Browsing by Author "Brijlall, Deonarain."

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An APOS exploration of conceptual understanding of the chain rule in calculus by first year engineering students.
(2011) Jojo, Zingiswa Mybert Monica.; Brijlall, Deonarain.; Maharaj, Aneshkumar.
The main issue in this study is how students conceptualise mathematical learning in the context of calculus with specific reference to the chain rule. The study focuses on how students use the chain rule in finding derivatives of composite functions (including trigonometric ones). The study was based on the APOS (Action-Process-Objects-Schema) approach in exploring conceptual understanding displayed by first year University of Technology students in learning the chain rule in calculus. The study consisted of two phases, both using a qualitative approach. Phase 1 was the pilot study which involved collection of data via questionnaires which were administered to 23 previous semester students of known ability, willing to participate in the study. The questionnaire was then administered to 30 volunteering first year students in Phase 2. A structured way to describe an individual student's understanding of the chain rule was developed and applied to analyzing the evolution of that understanding for each of the 30 first year students. Various methods of data collection were used namely: (1) classroom observations, (2) open-ended questionnaire, (3) semi-structured and unstructured interviews, (4) video-recordings, and (5) written class work, tests and exercises. The research done indicates that it is essential for instructional design to accommodate multiple ways of function representation to enable students to make connections and have a deeper understanding of the concept of the chain rule. Learning activities should include tasks that demand all three techniques, Straight form technique, Link form technique and Leibniz form technique, to cater for the variation in learner preferences. It is believed that the APOS paradigm using selected activities brought the students to the point of being better able to understand the chain rule and informed the teaching strategies for this concept. In this way, it is believed that this conceptualization will enable the formulation of schema of the chain rule which can be applied to a wider range of contexts in calculus. There is a need to establish a conceptual basis that allows construction of a schema of the chain rule. The understanding of the concept with skills can then be augmented by instructional design based on the modified genetic decomposition. This will then subject students to a better understanding of the chain rule and hence more of calculus and its applications.
The application of artifacts in the teaching and learning of grade 9 geometry.
(2005) Jojo, Zingiswa Mybert Monica.; Brijlall, Deonarain.; Maharaj, A.
The main focus of the study was to explore how the experiences that the learners went through in the Technology class during the construction and design of artifacts, could be used to inform the teaching of Geometry in the mainstream Mathematics classes. It was important to find out how the teaching of Geometry would allow the learners to both reflect and utilize the Geometry they know, as a starting point or springboard for further study of Geometry. Data was collected through observations, structured and semi-structured interviews of a sample of twenty grade 9 learners of Mashesha Junior Secondary School of Margate in KwaZulu Natal. It was collected through observation of drawings and completely constructed double-storey artifacts at different intervals of designing. Observations and notes on every activity done by the learners for example, measurements, comparisons, estimations, scaling, drawings use of symmetry and perspective drawing were kept and analyzed. Data for the interviews was collected in the form of drawings, photographs, transcriptions of video and audiotapes. The observations in particular were looking for the Geometry in finished artifacts. Interviews with the learners were directed at how each learner started drawing a house to the finish. When and how scale drawing, projections, angles made and length preservation were used by the learner, was of utmost importance. It is believed that grade 9 learners of Mashesha have Geometric experiences which can be used to inform the teaching of Geometry in mainstream mathematics. It was found that this experience brought by the learners from the Technology construction of artifacts could cause the learners to find mainstream mathematics interesting and challenging. It is also believed that the use of projective Geometry already employed by the learners can be incorporated in mainstream mathematics so as to improve how learners understand Euclidean Geometry. In this way, it is believed, that the teaching of Geometry will allow the learners to utilize and reflect the Geometry already known to them. This Geometry would therefore be used as a starting point for further study of Geometry. Suggestions for further research and recommendations for the improvement of Geometry teaching and learning have also been made.
The changing nature of female labour supply and its effect on the South African labour market.
(1991) Lalthapersad, Pinglawathie.; Brijlall, Deonarain.
No abstract available.
Closure operators on complete lattices with application to compactness.
(1995) Brijlall, Deonarain.; Sturm, Teo.; Jordens, Olav.
No abstract available.
The design and implementation of a classroom-based support programme in trignometry for use by underqualified educators.
(2005) Mkhize, Sabelo Andrias.; Brijlall, Deonarain.; Maharaj, A.
The main purpose of the study was to show the necessity of a classroom-based educator in-service support programme. Educators have unique problems being derived from the uniqueness of their school situations. Thus, the feeling that this kind of support could improve the quality of mathematics teaching and learning.
The effects of trade policy on intra-industry trade within the context of trade liberalization in South Africa.
(2001) Naicker, S. S.; Brijlall, Deonarain.
Intra-industry trade is a new phenomenon in international trade theory and has attracted interest from economists, in the form of both empirical and theoretical work. The first attempt to measure the extent of intra-industry trade in South Africa was under taken by Simson (1987). In his study Simson (1987) found that the amount of intra-industry trade accounted for only one-third of total trade. This is low compared to many industrialized countries. This thesis aims to analyze the extent of intra-industry trade within the context of trade liberalization. Chapter two provides the evolution, background and an overview of the literature of the concept of intra-industry trade. This chapter is followed by a presentation of the different measurement of intra-industry trade. But, however the Grubel Lloyd (1975) index remains the most commonly used index in the literature. A fourth chapter estimated the level of intra-industry trade in South Africa for the period 1972 to 1993. This chapter concludes that intra-industry trade in South Africa is a real phenomenon and not just a statistical novelty as argued by Finger (1975). It was is concluded that intra-industry trade is low when compared to most of its trading partners and there remains much scope for the growth of intra-industry trade. The fifth chapter discusses the role of regional integration and intra-industry trade. It is concluded that the levels of intra-industry trade between South Africa and with the countries in the Southern African region is relatively low when compared to the intra-industry trade between South Africa and its major trading partners, nevertheless there remains scope for the growth of intra-industry trade within the region as the countries become more similar. Chapter six discusses the commercial and welfare effects of intra-industry trade, concluding that there are advantages to be gained from intra-industry trade. Chapter seven analyses the effect of tariff levels on intra-industry trade in South Africa. Weak support was found for the height of tariffs and intra-industry trade in South Africa. Given the reduction of tariff lines in terms of the GATT requirement, it is anticipated that levels of intra-industry trade in South Africa will increase and there is much to gain in terms of welfare than inter industry trade.
An exploration of the design and development of a semi-integrated curriculum for a mathematical literacy course offered in a B-Ed. programme at a South African university.
(2016) Krishnannair, Anilkumar.; Maharaj, Aneshkumar.; Brijlall, Deonarain.
An exploration of the design and development of a Semi-Integrated Curriculum conceptualized for the Mathematical Literacy module, offered as part of the Bachelor of Education course, was conducted at the University of Zululand, South Africa. The research focussed on exploring the feasibility and sustainability of integrating various curriculum elements, namely: context, content, and a set of predetermined essential skills and concepts. The research further explored the effectiveness of consolidating essential skills and concepts prior to the introduction of context-based problems. The appropriate level at which those elements should be integrated was also investigated. Another significant objective of the study was to explore the extent to which Higher Order Thinking Skills could be developed and sustained by a curricular innovation such as the Semi-Integrated Curriculum. The mathematical-literacy-related competency levels attained at school by first-year students in the Faculty of Education and reinforced by the first-year university mathematical literacy module, were of concern to the faculty. A need for significantly improving the mathematical literacy competency levels of students across majors was therefore the principal rationale of this research. Non-science major students made up a large portion of the Faculty of Education’s student population. Ensuring a satisfactory level of mathematical literacy in the student teachers across the faculty was thus imperative. Based on a qualitative research paradigm, this research used a case-study research method that involved a single case study with multiple units of analysis. The research was guided by the overarching research question related to the design and development of a Semi-Integrated Curriculum, the answer to which was constructed by the five sub-questions that were simultaneously answered. Ten student participants were selected from the first-year mathematical literacy student cohort. These students were taken through a series of specially designed mathematical literacy teaching and learning sessions. The content matter taught was designed according to the Semi-Integrated Curriculum format. A pre-test administered prior to the contact sessions and a post-test administered after the contact sessions indicated levels of attainment and the influence the curricular intervention had had on the participants’ mathematical performance. The post-test also incorporated tasks that were designed to measure the levels of attainment of Higher Order Thinking Skills. Data collected included semi-structured interviews with the participants conducted before and after the contact sessions; and an interview with the Head of Department. Sources of data collected also included informal working of participants gathered during contact sessions, curriculum materials published by the faculty, and relevant literature. Examination, test and assignment papers were also analysed to assess the level at which the current curriculum functioned and to explore the improvements needed. Excerpts from transcripts of interviews and faculty curriculum documents were thematically analysed to determine initial categories which were later reduced to themes and concepts. The analysis focussed on deriving a broad understanding of the purpose with which the mathematical literacy course currently functioned, and possible changes in the formulation the purpose itself. The analysis also focussed on the formulation of a set of aspects that characterized the Semi-Integrated Curriculum. The influence of Higher Order Thinking Skills and their sustainability were also aspects that were scrutinised. The effect of a Semi-Integrated Curriculum on the development of mathematical-literacy-related competencies and Higher Order Thinking Skills were explored, in accordance with the conceptual framework that envisaged significant levels of attainment in such aspects of learning. Pre-test and post-test scripts were also analysed to ascertain the levels of attainment of mathematical literacy competencies, and the extent to which Higher Order Thinking Skills were fostered and sustained. The results indicated that a focussed curricular intervention such as the Semi-Integrated Curriculum does have an effect on the general mathematical-literacy-related competencies. However, major changes in the levels of attainment could not be established. The development and sustainability of Higher Order Thinking Skills were also noticed at a relatively low level despite instances of satisfactory performances from participants that were noteworthy. However, significant changes in the approach to learning and the influence that a curricular focus on Higher Order Thinking Skills can have on learning were remarkable. Participants developed noticeable positive changes in their mathematical learning approach that placed a heavy emphasis on conceptual mastery as opposed to procedural focus; which in turn led to changes in the attainment of Higher Order Thinking Skills. The significance of this research is, therefore, that curricular interventions focussing on consolidation of Essential Skills and Concepts prior to the introduction of context-based problems, in a mathematical literacy context, underpinned by an emphasis on Higher Order Thinking Skills, do produce positive changes in mathematical literacy competencies.
An exploration of the utilisation of mathematics skills by technology education pre-service teachers to enhance conceptual understanding of electronic systems.
(2012) Thabethe, Bhekisisa Maxwell.; Brijlall, Deonarain.
The study focused on an exploration of utilisation of Mathematics skills by Technology Education pre-service teachers to enhance conceptual understanding of Electronic Systems during the design and construction of artefacts. This study attempted to discover Mathematics concepts that pre-service teachers utilised in the completion of their artefacts and it encapsulated design and making of a model of a house and an electronics circuit. Data were collected through qualitative participant observation, semi-structured interviews and the submission of working artefacts. A sample considered for this study was the whole cohort in the EDTE 210 Electronic Systems course at the University of KwaZulu-Natal. Data were collected through observation of construction of a model house and design of a circuit for Electronic Systems in different phases. In each phase of design, observations and notes were supplemented by semi-structured interview questions as design and construction unfolded. Observation looked for the geometry involved in design of a model house and algebra involved in the design of electronic circuits. Data from interviews with the pre-service teachers indicated mathematical connotations in both the modelling of the house and electronics circuits. It was imperative to know how and why certain measurements, angles and shapes were used for their model houses. Furthermore, it was essential to understand the motives behind particular manipulation of different formulas, conversions and fraction implications by pre-service teachers in their design of effective circuit diagrams. Pre-service teachers at a university level have arithmetic experience which can be used in Technology and may be extended to mainstream Mathematics. It was observed that design and making of this project exposed concepts of Mathematics that made Electronic Systems manageable and comprehensible. Use of projects was discovered to have a positive impact on enhancing understanding of abstract concepts in Mathematics that are essential for Electronic Systems. It is believed that these skills of integrating different areas of learning through interdisciplinarity are paramount for pre-service teachers, as they will soon assume autonomous professional positions for curriculum design in Technology. This provides a diverse approach to conceptual understanding of Electronic Systems through participative learning. Findings and recommendations for effective teaching of Electronic Systems through mathematical skills/concepts are outlined.
Exploring pre-service teachers' mental constructions of matrix algebra concepts : a South African case study.
Ndlovu, Zanele Annatoria.; Brijlall, Deonarain.
At the university where the study was conducted matrix algebra is one of the first advanced mathematics courses that pre-service teachers encounter. The transfer of knowledge from a primarily procedural or algorithmic school approach to formal presentation of concepts is a priority for conceptualisation of matrix algebra concepts. However, it seems to be creating many difficulties for many pre-service teachers. This is due to the fact that many of them are barely coping with procedural aspects of mathematical concepts. The aim of conducting the study was to explore the pre-service teachers’ mental constructions when learning matrix algebra. The study was guided by the belief that understanding the mental constructions the pre-service teachers made when learning mathematical concepts leads to improved instructional methods. The study is underpinned by APOS theory (Action, Process, Object and Schema) and uses APOS theory to describe the nature of mental constructions displayed by pre-service teachers when learning matrix algebra concepts. To understand and explain the mental constructions made or not made, the preliminary genetic decompositions for matrix algebra concepts was used to analyse the nature of mental constructions made by these pre-service teachers together with triad mechanism which originates from Piaget’s work of reflective abstraction. APOS theory is an extension of reflective abstractions so using these two tools to analyse pre-service teachers’ mental constructions strengthen the trustworthiness of this study. As part of this research project several case studies were conducted where groups of first and second year students were exposed to teaching and learning of some of matrix algebra concepts. These concepts explored are the ones that these students learn under matrix algebra at this university. These concepts were first taught to students and students were expected to express their thinking through solving matrix algebra related problems during tutorials and taking part in the interviews. Analysis of written work and interviews from ten pre-service teachers provided insight into their mental constructions, revealing ways in which they understood the concepts. In explaining and synthesising the results major themes emerged from which conclusions were drawn about the mental constructions that were or not made in the learning of matrix concepts. Several themes emerged which were categorised in certain headings in order to identify patterns that emerged from all tasks. What mostly transpired across all tasks was that background knowledge and understanding of notation are important aspects for students to understand in order to conceptualise the concepts in matrix algebra. It was noted that those students who had a weak schema of basic algebra were not able to make the necessary mental constructions or vice versa. Also, it was noted that students often made nonstandard notation and linguistic distinctions. For example, students use A11 when referring to entries of a matrix or use |𝐴| while determining the determinant of matrix C. Moreover, evidence from their responses revealed that many pre- service teachers had limited knowledge constructed of the taught concepts. This was observed as they struggle to represent the solutions of a system geometrically, recognise concepts in different registers and unable to link major concepts. Findings from this study revealed that the mental constructions made by pre-service teachers in most cases concur with the preliminary genetic decompositions. In terms of APOS theory students responses revealed that many were mainly operating at an action and process stages, with few pre-service teachers operating at an object stage. Since difficulties with the learning of linear algebra by average students are universally acknowledged, this study provided a modified itemised genetic decomposition which is anticipated to help in the teaching and learning of matrix algebra concepts. The aim of providing the modified genetic decomposition is to contribute in the teaching and learning of advanced mathematics as lectures could use the modified genetic decomposition to analyse the mental constructions of their students when learning matrix algebra concepts. Besides making a contribution to the teaching and learning of some mathematical concepts, the modified genetic decomposition is a contribution to APOS theory as it is shown it can be used in other mathematical concepts in different context.
Exploring university students' mental constructions of the limit concept in relation to sequences and series.
(2019) Chagwiza, Conilius Jaison.; Maharaj, Aneshkumar.; Brijlall, Deonarain.
The present thesis refers to some first semester calculus 1 university students’ mental constructions of the limit concept in relation to sequences and series. A plethora of research on the limit concept is available and suggests that the concept is on record of being difficult for students to learn and comprehend. However, in Zimbabwe, there is inadequate research on mental constructions made by students of the limit concept in relation to sequences and series. This research aims at filling this gap in the literature. This study utilized the Action-Process-Object-Schema (APOS) theory in exploring conceptual appreciative displayed by students when dealing with limits of sequences and series. The study proposes the genetic decompositions on how students might construct the mental constructions in learning the sequences and series through the use of Activities-Classroom discussions –Exercises (ACE). Collection of data was done by the use of a methodology that used practical teaching. All the thirty students who took calculus 1 accepted to participate in this study and answered the limit test questions. The students’ written responses were analyzed using APOS theory. Ten students were selected for interviews through purposive sampling. Two declined to take part leaving eight to take part in the process. The APOS theory was used to analyze the interview results. The revision of preliminary genetic decomposition was done basing on the analyzed data. The instructional method employed, facilitated the appreciation of the limit concept in relation to sequences and series by the students. Nearly all students showed that they operated at the Action level, a good number showed that they operated at least at the Process level and more than half of the students showed that they operated at the Object level. Three out eight interviewed students indicated that the managed to operate at the Schema level on some of the test questions. However, there is need for the establishment of a conceptual basis that promotes and allows the construction of the limit concept schema in relation to sequences and series. Furthermore, interviewed students’ responses paralleled the chronological improvement of the limit concept as reported in literature. Historical analysis of the development of concepts needs to be reflected upon when preparing and designing instruction. This would help the lecturer to foresee the challenges that lay ahead and address students’ difficulties during the learning process. The implementation of APOS Theory is recommended for the learning of other mathematical aspects, which cause difficulties in students’ learning. Moreover, other constructivist learning methods can be fused together with the APOS Theory to obtain improved results on students’ performance in mathematics.
First-year engineering students' concept development of integral calculus at a South African university of technology.
(2015) Ndlazi, Nokwethemba Jubilee.; Brijlall, Deonarain.
This thesis reports on a study to explore the development of the concept of integration among the first year engineering students at a South African university of technology. The study focused on concept definitions that were evoked through symbolic as well as visualisation of integrals. It further explored various concept images evoked the techniques of integration. A framework combining the Action-Process-Object-Schema (APOS) and the Three-Worlds of Mathematics (TWM) theories was adopted as a tool to analyse students’ concept formation of an integral. This was a qualitative case study that consisted of two phases. Firstly, a pilot phase was introduced as Phase 1 of the study to uncover issues that could be probed more deeply when the study was rolled out to a larger group of students. The activity sheet was administered and interviews were conducted with seven students who were willing to participate in the study. Secondly, as Phase 2 of the study, the modified activity sheet was then administered to 22 first year students who also volunteered to be in the study. The intention was to provide comprehensive investigation of concept development of integral calculus. Students were also organised into focus groups in order to explore emerging mental constructions during the discussions among the students. The findings of the research indicated that students operated mainly at an action level of cognition for integral calculus. Their definition of an integral was restricted to the notion finding an integral with no association to the area below the graph of a function. Students mainly conceptualised an integral as an anti-derivative. With regard to techniques of integration, students relied on rules and algorithms without reflecting on objects and processes embedded within the rules. Cases of inadequate perquisite schemas for integral calculus such as basic algebra, inverse trigonometric functions and some aspects of differentiation were also noted. Although there were notable strengths in skills such as completing a square and resolving fraction into partial fractions, there was little understanding of the underlying concepts. This study contributed by presenting a genetic decomposition for integration that is premised on APOS and TWM theories. While the action level of APOS was dominant, the proceptual-symbolic was the main prevalent world of mathematics learning.
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.
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).
Learners' conceptual understanding of congruent triangles in transformation geometry
(2011) Mbili, Lungelo Aaron.; Brijlall, Deonarain.
No abstract.
Learners' views of practical work in addition of fractions : a case study.
(2013) Mdluli, Fortunate Gugulethu.; Brijlall, Deonarain.
This study considered use of practical work as one of the strategies that may be used to teach and learn fraction concepts in primary school Mathematics. Although an educator and learners were participants in the study, the focus was mainly on the learners. The class educator’s perception of practical work was investigated and the results confirmed the assumption that most educators use minimal or no practical work when teaching learners fractions. The researcher carried out an experiment with learners to find out whether they saw any value in doing practical work. Data collection instruments used were an observation schedule which was collated by the researcher in teaching four lessons, written responses of learners to a series of activities they did as class work and their responses to interview questions. Data collected from learners confirmed that practical work did have value in the teaching of fraction concepts, especially addition of fractions. Other than confirming the value of practical work, much other valuable data emerged from the findings. The data have important implications for the teaching and learning of fractions, especially addition of fractions, teacher training in practical work and also further research. These are intended to improve teaching of fractions, particularly addition of fractions.
Learning of mechanical systems in grade 9 technology classroom by deaf learners in KwaZulu-Natal : an exploration of a learning of technology in a non-hearing environment.
(2018) Thabethe, Bhekisisa Maxwell.; Bansilal, Sarah.; Brijlall, Deonarain.
The purpose of this study was to explore the learning of Mechanical Systems in a Grade 9 Technology classroom by Deaf learners in KwaZulu-Natal. The study focused on how Technology is learned in a non-hearing environment, considering the nature of Technology and the interdisciplinarity between Technology and Mathematics. This is a case study set within an interpretive paradigm. Since there were five Deaf learners constituting the Grade 9 Technology class, all were considered to be participants in this study. A blended learning model (BLM) was identified as the theoretical framework for this study. BLM is foregrounded on cognitive and social constructivism, with an intention to explore the learning of Mechanical Systems in a non-hearing environment. The data collection schedule included the following methods: • Classroom observation; • Document analysis; and • Semi-structured interviews. The results of this research were analysed qualitatively in order to adhere to the principles of the interpretive paradigm. The research findings of this study highlighted that Deaf learners’ previous experience limited their exposure to daily practices, resulting in misunderstanding of concepts in Mechanical Systems. Furthermore, the results showed effectiveness of demonstrations and simulations in enhancing the comprehension of concepts in Mechanical Systems. The findings of my study concur with Piaget’s view that the comprehension of a child is enhanced when learning is made concrete to them. Deaf learners’ participation in Technology activities assisted them to develop an understanding of concepts in Mechanical Systems, and facilitated effectiveness of interdisciplinarity in scientific subjects.
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.
The role of practical work in learning the division of fractions by grade 7 learners in two primary schools in Mpumalanga ward of Hammarsdale circuit in Kwazulu-Natal.
(2005) Molebale, J. J. L.; Maharaj, A.; Brijlall, Deonarain.
The researcher's personal conviction that major problems in the teaching of mathematics are inherited from elementary levels inspired the investigation of the contribution of practical work in the teaching of fraction division in grade seven. The all encompassing approach of the study dictated the involvement of teachers and learners as participants. Teachers' perceptions of practical work and their classroom practices were investigated to confirm or refute existing assumptions and literature claims. Questionnaires in which teachers expressed their views on practical work and fraction teaching were administered to teachers. Lessons on the division of fractions were observed to determine teachers' practices in relation to the researcher's assumptions and claims by literature. Data yielded by these research instruments confirmed or refuted assumptions and literature claims. Learners underwent an experiment and their views were sought to establish the value of practical work in the teaching of fractions and fraction division. Instruments used for the experiment were the pre-test, post-test and worksheets. Data from these instruments gave an indication of the value of practical work in enhancing learners' understanding of fraction division. Learners' responses to interview questions further elucidated and confirmed the valuable role played by practical work in learners ' understanding of fraction division. Learners' responses also provided deeper insight into facets of learners ' cognitive development as they engaged with different aspects of practical work in the division of fractions . Besides confirmation and refutation of some established assumptions and literature claims, previously unknown realities about aspects of practical work and fraction division also emerged from findings. This wealth of the data carried crucial implications for teacher training, the teaching of fractions and fraction division, and further research. A look at these implications hopes to contribute to the enhancement and improvement of the teaching of fractions and fraction division. Teacher training institutions, designers of INSET programmes, policy makers and teachers should all benefit from findings of this study.
Using artefacts to support an embodied approach to learning trigonometry : a case study of grade 10 learners.
(2013) Niranjan, Caresse.; Brijlall, Deonarain.
The purpose of this study was to explore the role of artefacts (manipulatives) in the teaching and learning of trigonometric ratios in grade 10. The study focused on how the use of manipulatives aided learners’ mathematical proficiency in the use of trigonometric ratios. The foundation of this research was a case study contained in the interpretative paradigm involving five grade 10 mathematics learners at a secondary school in South Africa. The data collected included a range of methods such as: Activity sheet containing written responses of learners. Observations. Semi-structured interviews. The results in this research was analysed qualitatively. The research findings in this case study indicated that the learners were interested and motivated and that the use of manipulatives assisted learners in understanding the concept of trigonometric ratios. In addition the results showed that the use of manipulatives in teaching and learning mathematics played a positive role in leaners understanding of trigonometric ratios at grade 10 level. The findings of my case study were similar to other research studies regarding the significance of using artefacts (manipulatives) in classrooms in teaching and learning of mathematics. The findings support other research findings that confirm that manipulatives were important mediating tools in the development of conceptual and procedural understanding of mathematical concepts.