the task design, which relied on grounding each task within one context, was problematic for the learners. The learners struggled with the language used in the tasks and often could not pick out crucial information from all the details associated with the contextualization. The language of the tasks was set at a high level of readability, higher than the average Grade 9 level. Furthermore, the teacher's interventions often seemed to hinder rather than facilitate their understanding of the mathematics. The results of the study have implications for teachers (to be careful of how they mediate the tasks), curriculum developers (to take note of the criticisms levelled at assessment tasks set in real life contexts) and mathematics educators (to voice their concerns about national assessment instruments which may themselves not be valid indicators of what learners can and cannot do).
Current difficulties experienced by grade 10 mathematics educators after the implementation of the new curriculum in grade 9.
(2005) Malinga, Mxoleleni Alfred.; Mudaly, Vimolan.
The purpose of this study was to establish current difficulties experienced by grade 10 mathematics educators after the implementation of the new curriculum in grade 9 (Senior Phase). Qualitative approach, using questionnaires' as a research tool was employed. The study was conducted from twenty grade 10-mathematics educators in a variety of schools. The questions were based on the current difficulties that educators were experiencing in grade 10 after the new curriculum was implemented in grade 9 in 2002. The research study was undertaken in different schools with different backgrounds in one District; UMgungundlovu of the Kwazulu - Natal Department of Education. These educators were from schools with the following backgrounds: • Rural schools • Township schools • Former White schools • Former Indians/ Coloureds schools The findings of the study are presented and these are interpreted and discussed under two categories: these being the kinds of difficulties enunciated by grade 10 mathematics educators and the researcher's comments on the findings. The Key Findings of this research study are the following: Grade 10 Mathematics educators complained that they have problems in teaching mathematics in grade 10 learners because: • Methods used in grade 9 are totally different from those they are using in grade 10. • There is no linkage between grade 9 and grade 10-mathematics syllabus. • Educators' lack training and teaching in outcomes - based approaches. • The new curriculum does not prepare learners to do pure mathematics in grade 10. • Learners cannot even work independently, only rely on the constant guidance from the educators and other members of the group. • Learners find it difficult doing individual work and completing homework and other class work. • Many learners drop out in mathematics classes and others even become worst in mathematics. The examinations or assessment (eTAs) which is an exit point from grade 9 to grade 10 have no value for the type of mathematics that is done in grade 10. • Textbooks used in grade 9 have lots of activities and lots and lots of stories and less mathematics. • Textbooks used in grades 8 and 9 are of poor quality and exercises are of pathetic quality. • Educators in grade 10 have to teach grades 8 and 9 work because it was not taught. • No clear focus on content part in grade 9, which form the basics of grade 10 mathematics. • The new curriculum in grade 9 gives emphasis to very few topics. • The level of mathematics that learners are exposed to, in grade 9 is far lower than the one they encounter in grade 10. • No support from parents in terms of doing homework. Finally, the recommendations are made for addressing the difficulties that are experienced by these educators as well as suggestions for further study.
Instructional appproaches in the teaching of Euclidean Geometry in grade 11.
(2007) Mthembu, Sibusiso Goodenough.; Brijlall, Deonarain.
The main focus of the research was to find out the causes of a poor performance in euclidean geometry especially in a grade eleven class. An easier way to find that information was to investigate the techniques that educators who are teaching grade eleven are following when they teach euclidean geometry. The necessary data was therefore collected from the educators as well as learners who were in grade eleven. This study is guided by the constructivist's VIew. The theoretical framework of this research is based on the ideas of theorists like Piaget, Vygotsky and other authors who conform to constructivism. Changes that affected the education system of South Africa due to the adoption of the new constitution were also visited. A shift from the traditional way of teaching and an Outcomes Based Education system, as a recommendation by the National Curriculum Statement was highlighted. The data was collected through both interviews and questionnaires. The semi-structured interviews of three educators from three participating schools were audio taped. In each school one educator was interviewed and six learners were given questionnaires to answer. The above gave a total of eighteen learners and three educators. Written responses from learners and audio taped responses from educators were kept and analyzed. The interview was focused on the techniques that educators employ in their teaching of euclidean geometry in grade eleven. The questionnaires administered to learners were aimed at confirming the responses from the educators. It is envisaged that the educators participated in the study can provide enough information which can assist in correcting the teaching approach in euc1idean geometry. The findings show that the conditions under which educators teach contribute to their methods of teaching euclidean geometry. The testing system and the focus on better results by the education department proved to be the main determining factors of the methods that educators resort to when they teach learners. It also came up from this study that some learners do not take mathematics out of their will. Their parents or the school forces them to take mathematics. Those who like to take mathematics are constantly discouraged by comments of educators who deem mathematics as a subject responsible for bringing down the pass rate of the school. The above diminishes the love of mathematics to learners and euclidean geometry becomes the section that suffers the most. Suggestions and recommendations aimed at improving the teaching and learning of the euclidean geometry have been made.

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