Browsing by Author "Mudaly, Vimolan."

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An analysis of pre-service mathematics teachers’ geometric thinking and classroom discourse using a commognitive lens.
(2022) Larbi, Ernest.; Mudaly, Vimolan.
Learning geometry equips learners with cognitive skills such as visualisation, critical thinking, spatial reasoning and problem-solving abilities, that are necessary for learning mathematics in general. However, geometry is noted to be difficult for learning as well as teaching. An investigation of this difficulty, especially with teachers, will help address its teaching and learning. The purpose of this study was to analyse pre-service teachers’ geometric thinking and classroom discourse using the commognitive lens. The study was guided by three objectives, which were to analyse the pre-service teachers' discursive thinking in geometry; the nature of their routine thinking in solving the geometric tasks, and how these informed their classroom geometric discourse. The study aligned itself to the qualitative approach and was underpinned by the interpretivist research paradigm. Eight pre-service teachers who were second-year university students and had taken geometry as part of their programme modules, participated in the study. The study site was conveniently selected, whilst the participants were selected on purposively. Geometry worksheet (test), interview and classroom observation, were used to generate written, verbal (oral) response, and visual data in relation to the study objectives. The data was analysed using the themes of the commognitive framework. The results show that both literate and colloquial word use were found in the discourses of the pre-service teachers. Many participants in Group A used more literate words to define and explain geometric concepts and how they solved the geometry problems, than the participants in Group B, who used both literate and colloquial words. Also, the routine solution strategies of many in Group A showed more of an explorative way of thinking compared to those in Group B, who demonstrated more of a ritualised way of thinking. In addition, multiple solutions to tasks were found by many of Group A participants than those in Group B. Generally, many of the study participants demonstrated limited geometric thinking. Misconceptions were evident in the discourses of some pre-service teachers in both groups. Other key findings from the classroom observation were that, many participants in Group A demonstrated an explorative instruction that is characterised by developing learner understanding and using different kinds of visual mediators as compared to participants in Group B, whose classroom geometric discourse was ritualised in nature. In other words, their teaching was more procedure-driven than conceptual. The study concludes that many of the PSTs possess limited geometric thinking. In addition, those who possessed good geometric thinking were more capable of engaging learners in explorative instruction compared to those with limited geometric thinking. These findings may have an influence on mathematics teacher educators’ efforts to develop teaching competence among pre-service teachers.
An exploration of preservice teachers’ use of educational technologies as visualization tools when teaching mathematics.
(2022) Zulu, Mzwandile Wiseman.; Mudaly, Vimolan.
This interpretive qualitative study explores the use of educational technologies by preservice teachers as visualization tools during mathematics teaching at secondary schools. Sfard’s commognitive framework and Koehler and Mishra’s technological pedagogical content knowledge theoretical frameworks undergird the study. Data were collected from ten preservice mathematics teachers at a university in the province of KwaZulu-Natal, South Africa. Performance tests, semi-structured interviews, focus group discussions, and observations were employed to collect data, which was analyzed using reflexive thematic analysis. The study found that preservice teachers employed two primary visualization strategies when they engaged in mathematical problem-solving: symbolic mental visualization, which they combined with their understanding of word usage, endorsed narratives and routines to arrive at a solution; and graphic visual mediators, such as diagrams, which they sketched to contextualize the problem statement and verify they solutions and use of mathematical word usage, routines, and endorsed narratives. Participants were found to be unable to solve a mathematics problem if they had not visualized it effectively; using a graphic visual mediator to understand the problem statement did not, however, guarantee success when solving a problem. A relationship was found between the visualization techniques that the participants used in their own attempts to solve mathematical problems and the visualization techniques they used in their lesson planning and teaching of mathematics in the same content area. Participants used innovative strategies to mediate learning, including educational technologies that facilitated visual mediators to enhance learners’ engagement with concepts. Synergies were found between the elements of the commognition and TPACK frameworks as these were used in tandem to analyze data. A model was developed (C+TPACK) that integrates the key elements of these frameworks. Further research is recommended to establish the viability, credibility and generalizability of the model.
A comparative analysis of three high school textbooks’ concepts in Algebra in South Africa and Angola.
(2018) Pedro, Isabel Maria Joaquim Borges.; Mudaly, Vimolan.
The purpose of this study was to conduct a comparative analysis of algebra sections in three textbooks; one South African grade 9, one South African grade 10, and one Angolan grade 10. Firstly, I compared the textbooks in terms of topics covered. Secondly, I compared the distribution of the text on explanations, examples and exercises, respectively. Thirdly, I used the levels of understanding of algebraic expressions suggested by Sfard and Linchevski (1994) to investigate progression and consistency of the texts. Finally, I looked at the number of steps required to move from task to solution in the examples and exercises, providing a different measure of progression. The findings revealed that the textbook for Angola is more advanced than the textbooks for South Africa in terms of topics, explanations and examples, and contains far fewer exercises. Therefore, in terms of their explanations, the textbooks from Angola are denser and have more detailed clarifications than the South African textbooks. In terms of examples and exercises, the textbooks from Angola have fewer exercises than South African textbooks. The progression both in terms of levels of understanding of algebraic expressions and in terms of number of steps required to solve tasks is swifter in the Angolan textbook. Also, there is less focus on symbol manipulation without conceptual content in the Angolan textbook. Although much depends on the ways in which textbooks are used in the classroom, this suggests that the Angolan textbook offers the learners more opportunities to learn. There were some signs that the South African textbooks had been organized in ways informed by research, and in a few cases the exercises in the South African textbooks were more explorative, allowing learners more opportunities to develop deeper conceptual understanding. This was, however, not a dominant feature.
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.
The effects of using visual literacy and visualization in the teaching and learning of mathematics problem solving on grade 6 and grade 7.
(2009) Budram, Rajesh.; Mudaly, Vimolan.
In this study I examine the effects of visualization in the teaching of problem solving in grades 6 and 7 in a school south of Durban in KwaZulu Natal. One of the goals of mathematics instruction according to the Department of Education is to prepare learners to become proficient in solving problems (DoE, 2003). Whilst many studies have been conducted in the field of problem solving, using visualization as a strategy to solve problems has been a neglected area in mathematics teaching in some schools. A literature survey shows that the link between solving problems and visualization strategies is making finding solutions easier for learners. The literature suggests that visualization assists learners to develop their problem solving skills as it allows them an opportunity to show their interpretation of the problem and the understanding of mathematical concepts. Through the use of problem centred mathematics, problem centred learning, growth of mathematical understanding and realistic mathematics education, learners see the connection and employ appropriate strategies to solve problems. This study examines the strategies employed by educators in the teaching and learning of problem solving and the strategies used by learners when solving problems. Data was collected from educators using a questionnaire, observation of grade 6 and 7 learners in the classroom and semi structured interviews. The conclusions from the data analysis have shown that problem solving is been neglected and that visualization does assist learners in solving problems.
An exploration of a visualization intervention in a Grade 7 mathematics classroom in the Pinetown District.
(2021) Bakare, Onozare Mercy.; Mudaly, Vimolan.
With the growing research on visualization in mathematics, it is important to understand how visualization intervention strategies impact learners' solving and success of mathematical word problems. This study focused on exploring a visualization intervention in a grade 7 mathematics classroom in the Pinetown District of KwaZulu-Natal. The methods used by learners and their effectiveness in solving word problems were investigated as this formed the basis of this study. Their understanding of the methods and strategies chosen was revealed through an interview, leading to a visual intervention on how they (learners) can become better visualizers. Boonen, Van der Schoot, Van Wesel, De Vries, and Jolles, (2013, p. 57) asserted that the difficulties learners encounter in solving word problems emancipate from lack of understanding of the problem text, identifying solution-relevant components, the relations between them, and making a complete and clear representation of the situation described in the problem. Good problem solvers ought to have a good understanding of the text and strategies required for every given problem, and for this to take place, learners are required to think visually. Visualization and its importance in mathematics or in solving mathematical word problems cannot be overstressed. It is a skill that learners ought to possess to become good problem solvers. Therefore, it is not enough for learners to possess these skills and form visual images, but they also should be able to use the skills when required and for analytical reasoning. Hence, the reason for conducting this study is for learners to be taught these skills and strategies through an intervention process and determine the effectiveness of the intervention given to them. Data was gathered using a qualitative research method. An interpretative approach was used, which helps to understand what is being understudied. Learners were given word problems to solve, and a one-on-one open-ended interview was conducted on randomly selected learners from the class. This research was conducted in the naturalistic setting of theparticipants; the sample was purposive and convenient. The conclusion drawn from the investigation findings has shown that learners do not have a natural inclination to use diagrams or any visualization form before the intervention strategies were introduced. Secondly, evidence suggested that learners' strategies in completing the initial task administered were not all effective. Finally, there was a significant improvement in learner’s performance, their use of visuals, and the accuracy of their methods after the intervention process.
An exploration of General Education and Training (GET) teachers’ mathematical knowledge and its influence on the quality of instruction in the teaching of functions.
(2020) Nguse, Hlengiwe Abigail.; Mudaly, Vimolan.
This thesis documents a study of the General Education and Training teachers’ mathematical knowledge of functions and what this knowledge brings to the quality of instruction. The study made use of Variation Theory and Mathematical Knowledge for Teaching as theoretical frameworks. With regard to the methodology, data generation methods included, semi-structured interviews, pen and paper (written items), lesson observations, field notes and document analysis. The sample was chosen through purposive sampling. The participants were four mathematics teachers from four varying schooling contexts in KwaZulu-Natal. Data generation took place in 2016 and 2017 and a total of 28 lessons were observed. Data generated from pen and paper items corroborated the results of the interviews and the data generated from the classroom observations. This suggested that teacher knowledge does influence the quality of classroom instruction. The findings support the literature which shows that teachers’ subject matter knowledge hugely impacts on the quality of instruction. The study, however, concluded that a lack of subject matter knowledge does not stop teachers from delivering lessons of an acceptable level as required by the Curriculum and Assessment Policy Statement if they follow readily designed lesson plans and make use of prescribed curriculum materials including learner workbooks. It was concluded that when out of field teachers use these prescribed curriculum resources effectively, they are able to involve learners in worthwhile learning of mathematics similar to that made available to learners in classrooms where the teacher has a sound knowledge of the subject matter. It is equally important that textbooks and learner workbooks are checked thoroughly for errors before being printed out and distributed to schools as this can have an adverse effect on learning especially in subjects like mathematics. It is the conclusion of this study that when teachers focus on creating a space of learning which enhances in learners the capabilities to discern which knowledge is germane, the learner and the content are placed at the centre of the process of teaching and learning which improves the quality of instruction. Finally, the study proposes a new knowledge domain based on the model of reflective practice which aims to assist teachers with identifying individual knowledge areas of need for continued professional development.
An exploration of mathematics learner transition from primary school to secondary school.
(2011) Sukhdeo, Swathi.; Mudaly, Vimolan.
This research study explores six primary school learners’ transition to secondary school and the influences that this may or may not have had on their mathematical performances. The study was carried out over a seven month period, that being the latter part of their final primary school year until the end of the first term of high school (October 2010 to April 2011). Various data collection methods were employed to retrieve information and much literature was used to inform this study. In the chapters to follow there are detailed descriptions of various stakeholders in the transition process as well as the factors that affect mathematics learning. The analysis of data reflects the findings of this study and discusses some of the implications regarding mathematics teaching and learning that should considered during the transitional period from primary school to secondary school.
An exploration of pre-service science and mathematics teachers' use of visualisation in a problem solving context : a case study at a South African university.
(2015) Govender, Levashnee.; Mudaly, Ronicka.; Mudaly, Vimolan.
The poor performance of learners in Science and Mathematics in South Africa is a persistent cause for concern to stakeholders in education, and to society at large. Teacher training institutes form crucial stakeholders in Science and Mathematics education. This has been the underlying motivation for this case study, which is based on an exploration of pre-service Science and Mathematics teachers’ use of visualisation within a problem solving context. The study is grounded in the interpretivist paradigm. The purpose of this study stems from anecdotal evidence that has showed teachers’ reluctance to teach problem solving because they are unequipped and/or not confident in solving problems. The exploration of pre-service Science and Mathematics teachers’ use of visualisation in a problem solving context revolved around the following critical questions: 1. What do pre-service Science and Mathematics teachers understand by problem solving within a visualisation context? 2. Why do pre-service Science and Mathematics teachers choose to use the visualisation strategies they use when teaching problem solving? 3. How do pre-service Science and Mathematics teachers plan the use of visualisation when preparing their lessons? The framework used to guide this study falls within the interpretivist paradigm and the theory used is the metacognition theory. This theory refers to a higher order of thinking and, simply put, thinking about thinking. In this study, it was analysed how pre-service teachers view their teaching and what their understanding of visualisation is within a problem solving context. The pilot group comprised five pre-service Science and Mathematics teachers at a South African teacher training institute who were registered for two modules, namely Natural Science Method Two, and Mathematics Method Two. These modules include the teaching of problem solving. A purposive sample population of eighty pre-service teachers were invited to participate in this project, and twelve completed part of the project, while five pre-service teachers participated until the conclusion of the project. A qualitative methodological approach was used and pre-service teachers participated in four stages of data collection. Firstly, a semi-structured questionnaire was used to collect the biographical data of the participating pre-service teachers, and their understanding of problem solving and visualisation. Secondly, a task sheet was administered, which included a Science as well as a Mathematics selection of problems for the pre-service teachers to solve. All problems were purposively selected because visualisation methods could have been used to solve them. This tool was used to decipher what visualisation strategies pre-service teachers use when solving problems and why they use these strategies. Thirdly, a lesson plan was developed by participants to enable an exploration of how they taught problem solving using visualisation, as well as what cognitive processes they used to incorporate visualisation into problem solving. The fourth stage involved engaging participants in individual, face-to-face interviews. Semi structured interview schedules were used for both interviews. All responses were analysed and focused on the three research questions. The findings revealed that the majority of the pre-service teachers understood visualisation as a set of teaching aids that made solving problems easier. The majority of participating pre-service teachers solved Mathematics problems accurately when they used a combination of diagrams and formulae. The responses to the Science problems revealed that the majority of participating pre-service teachers used formulae instead of diagrams to solve them. However, the opposite scenario was presented by these participants when they generated their lesson plans. A greater variety of visualisation strategies were used in the Science lesson plans than in the Mathematics lesson plans. The findings show that the use of visualisation in problem solving helped pre-service teachers solve Science and Mathematics problems successfully. It is anticipated that the pre-service teachers will take this finding and make use of it in their classes in the near future, which should in turn develop more competent problem solvers at schooling level.
An exploration of pre-service teachers use of visualization when teaching and solving problems in the mathematics classroom.
(2020) Budram, Rajesh.; Mudaly, Vimolan.
One of the objectives of mathematics instruction, according to the Department of Education (DoE) in South Africa, and elsewhere globally, is to prepare learners to become proficient in mathematics problem solving. There are many factors that contribute to learners becoming proficient in problem solving. The literature and many studies mentioned within this research present the many arguments for the field of problem solving and visualization. Extant literature related to the range of problem solving is plentiful but there is insufficient or limited studies in the neglected field of visualization especially in how pre-service teachers use visualization and problem solving strategies in the classrooms. This study examines the use of visualization to support the teaching of problem solving strategies by pre-service teachers. The literature survey within this study intimates that a relationship is forged between solving problems and visualization. The available literature suggests that visualization assists learners to develop problem solving skills as it allows them to interpret the problem and show an understanding of the mathematical concepts. Literatures also indicate that when problem solving strategies are used in conjunction with the visual skills, the learners become more proficient in solving problem in the mathematics classroom. Thus, this research looks in a fine grained manner at how visualization and problem solving strategies are used by pre-service mathematics teachers. Data was collected in phases from the pre-service teachers using a questionnaire, lesson observations, semi-structured interviews, evaluation worksheets and learner‟s books. The pre-service teacher‟s verbal and written responses were examined and their classroom practices were observed in conjunction with learner‟s material. The results from the data analysis have shown that some of the pre-service teachers have limited knowledge in the use of visualization and mathematical strategies when solving problems. It was also noted that they need to improve their mathematical content knowledge and how to use mathematical problem solving strategies together with visualization when teaching problem solving. These aspects need to be urgently addressed during their teacher training programmes.
An exploration of preservice teachers’ Mathematics knowledge for teaching in Trigonometry at a higher education institution.
(2020) Tatira, Benjamin.; Mudaly, Vimolan.
This study investigates the extent of final-year preservice teachers’ understanding and development of the mathematics knowledge for teaching in trigonometry. Teachers’ lack of adequate mathematics knowledge to teach mathematics effectively is one of the major source of low mathematics attainment in South Africa. On this basis, the readiness of prospective teachers to teach mathematics must be established at the point of exit. The purpose of the present research study is to explore preservice teachers’ understanding and development of content knowledge and pedagogical content knowledge in teaching trigonometry. The review of literature revealed that many preservice teachers lack the conceptual understanding of school mathematics. Thus, preservice teachers exit teacher education and enter the world of teaching with limited skills and abilities of teaching mathematics. The content test, task-based interview, lesson planning and lesson observations were used to gather data on preservice teachers’ understanding of content knowledge in trigonometry in response to three research questions. The sample of the study was composed of fifteen mathematics final-year preservice teachers who were registered for a Bachelor of Education degree programme at a rural-based institution of higher learning in South Africa. The sample was selected purposively. The mathematics knowledge for teaching conceptual framework by Ball, Thames and Phelps was used to structure the present study and provided lens for data analyses. The analysis of the content test results revealed that preservice teachers’ mastery of content knowledge in trigonometry was inadequate. The results from the task-based interview, lesson plan and lesson observation analyses indicated that the preservice teachers’ mastery of pedagogical content knowledge in trigonometry was limited. Moreover, the extent of preservice teachers’ development of mathematical knowledge for teaching based on results from classroom practices was sub-standard. The traditional teaching methods and learner-misconceptions never left preservice teachers all through the four years of teacher education. Therefore, more needs to be done by the higher education institution to accelerate growth of content knowledge and pedagogical content knowledge through the provisions of methodology, content and teaching practices courses. The interplay of the three, methodology courses, content courses and teaching practice form the basis of an ideal preservice teacher.
An exploration of the barriers to effective geometric thought in the Further Education and Training phase of selected secondary schools in the Umlazi District.
(2021) Naicker, Kalavani.; Mudaly, Vimolan.
ENGLISH ABSTRACT: Geometry, a branch of mathematics has a history from the study of practical measurement in ancient Egypt to properties of shapes in Greek geometry. Learning and teaching of geometry in South Africa has posed many challenges for educators and learners. In 2011 Euclidean geometry was reintroduced after the removal to redress the inequalities of apartheid and to provide uniform access to mathematics for all learners. This study was therefore conducted in three secondary schools, conveniently selected, to explore the barriers that hamper the performance of Euclidean geometry in the FET phase and to explore ways of eradicating these barriers. Research questions generated data from educators and learners aimed at identifying factors influencing effective geometric thought. This study was guided by the two metaphors, namely acquisition and participation and their impact on the teaching and learning of geometry. The study focussed primarily on the cognitive developmental theory of Piaget and social constructivist theory of Vygotsky both of which supported the acquisition metaphor. It further examined the participative metaphor of Sfard’s theory of commognition. The study adopted the interpretive paradigm with the qualitative design. Purposive sampling was used since the study was conducted with grade 11 learners and educators teaching in the FET phase. Questionnaires, semi structured interviews and focus group discussions were used to collect the data. Lesson observations were used for triangulation purposes. The research instruments were piloted in order to ensure validity and reliability. Data was first organized according to the research questions which was then coded and divided into themes. It was found that many of the barriers to learning geometry are primarily attributed to a lack of engagement of learners in meaningful learning situations. Findings also highlighted language, attitude, the classroom environment, and gaps in educators’ methodology and content knowledge has being some of the factors that contributed to the poor learner participation. Recommendations are made for stakeholders to develop effective geometric thought. This study proposes that greater emphasis be placed on learner-centred methods of teaching. Communication in the form of verbal, written and visual should be considered when teaching geometry. Allowing learners to express their experiences to think and develop new knowledge is essential. Learners need to become active participants of their learning and learning needs to take place in more realistic situations to improve understanding. IQOQA LOCWANINGO: I-Jiyomethri, igatsha lezibalo linomlando osuka ekutadisheni kwesilinganiso esisebenzayo Egibhithe lasendulo kuya azakhiweni zomumo weJiyomethri yamaGrikhi. Ukufunda nokufundisa iJiyomethri eNingizimu Afrika kudale izingqinamba eziningi kothisha nabafundi. Ngo-2011 iJiyomethri yaphinde yafakwa ngemuva kokususwa ukuze kulungiswe ukungalingani kobandlululo kanye nokuhlinzeka ngokulingana ukuthola izibalo zabo bonke abafundi. Ngakho-ke lolu cwaningo lwenziwe ezikoleni zamabanga aphakeme ezintathu, ezikhethwe kalula, ukuhlola imigoqo ephazamisa ukusebenza kweJiyomethri esigabeni seFET nokuhlola izindlela zokuqeda lezi zithiyo. Imibuzo yocwaningo yakhiqiza idatha evela kothisha nakubafundi ehlose ukukhomba izinto ezinomthelela ekucabangeni okusebenayo kweJiyomethri. Lolucwaningo beluqondiswa izingathekiso ezimbili, okungukuthi ukuzuza nokubamba iqhaza kanye nomthelela wazo ekufundisweni nasekufundweni kweJiyomethri. Ucwaningo lugxile kakhulu kumqondo wokuthuthuka wokuqonda kaPiaget kanye nethiyori yezakhi zenhlalo kaVygosky zombili ezazisekela isingathekiso sokutholwa. Iphinde yahlola umbono kaLave noWenger (1991) owawugqamisa ukubaluleka kwesifaniso sokubamba iqhaza futhi okokugcina, umbono kaSfard wokuhlonishwa. Ucwaningo lwamukele ipharadigm yokuhumusha ngomklamo wekhwalithi. Isampuli enenhloso isetshenzisiwe kusukela isifundo senziwa nabafundi bebanga le-11 nothisha abafundisa esigabeni se-FET. Amaphepha emibuzo, izingxoxo ezihleleke kancane kanye nezingxoxo zamaqembu okugxila kuwo kusetshenziselwe ukuqoqa imininingwane. Ukubheka izifundo kusetshenziselwe izinhloso zonxantathu. Amathuluzi zocwaningo ahlolwa ukuze kuqinisekiswe ukuba semthethweni nokwethembeka. Idatha yayihlelwe ngokuya ngemibuzo yocwaningo eyabe isibhalwa ngamakhodi yahlukaniswa yaba ngamatimu. Kunconyelwa ababambiqhaza ukuthi bathuthukise umcabango weJiyomethri osebenzayo. Lolu cwaningo luphakamisa ukuthi kugxilwe kakhulu ezindleleni ezigxile kubafundi zokufundisa. Ukuxhumana ngendlela yokukhuluma, okubhaliwe nokubukwayo kufanele kubhekwe lapho kufundiswa iJiyomethri. Ukuvumela abafundi ukuthi baveze ulwazi lwabo ukuze bacabange futhi bathuthukise ulwazi olusha kubalulekile. Abafundi kudingeka babe ngabahlanganyeli abakhuthele ekufundeni nasezidingweni zokufunda kwabo okumele ukwenzeke ezimeni ezingokoqobo ukuthuthukisa ukuqonda.
An exploration of the integration of technology by mathematics teachers: the case of 10 schools in KwaZulu-Natal under Umlazi District.
(2020) Zulu, Mzwandile Wiseman.; Mudaly, Vimolan.
This interpretive qualitative study sought to explore the integration of technology by mathematics teachers in Umlazi district of KwaZulu-Natal province. A purposive non-probability sample of ten teachers from ten different schools in Umlazi district participated in the study. Data was collected from the participants using a questionnaire, interview, classroom observation schedule and document analysis, while the thematic analysis method was employed to analyse the data. The findings of the study revealed that the South African Department of Basic Education advocates for the integration of technological tools for all teaching and learning processes in basic education. However, the study showed that teachers underutilise the technological resources they have at their disposal and that they mainly rely on the teaching of mathematics using traditional methods of teaching. The findings established possible factors contributing to the under utilisation of technology by mathematics teachers in Umlazi district. These factors include: (1) lack of training to confidently integrate technology; (2) lack of technology pedagogical content knowledge; (3) limited access to technological tools; (4) crime (break-ins); (5) overcrowded classrooms; (6) lack of technical support for software updates; (7) electric power failure during the teaching and learning hours; and (8) lack of exposure to government policies advocating for technology integration in teaching. Lastly, the study found that though teachers are not actively utilising the technological tools in the teaching of mathematics, they however demonstrated a positive attitude towards its use. The results further showed that if the factors above are well addressed, the mathematics teachers in Umlazi district would be utilising their tools effectively in their teaching practices.
An exploration of the role of visualization in the proving process of Euclidean geometry problems.
(2015) Reddy, Lola.; Mudaly, Vimolan.
Abstract available in PDF file.
An exploration of the teaching and learning of Information Technology (IT) programming in a higher education institution in KwaZulu-Natal (KZN)
(2019) Govender, Thamotharan Prinavin.; Mudaly, Vimolan.
In this study, classic grounded theory, threshold concepts, self-study and practitioner research capture the processes of Information Technology (IT) academics who teach computer programming to first-year IT students at a university of technology in Kwa-Zulu Natal. The qualitative data analysis revealed the basic pedagogy of teaching and learning computer programming, and described how IT academics perceived their vocation and their decisions to take action to ultimately improve the quality of teaching and learning of IT programming. From the data, the following four themes emerged in the process of teaching and learning computer programming: 1) Teaching IT; 2) Learning IT and its impact; 3) Challenges in teaching IT; 4) Recommendations for teaching IT programming. This study will assist first-year IT programming academics to understand their pedagogical impact at an institution of higher learning. This study will further potentially serve as a path for future research and aid in understanding the pedagogical impact of the teaching and learning of IT on first-year IT students.
Exploring different types of knowledge required for mathematics teaching in selected schools in Mthatha.
(2018) Senoo, Godsway Kofi.; Mudaly, Vimolan.
The study sought to explore different types of knowledge for teaching mathematics in selected schools in Mthatha in South Africa. A survey design which used both quantitative and qualitative aspects of research was used in the study. Task sheets, observational schedules and interview schedules were used to collect data. Participants were made up of 6 Grade 9 mathematics teachers from 6 schools out of 25 schools in circuit 3 in the Mthatha District of Education. Descriptive statistics and content analysis were used to analyse the data. Frequency tables, pie charts and histogram graphs were used to present quantitative data based on observation while verbal quotes were presented to support themes that emerged from qualitative data gleaned from task sheets and interview schedules. These were analysed by means of content analysis. The findings of the study revealed that mathematics knowledge (conceptual understanding, procedural fluency, strategic competence, adoptive reasoning and productive disposition), knowledge of instructional practices (curriculum, tasks and tools for teaching) were limited with regard to most of the teachers in the Mthatha District. These related to many factors such as unqualified mathematics teachers, lack of in-service training, inadequate teaching and learning material, teachers’ attitudes towards mathematics etc. It was recommended that the Department of Education should organize regular in-service training for mathematics teachers in order to improve the quality of mathematics teaching and also keep mathematics teachers updated. There is also a need for department to supply adequate teaching and learning resources to schools in order to improve teachers’ knowledge of instructional practices. Furthermore, teachers need to update themselves in order to acquire sound pedagogical content knowledge for effective teaching. The Department of Education should try to motivate mathematics teachers by financing their efforts to upgrade themselves. Moreover there is a need for the department to strengthen their supervision team in order to monitor mathematics teachers in schools. This will help teachers to prepare better for mathematics lessons.
Exploring higher education engagement in computer programming within a blended learning environment : an action research approach
(2014) Jugoo, Vikash Ramanand.; Mudaly, Vimolan.
Many novice programmers in higher education find computer programming particularly difficult due to its problem solving nature. High dropout rates have been observed both internationally and locally, but in South Africa, the circumstances of students coming from disadvantaged schools where they struggle in subjects like Mathematics and Science, especially compounds their challenges in computer programming when they enrol at a tertiary institute. In this study, I explore the engagement of computer programming at a higher education institution using an innovative approach of incorporating tools in the form of online learning and support structures to supplement the existing face-to-face and practical lessons thereby creating a blended learning environment (BLE). This study, which is a qualitative one, used an interpretivist paradigm to explore the engagement of sixty, first year students in an introductory computer-programming course at a selected university in South Africa, using an action research approach within the context of a BLE. Action research refers to an evaluation of one’s own practice with a view to improving one’s effectiveness, in this case, analysing my own efficacy as a teacher, and the learning that occurred by my students (McNiff, 2013; Whitehead, 1989). This study used two lenses: The first lens was my own as a lecturer/researcher who developed a variety of support structures in the form of notes, videos, animations, and blogging, to support student engagement in computer programming, and the second lens was the students’ engagement with these tools. The study explored this dual engagement and asked two critical questions: 1) How does engagement of computer programming take place within a BL context using an action research approach, and, 2) Why does engagement of computer programming take place within a BL context using an action research approach, in the way it does? A dual form of engagement occurred creating a dynamic BLE. In the study, students were exposed to one theory classroom lesson, and three practical lessons. As the lecturer, I received feedback from the students which informed my attempts to improve the environment. Observations, a personal diary, electronic questionnaires, and focus group meetings were used to gather feedback on how students engaged in the BLE. The action research methodology was based on planning, acting, observing and reflecting. The analysis of the reflections was used in the re-planning phase of the next cycle and a total of three cycles were used. Although there were three main action research cycles, each tool was transformed resulting in smaller cycles emanating within the main action research cycle. Activity Theory was used as a theoretical framework to describe and analyse the actions and engagement that transpired within the BLE. The results from this study highlight positive student engagement in learning through the use of examples and visual tools although the use of language was found to be a barrier under certain circumstance. Support and planning were also identified as important factors for both student and lecture engagement. Other aspects concerning feedback and reflection were established as important during the dual engagement employed resulting in the creation of a dynamic action research model of engagement.
Exploring master teachers' use of visuals as tools in mathematical classrooms.
(2011) Naidoo, Jayaluxmi.; Mudaly, Vimolan.
The teaching and learning of mathematics has presented a great challenge for mathematics educationalists over many decades. Researchers have been searching for new strategies and techniques for improving the understanding of abstract mathematical concepts. With the current changes in the mathematics curriculum in South Africa, it is important to ensure that no learner is left behind in the pursuit to produce mathematically literate learners nationally. Teachers are encouraged to teach a common curriculum so that all learners have equal opportunities of attaining success in a democratic society in any chosen field. Some teachers achieve mathematical success easily while others struggle to achieve similar outcomes. Whilst we acknowledge that teachers ought to emulate the practices of other good teachers, we often do not seek explanations of what makes a teacher effective and how they achieve success in a classroom. As can be conceived, apart from probing teachers’ content knowledge, it is necessary to know how this knowledge can be used for optimal results in the course of teaching within the diverse South African classroom. In other words, it becomes necessary to interrogate the teacher’s pedagogical content knowledge because of the uniqueness of the South African context. It is for this reason that an in-depth study was done to explore Master teachers’ use of visuals as tools within mathematics classrooms. This study focused on six experienced mathematics teachers or Master mathematics teachers. These teachers were selected from six Dinaledi schools located in KwaZulu- Natal. The schools catered for learners from multicultural and multiracial backgrounds. Activity theory was used as a framework to locate the study. Each activity system was interrogated within an interpretivist paradigm. Data was collected using six methods and five research instruments.
Exploring the discourses of preservice mathematics teachers when solving geometry problems=Kuhlolwa ingxoxo yothisha bezibalo abangakasebenzi ngesikhathi bexazulula izinkinga zegeometry.
(2021) Mahlaba, Sfiso Cebolenkosi.; Mudaly, Vimolan.
Research on teaching and learning that aim to improve preservice mathematics teachers’ (PMTs) knowledge of geometry is increasing globally. The current study explored PMTs’ discourses when solving geometry problems. The amalgamation of the commognitive theory and the Van Hiele levels of geometrical thinking theory was used as the theoretical basis for this study. The study uses the difference between ritualistic and explorative discourse as explicated by Sfard (2008) in commognition together with the four Van Hiele levels of geometrical thinking to view and analyse the data. It goes deeper into the theory of commognition to use not only objectification of mathematical discourse but also the four elements of mathematical discourse to reach its conclusion. The current study aimed to answer the main question: How does preservice mathematics teachers’ thinking as evident in their mathematical discourse during Euclidean geometry problem solving relate to their teaching practices in Euclidean geometry? This will be done through answering four subsidiary questions. A qualitative research approach was used to generate rich and descriptive data to answer the posed research questions. Furthermore, the qualitative approach allowed for the collection of data representing participants’ geometry problem solving experiences which was the core of the current study. I purposively and conveniently sampled 6 participants in this study where they completed a task-based and face-to-face interviews. Consent was obtained from these participants prior their participation in the study. Data generated from the two instruments was thematically analysed. Findings from this study revealed that most PMTs use ritualistic discourse when communicating about their geometry problem solving actions. These findings are a consequence of them performing routines for social acceptance instead of generating endorsed narratives. Furthermore, it was observed that others used ritualistic discourse because they rely on scaffolding from others to perform their routines instead of developing their own routines. Despite the dominance of ritualistic discourse participation in the current study, there were instances where PMTs seemed to be using explorative discourse but get stuck somehow and return to ritualistic discourse. The Van Hiele theory revealed that most PMTs still operate within the lower levels of geometrical thinking. The main findings and contribution of this study is that for PMTs to advance their geometrical thinking from level 0 to level 3, they need to transform their discourse participation from ritualistic to explorative. IQOQA Ucwaningo mayelana nokufundisa kanye nokufunda oluhlose ukuthuthukisa inkonzo yokulekelela othisha bezibalo ngolwazi lwe-geometry luyakhula umhlaba wonke. Okufundwayo kuhlola ukusetshenziswa kolimi ngesikhathi kuxazululwa izinkinga zegeometry. Ukuqoqela ndawonye kwethiyori ye-commognitive kanye neVan Hiele yamazinga e-geometrical yenjulalwazi yokucabanga yasetshenziswa njengesisekelo sobunjulalwazi sesifundo. Uhlelokwenza locwaningo ngekhwalithethivu lwasetshenziswa ukuchamusela ulwazi oluchazayo nolunonile ukuphendula imibuzo yocwaningo eyaphonswa. Uma sihlabela phambili, uhlelokwenza ngekhwalithethivu lwavumela ukuqoqwa kolwazi olumele abazibandakanya mayelana nabasebekwazi ukusombulula izinkinga ze-geometry okwakungumgogodla wesifundo. Ngisampule abayisithupha (6) ababamba iqhaza ngenhloso nangokufaneleyo kulesi sifundo njengoba benza umsebenzi kanye nohlelongxoxo ubuso nobuso. Ukuvuma kwababambe iqhaza kwatholakala ngaphambi kokuba basetshenziswe esifundweni. Ulwazi olusengwe emathuluzini amabili lwacutshungulwa ngokobungqikithi. Imiphumela iveza ukuthi iningi lothisha abamukela inkonzo yokusizwa ngokwezibalo basebenzisa inkambiso ethile ngokwezingxoxo uma kukhulunywa ngezinyathelo zokuxazululwa kwezinkinga ze-geometry. Lemiphumela iyizimpendulo zabo zokwenza izinto ezizodwa ukuze bamukeleke ngokwenhlalo esikhundleni sokuphehla izinkulumo ezivunyiwe. Uma sihlabela phambili, kwabhekwa ukuthi abanye basebenzisa inkambiso ngokwengxoxo ngoba bathembele ekufukulweni ngabanye ukwenza inhlalakhona yabo esikhundleni sokukhulisa eyabo inhlalakhona. Ngaphandle nje kokugxila kwenkambiso yengxoxo yababamba iqhaza kulesi sifundo, izibonelo lapho othisha abenkonzo yokusizwa ngokwezibalo kubukeka besebenzisa ingxoxo kusinga kodwa bese beyakhingxeka kwezinye izindawo bese bebuyela enkambisweni ngxoxo. Injulalwazi yeVan Hiele iveza ukuthi iningi lalabothisha abasizwa ngezibalo nanamhlanje badidizela emazingeni aphansi ngokomcabango wegeometry. Okutholakele okunqala kanye nomnikelo walesi sifundo ukuthi labo thisha abasizwe ngokwezibalo uma befuna ukuqhubekela phambili ngokomcabango we-geometry kusukela ezingni leqanda (0) kuya kwelesithathu (3), kuzodingeka bayiguqule ingxoxo yabo yokuzibandakanya kusukela enkambisweni kuya enhlolweni.
Exploring the effectiveness of parent engagement in the teaching of foundation phase geometry.
(2021) Hopkins, Siobhan Kerry.; Mudaly, Vimolan.
Learners need mathematics to fulfil academic and vocational dreams, to learn to think in a particular manner and to survive in a world where so many mathematics skills are prevalent. Learners show improvement when they understand the mathematics they are doing, and it is not merely seen as a set of rules. When you connect the dots meaningfully for the learners using diagrams, technology, physical objects, and everyday examples, they start to really understand and problem solve. However, in my experience, the one area where many learners were not showing significant improvement and seem to lack understanding, was geometry. This sparked a sincere interest in studying the cause of the geometry struggle and means of addressing it. The more I looked into it, the more research was pointing to the fact that geometry understanding has to start at a foundation level. You cannot expect learners to engage in complex geometric proofs involving difficult deductive reasoning when they do not know and understand the basics leading up to this. Thus, this master’s thesis explores the teaching of foundation phase geometry and how intervention can happen at the grass roots in order to see long term benefits. One of the essential ingredients in developing correct concept formation at foundation phase, is having access to hands on activities through adult-guided play. The reality in South Africa, is that the ratio of learners to teachers is too high to allow this to happen in a meaningful way in the classroom. Too little time is assigned to geometry in the foundation phase curriculum as more important numeracy concepts and learning to read and write, are prioritized. However, lockdown brought to the foreground, the important role that parents can play in improving the education of children. Although not all parents were effective teachers, surprisingly, many very effective in assisting in the educational process of their child when asked to do so. This study therefore looks at parents’ input as an interventive means of assisting in the process of teaching foundation phase geometry. Although we all know the ideal solution is a highly qualified teacher in a small classroom with all the necessary resources, this is only a reality for about 3% of the South African population. This study is seeking intervention for the other 97% who do not have the privilege of the ideal. This study was a case study using qualitative methodology. Video analysis of one-on-one time with parents and their children was used to analyse the effectiveness of parent involvement. Teacher interviews were used to assess how space and shape is currently being taught and parent questionnaires were used to gather data on how parents felt about being involved in helping their child with space and shape learning. This study showed that through simple communication with parents, regardless of what socio-economic background they came from, effective activities can be designed to bring about meaningful scaffolding in geometry learning. Although video-analysis revealed very positive findings, parents felt that many other parents would not help their own children due to circumstantial constraints.