Дисертації: "Mathematics Study and teaching South Australia"

1

Debela, Nega Worku. "Minority language education with special reference to the cultural adaption of the Ethiopian community in South Australia /." Title page, contents and abstract only, 1995. http://web4.library.adelaide.edu.au/theses/09PH/09phd2858.pdf.

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Seah, Wee Tiong. "The negotiation of perceived value differences by immigrant teachers of mathematics in Australia." Monash University, Faculty of Education, 2004. http://arrow.monash.edu.au/hdl/1959.1/5456.

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Mahomed, Shaheed. "Integrating mathematics into engineering : a case study." Thesis, Cape Peninsula University of Technology, 2007. http://hdl.handle.net/20.500.11838/1255.

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Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2007
Twelve years into a democracy, South Africa still faces many developmental challenges. Since 2002 Universities of Technology in South Africa have introduced Foundational Programmes/provisions in their Science and Engineering programmes as a key mechanism for increasing throughput and enhancing quality. The Department of Education has been funding these foundational provisions since 2005. This Case Study evaluates an aspect of a Foundational provision in Mechanical Engineering, from the beginning of 2002 to the end of 2005, at a University of Technology, with a view to contributing to its improvemenl The Cape Peninsula University of Technology {CPUn, the locus for this Case Study, is the only one of its kind in a region that serves in excess of 4.5 million people. Further, underpreparedness in Mathematics for tertiary level study is a national and intemational phenomenon. There is thus a social interest in the evaluation of a Mathematics course that is part of a strategy towards addressing the shortage in Engineering graduates. This Evaluation of integration of the Foundation Mathematics course into Foundation Science, within the Department of Mechanical Engineering at CPUT, falls within the ambit of this social need. An integrated approach to cunriculum conception, design and implementation is a widely accepted strategy in South Africa and internationally; this approach formed the basis of the model used for the Foundation programme that formed part of this Evaluation. A review of the literature of the underpinnings of the model provided a theoretical framework for this Evaluation Study. In essence this involved the use of academic literacy theory together with learning approach theory to provide a lens for this Case Study.

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Kunene, Looksmart Lucky Zamokuhle. "Classroomlevel factors affecting mathematics achievement : a comparative study between South Africa and Australia using TIMSS 2003." Diss., University of Pretoria, 2011. http://hdl.handle.net/2263/25819.

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The purpose of the study was to explore and compare key classroom level factors affecting mathematics learner achievement for South Africa and Australia. The study focused in the classroom where teaching and learning takes place. This is a secondary analysis of classroom level factors influencing Grade 8 mathematics learner achievement using the Trends in International Mathematics and Science Study (TIMSS) 2003. TIMSS 2003 was chosen because it was the latest international study available to measure trends in mathematics learner achievement, where South Africa had participated. Quantitative research approach was employed and a survey research method was used which seeks, among others, to explore relationships and patterns. Survey research method was suitable to provide data that responded to the research questions. The data collection in South Africa and Australia was conducted in October-December 2002 as both countries are located in the Southern Hemisphere. The sample for South Africa consisted of 255 schools with 100% coverage and stratification done by a total of nine provinces, and language. This resulted in 8952 learners tested across the provinces (Joncas, 2004, p. 212). For Australia, the sample consisted of 207 schools with 100% coverage and stratification done by a total of 8 States and Territories and school type. This resulted in 4791 learners participating in the study. The sample included teachers of learners who were selected to participate in the TIMSS 2003 study for South Africa and Australia. The intended target was teachers of all learners at the end of their eight year of schooling. For each participating school, a single mathematics class was sampled and the mathematics teacher of the selected class was asked to complete a mathematics questionnaire. Mathematics teachers of sampled learners responded to questions about teaching emphasis on the topics in the curriculum frameworks, instructional practices, professional training and education and their views on mathematics. The mathematics teacher questionnaire was designed to take about 45 minutes to complete The main question for this study was “What are the key classroom factors that influence learner performance in mathematics?” The three sub questions for the study were: What key variables on classroom level are related to learner achievement in mathematics for South Africa? What key variables on classroom level are related to learner achievement in mathematics for Australia? How do the classroom level factors in mathematics performance of South Africa compare with classroom level factors in Australia? The conceptual framework for the study stressed classroom level factors including instructional quality, which includes teacher background factors, classroom climate, teaching requirements and mathematics curriculum. The framework describes the factors related to classroom interactions within the comprehensive education system, with regard to inputs – process – outputs – outcomes. The selection of variables for the inclusion in the models was guided by the conceptual framework and extensive preliminary analyses. Preliminary statistical analyses included exploring descriptive statistics, Varimax factor analysis, reliability, correlation analysis and stepwise multiple regression analysis. The results of the study indicate that several specific classroom level factors were associated with the higher levels of mathematics achievement of South Africa and Australia. The results for the final South African model were: age of teacher; years been teaching; outside school day grading tests; outside school day other; and computer shortage were identified to predict learner achievement. For Australia ten classroom factors, namely, teacher perception of school climate; teacher perception of school safety; teacher emphasis on mathematics homework; teacher repeat mathematics limiting factors; homework contribute towards learning; work conditions; unhappy learners; shortage of instructional equipment; geometric shapes; and algebraic functions were identified to predict learner achievement. South Africa has factors like teacher background and outside school activities by the teacher. Australia has factors like classroom climate, work conditions and curriculum quality. In the light of schools effectiveness research and school improvement research, a comparative study like this one would require more than one level (classroom level), two or three levels would have been ideal to draw other variables and enrich the analysis, especially the learner level and school level. School effectiveness places an emphasis on the ability and social background of the learners as factors that shape academic performance
Dissertation (MEd)--University of Pretoria, 2011.
Science, Mathematics and Technology Education
unrestricted

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Buckingham, Elizabeth Ann. "Socialisation to higher mathematics : men's and women's experience of their induction to the discipline." Monash University, Faculty of Education, 2004. http://arrow.monash.edu.au/hdl/1959.1/5425.

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6

Lee, Amanda Jane. "A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase." Thesis, Rhodes University, 2014. http://hdl.handle.net/10962/d1015664.

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This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.

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Mrowa, Colette. "Communication, discourse, interaction in language classes. /." Title page, contents and summary only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phm939.pdf.

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Thesis (Ph. D.)--University of Adelaide, Dept. of Linguistics, 1997.
Amendments and errata are in pocket on front end paper together with covering letter. Includes bibliographical references (leaves 168-185).

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au, Ronald Aubrey@det wa edu, and Ron Aurbrey. "Student and teacher perceptions of preparation in mathematics in middle school and its impact on students' self-efficacy and performance in an upper secondary school in Western Australia." Murdoch University, 2006. http://wwwlib.murdoch.edu.au/adt/browse/view/adt-MU20070419.111054.

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Middle school initiatives (including heterogeneous classes and an integrated, flexible curriculum together with promotion of student input) have been implemented in schools in Western Australia in response to a perceived need to align schools more closely with a more student-centred approach to learning, in the expectation of meeting more students needs and thereby reducing student dissatisfaction and increasing the possibility of students pursuing life long learning. Specific goals underlying the initiative include the development of independent learning and student responsibility for learning through a series of strategies such as self-paced learning, student involvement in negotiating their own learning, and a strong emphasis on respecting and valuing student input into the implementation of curricula. However, owing to the way that the curricula for Middle and Upper secondary school mathematics are currently structured, problems might arise for students in the transition from a relaxed to a highly discipline-based organization of content (as described by Venville, Wallace, Rennie, Malone (1998). Students accustomed to the current approaches implemented in Middle schools (Years 8 to 10) may be disadvantaged in the transition to Upper secondary school courses (Years 11 and 12) compared with those students who have been exposed to a more discipline-based organization of content throughout early adolescence and prior to entry into courses leading to tertiary entrance (T.E.E. courses). The aim of this project was to investigate the possible effects of Middle school initiatives in a group of students from three Middle schools in Western Australia in one subject area mathematics on the perceptions of self-efficacy and preparation in mathematics once the students encounter Year 11 Upper school courses. A survey containing Likert-type rating scales pertinent to four areas of interest Self-efficacy in mathematics; Self-Directed Regulation; Views on current teaching; and Views on prior teaching were administered to students transferring from three feeder Middle schools to Year 11 (Upper secondary school) classes in one Senior College in Western Australia for each of 4 consecutive years. Students were also asked for their comments regarding preparation for the challenges of their chosen courses in mathematics. In addition, their levels of performance in a range of mathematical skills were assessed using a teacher-developed test. The perceptions of their Middle and Senior School teachers were also sought. As the survey was administered to all students as a routine part of action research within the mathematics faculty at the Senior College, only the results of those students who subsequently agreed to be participants in the study are reported in this dissertation. Results indicated that a mismatch existed in approaches and skills between Middle School and Senior College Mathematics. The reliance on students making suitable choices for themselves, the absence of specialist teachers of mathematics in middle schools, mixed ability classes in which specialist teachers of mathematics find it difficult to operate successfully and a curriculum that was so flexible that teachers omitted key elements required for later studies were the main factors that resulted in a significant number of students making the transition from middle to senior school with insufficient preparation. Implications for the teaching of mathematics in these three Middle schools and the Upper school are discussed.

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Galant, Jaamiah. "Teachers, learners and mathematics : an analysis of HSRC research reports on mathematics education 1970-1980." Master's thesis, University of Cape Town, 1997. http://hdl.handle.net/11427/17548.

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Bibliography: pages 177-183.
The dissertation is concerned with the production of a systematic analysis of HSRC research reports into mathematics education in South Africa between 1970 and 1980. Drawing on the theoretical language of Dowling (1995), the analysis focuses on the (re)production of voice and message in the reports. This entails an analysis of positioning strategies that il1ark out voices in the texts and distributing strategies that distribute message across voices. Voices include bureaucratic, academic, teacher and learner voices and knowledge and practices that constitute message distributed to voices relate to mathematical knowledge, pedagogic knowledge and curriculum innovation practices. Positioning and distributing textual strategies with respect to learner and teacher sub-voices are related to the (re)production of theories of instruction that constitute models of acquirers, transmitters and pedagogic contexts and define pedagogic competence in particular ways. The (re)production of theories of instruction in turn are related to the reproduction of social relations in the broader society. It is hoped that the analysis illustrates the generality of Dowling's language for analysing texts. The substantive focus of the study is the analysis of the reports and the language developed in the analysis is used to make some suggestive comments about current mathematics curriculum development in South Africa. It is hoped, in particular, that the focus in this study on discourses in mathematics education in South Africa in the 1970s will contribute to the documenting of the history of mathematics curriculum development in South Africa.

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Du, Plessis Hester. "Evaluating the effectiveness of Advanced Programme Mathematics in preparing learners for university mathematics." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/97080.

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ENGLISH ABSTRACT: In today’s hi-tech global economy the fields of science, technology and engineering are becoming increasingly and undeniably central to economic growth and competitiveness, and will provide many future jobs. Qualifications in Mathematics are crucial gateways to further education and will provide access to the Science, Technology, Engineering and Mathematics (STEM) industries. This study focuses on the optional course in Mathematics, called Advanced Programme Mathematics (APM), which is offered and assessed by the Independent Examination Board in the final three years of high school in South Africa. At present, the South African school system does not adequately prepare students for the transition from school to university Mathematics, and APM has been designed to address this gap. The research question set by this study is: To what extent does the APM course succeed in preparing learners for the rigour of first-year Mathematics in the STEM university programmes? The sample group of 439 students was selected from the 2013 cohort of first-year Mathematics students at Stellenbosch University. First, an analysis of the relevant curricula was undertaken, and then an empirical investigation was done to determine the differences in performance between first and second semester examinations of first-year university Mathematics students who took APM, and those who did not. This was followed by an investigation by means of a questionnaire into the perceptions of students on how effective APM was in easing the transition from school to university Mathematics. The research was designed according to the Framework for an Integrated Methodology (FraIM) of Plowright (2011). From an extensive international literature study, it appears that APM is definitely a predictor of post-secondary success. Since no formal research has been recorded to support this claim, this study aims to provide a sound answer to whether APM is advantageous. The effect size results of this study show that APM marks of students explain 68% of the achievement in first-semester university Mathematics when combined with NSC Mathematics marks in a general regression model. There is a significant difference between the marks of students who took APM and those who did not in first-semester university Mathematics, specifically across the National Senior Certificate (NSC) Mathematics mark categories of 80-100%. APM course-taking leads to confidence in Mathematics, which combined with good domain knowledge of calculus, ease the transition from school to university Mathematics. The study recommends that not only students who intend pursuing a career in the STEM industries should take the APM course, but also those who intend to apply for admission to any other tertiary studies, as the cognitive and other skills provided by APM will give them the required edge to perform well in higher education. Schools are called upon to provide access to APM for mathematically gifted students, and teachers and guidance counsellors should encourage learners to enrol for AMP. This will enable them to share in the manifold academic and personal benefits accruing from the course, and to help alleviate the critical shortage of graduates in careers requiring a strong Mathematics background in South Africa.
AFRIKAANSE OPSOMMING: In die hoë-tegnologie-wêreldekonomie van vandag word die gebiede van wetenskap, tegnologie en ingenieurswese toenemend en onmiskenbaar die kern van ekonomiese groei en mededingendheid wat in die toekoms baie werkgeleenthede sal bied. Kwalifikasies in Wiskunde open beslis baie deure na verdere opleiding en verleen toegang tot die Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-industrieë. Hierdie studie fokus op die opsionele kursus in Wiskunde, genaamd Gevorderde Program Wiskunde (GPW), wat deur die Onafhanklike Eksamenraad aangebied en geassesseer word in die laaste drie jaar van hoërskoolonderrig in Suid-Afrika. Tans berei die Suid-Afrikaanse skoolstelsel nie studente genoegsaam voor vir die oorgang van skool- na universiteitswiskunde nie en GPW is ontwerp om hierdie gaping te oorbrug. Die navorsingsvraag wat hierdie studie stel, is: In watter mate slaag die GPW-kursus daarin om leerders voor te berei vir die streng vereistes van eerstejaar-Wiskunde in die Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-universiteitsprogramme? Die toetsgroep van 436 studente is gekies uit die 2013-groep eerstejaar-Wiskundestudente aan Stellenbosch Universiteit. Aanvanklik is ᾽n analise van die relevante leerplanne onderneem, waarna ᾽n empiriese ondersoek gedoen is om die verskille in prestasie in die eerste en tweede semester eksamens vas te stel tussen eerstejaar-Wiskundestudente op universiteit wat wel GPW geneem het en diegene wat dit nie geneem het nie. Dit is gevolg deur ᾽n ondersoek deur middel van ᾽n vraelys na die persepsies van studente oor hoe effektief GPW was om die oorgang van skool- na universiteitswiskunde te vergemaklik. Die navorsing is ontwerp op grond van ‘n model vir ‘n geïntegreerde metodologie van Plowright (2011). Dit blyk uit ᾽n uitgebreide studie van internasionale literatuur dat GPW definitief ᾽n voorspeller van post-sekondêre sukses is. Aangesien geen formele navorsing om hierdie aanspraak te ondersteun nog op skrif gestel is nie, poog hierdie studie om ᾽n deurdagte antwoord te verskaf op die vraag of GPW wel tot voordeel van studente is. Die effek grootte resultate van hierdie studie dui aan dat die GPW-punte van studente 68% van prestasie in Wiskunde in die eerste semester op universiteit verduidelik as dit in ᾽n algemene regressiemodel met die Nasionale Senior Sertifikaat (NSS) punte gekombineer word. Daar is ᾽n beduidende verskil tussen die Wiskundepunte van studente wat GPW geneem het en diegene wat dit nie geneem het nie in die eerste semester op universiteit, veral in die NSS-Wiskundepuntekategorieë van 80-100%. Om die GPW-kursus te neem, lei tot selfvertroue in Wiskunde, wat saam met ᾽n goeie kennis van die Differensiaalrekening-domein, die oorgang van Wiskunde vanaf skoolvlak na universiteitsvlak vergemaklik. Op grond van die studie beveel die navorser aan dat nie slegs studente wat ᾽n loopbaan in Wetenskap-, Tegnologie- Ingenieurswese- en Wiskunde-rigtings wil volg, die GPW-kursus behoort te volg nie, maar ook diegene wat vir toelating tot enige ander tersiêre studie wil aansoek doen, aangesien die kognitiewe en ander vaardighede wat GPW ontwikkel, hulle die nodige voorsprong sal bied om goed te vaar in verdere studie. Skole word aangemoedig om toegang tot GPW aan wiskundig begaafde leerlinge te verskaf en onderwysers en loopbaanraadgewers behoort leerlinge aan te moedig om vir GPW in te skryf. Sodoende kan hulle deel in die vele akademiese en persoonlike voordele wat die kursus bied, en help om die kritieke tekort aan gegradueerdes in die studierigtings waar ‘n sterk Wiskunde agtergrond ‘n vereiste is, te help verlig.

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11

Austin, Pamela Winifred. "A value-based approach to promoting excellence in mathematics education." Thesis, Nelson Mandela Metropolitan University, 2010. http://hdl.handle.net/10948/1656.

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This research study has emerged as a result of my concern regarding the apparent low self-efficacy amongst initial teacher education students in my mathematics education classes. It also reflects a reported renewed interest in values, and the promotion of excellence in education. The effects of a values-based approach to mathematics education towards improving students’ self-efficacy and promoting excellence have been investigated, grounded within my ontology of excellence in mathematics education, which incorporates the values of respect, fairness, accountability, honesty and compassion. An inquiry-based teaching and learning approach formed the framework within which the study took place. Notions of ‘new scholarship’, premised on the view that teaching is about engagement in participatory learning, and the development of communities of creative students, provided the theoretical framework. Both quantitative and qualitative data gathering methods were used. Data-collection tools included affective-disposition statements, interviews, journal entries, as well as a video recording of a mathematics education lesson. The quantitative and qualitative data generated suggest improved levels of self-efficacy amongst the students who participated in the study. The data also suggest that a valuesbased approach to teaching can be used as an effective approach by mathematics teachers – and mathematics teacher educators – for the purpose of promoting the pursuit of excellence. As teacher education worldwide is currently characterised by a lack of vitality in teacher preparation (Grossman, 2008), the findings of this study should provide insights for teacher educators, teachers and policy makers who wish to promote mathematics self-efficacy, excellence and facilitate enhanced vitality within the teaching profession.

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Hlam, Thandiwe Lillian. "A teacher collective as a professional development approach to promote foundation phase mathematics teaching." Thesis, Nelson Mandela Metropolitan University, 2017. http://hdl.handle.net/10948/15071.

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This qualitative study is a response to a request for help from a group of Grade 3 (year 3) teachers who were disheartened with the poor performance of their learners in Mathematics. In an attempt to address their challenge, they resolved to form a Teacher Collective (TC) amongst themselves. Their main objective was to support each other in their development of Mathematical Knowledge for Teaching (MKT). The participants, being frustrated by what they perceived as an inefficient and unhelpful cluster approach to professional development used by the Department of Basic Education initiated their own teacher collective strategy. I was approached by this TC to assist them in developing a strategy to make this TC suit the needs of the participants. A Lesson Study (LS) approach was used as an alternative Teacher Professional Development strategy within the TC. In studies conducted by Ono and Ferreira (2010) and Jita and Mokhele (2014), a LS approach is regarded as an essential tool desirable for enhancement of teacher collaboration and participant’s MKT. However, both studies reported on challenges related to contextual issues. Those contextual issues revealed themselves as similar to the challenges that threatened to weaken the collaborative structure initiated by the participants in this current study. To overcome these challenges, participants felt a need for some sort of adaptation for a LS approach to work in their context. In the application of the revised adapted version of a LS approach, participants experienced a Teacher Collective (TC) in action using real and useful experiences (Ono & Ferreira, 2010). The aim of this study was to examine the effects of a Teacher Collective for improving participating teachers’ pedagogical and disciplinary content knowledge in Foundation Phase (FP) Mathematics. As this study targeted a small group of teachers, it adopted a case-study methodology. The participants were five Grade 3 teachers purposefully self-selected from two Port Elizabeth township schools. Semi-structured interviews were used to determine participating teachers’ perceptions of a Teacher Collective as a Teacher Professional Development strategy necessary to promote Mathematical Knowledge for Teaching. Descriptive methodologies which concern inter alia practices that prevail, relationships that exists, point of views that were held, processes that are going on and effects that are felt by participants were used (Creswell, 2013). The following major findings emerged from the data analysis: For the TC to be a successful alternative TPD, it requires that: (1) Teachers must regard themselves as being responsible for the own professional growth and own the TPD programme. (2) Participants of the TC must adopt flexible strategies to allow for active participation of the participants in building meaning for themselves. (4) A TPD strategy should be sensitive to contextual issues and be addressed accordingly. (5) A TPD programme should seek to improve classroom instruction but this must be based on the needs of the participants. It is primarily the following structural features that affected teacher learning within the TC: (a) the form of the activity (joint lesson planning, observed lesson presentation, post lesson feedback, etc.), (b) collective participation of teachers within and across the schools and (c) the duration of the activity. In this study the LS approach worked well as it sought to address the needs of the participants.

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Wood, Leigh Norma. "Graduate voices the nexus between learning and work /." Phd thesis, Australia : Macquarie University, 2007. http://hdl.handle.net/1959.14/47704.

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"2006"
Thesis (PhD)--Macquarie University, Australian Centre for Educational Studies, Institute of Higher Education Research and Development, 2007.
Bibliography: p. 167-173.
Introduction -- Experience and expression -- Becoming a professional -- Study design -- Graduates' experiences: a narrative -- Reflections on communication -- Examples of texts -- Reflections on learning and teaching -- Reflections and implications.
The aim of this study is to inform curriculum change in the mathematical sciences at university level. This study examines the transition to professional work after gaining a degree in the mathematical sciences. Communication is used as the basis for the analysis of the transition because of the importance of language choices in work situations. These experiences form part of the capabilities that become part of a person's potential to work as a professional. I found a subtle form of power and, of the opposite, lack of power due to communication skills. It is not as obvious as in, say, politics but it is just as critical to graduates and to the mathematical sciences. -- There were 18 participants in the study who were graduates within five years of graduation with majors in the mathematical sciences. In-depth interviews were analysed using phenomenography and examples of text from the workplace were analysed using discourse analysis. Descriptions of the process of gaining employment and the use of mathematical discourse have been reported in the thesis using narrative style with extensive quotes from the participants. -- The research shows that graduates had three qualitatively different conceptions of mathematical discourse when communicating with a non-mathematical audience: jargon, concepts/thinking and strength. All participants modified their use of technical terms when communicating with non-mathematicians. Those who held the jargon conception tried to simplify the language in order to explain the mathematics to their audience. Those who held the concepts/thinking conception believed that the way of thinking or the ideas were too difficult to communicate and instead their intention with mathematical discourse was to inspire or sell their ability to work with the mathematics. The strength conception considers the ethical responsibility to communicate the consequences of mathematical decisions. Not one of the participants believed that they had been taught communication skills as part of their degree. -- Participants gained a 'mathematical identity' from their studies and acquiring a degree gave them confidence and a range of problem-solving skills. Recommendations are made about changes in university curriculum to ensure that graduates are empowered to make a high-quality transition to the workplace and be in a position to use their mathematical skills. Mathematical skills are necessary but not sufficient for a successful transition to the workplace. Without the ability to communicate, graduates are unable to release the strength of their knowledge.
Mode of access: World Wide Web.
xi, 195 p. ill

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14

Addam, Billey Bright Kwadwo. "Integrating information and communications technology (ICT) into teaching and learning: the case of mathematics, science and technology education in one higher education institution." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/d1019736.

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This study explores the integration of Information and Communication Technologies (ICT) into teaching and learning within one Higher Education institution. The main question driving the study was: How is ICT integrated in the teaching and learning of mathematics, science and technology education (MSTE) in a Bachelor of Education programme? This is a case study of lecturers and students in Mathematics, Science and Technology Education. It makes use of questionnaires, interviews, field notes and document analyses to collect data. MSTE lecturers and students were assumed to be well versed in ICT usage and, therefore, well placed to assess its integration into teaching and learning. There were five main findings: First, that Mathematics, Science and Technology Education lecturers showed some ambivalence in their ontological and epistemological orientation to using ICT. Some leaned towards the instruction paradigm and used ICT as a tool for the transmission of knowledge; others leaned towards the learning paradigm, showing an awareness of the need to elicit discovery through ICT. Secondly, that lecturers’ understanding of ICT integration was oriented towards teaching and learning from technologies rather than with technologies. Thirdly, that processes of ‘pedagogical evolution’ were taking place, in terms of which there was a gradual but perceptible shift in the teaching and learning practice of both students and lecturers. Fourthly, there was no evidence to show that lecturers used ICT to promote innovative and creative teaching; in fact, students appeared to be more creative in using ICT resources, than lecturers. Fifthly, and finally, lecturers did not assign ICT-based tasks that promote conceptual understanding. They assigned tasks that asked students to extract and reproduce information from computers, without demonstrating understanding. When used in this way, ICT can, in fact, be de-skilling. From these findings, it can be concluded that ICT integration cannot be understood without exploring the ontological and epistemological orientations, as well as the theoretical orientations, at play in the teaching and learning situation. It is on the basis of these that people, that is, lecturers and students, make use of, ICTs to achieve desired goals. It is therefore recommended that, for the improvement of integration, there should be a greater emphasis on developing and sharing pedagogical expertise concerning ICT use in teaching and learning. It is recommended that a country-wide research survey should be undertaken, based on probability sampling and focussing on pedagogical issues in ICT integration in teaching and learning.

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Mulcahy, Diana Leonie. "A case study investigation of the use of a textbook in a secondary mathematics classroom : issues of regulation and control." Master's thesis, University of Cape Town, 1995. http://hdl.handle.net/11427/17500.

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Bibliography: pages 82-84.
This dissertation is concerned with aspects of the role of the textbook in school mathematics. An attempt is made to uncover control strategies used by the teacher in textbook use in the classroom, and those implicit in a mathematics textbook. It is argued that these forms of regulation place constraints on the transformative role sometimes attributed to textbooks. The following research question is addressed: how does the teacher recruit the textbook in the classroom, how is he/she 'recruited' by it and how are both recruited by school mathematics? A case study methodology is described, involving a video-recording of a fifty minute mathematics lesson and a follow-up interview with the teacher. Transcriptions are used and a fine-grained analysis of data is attempted. A literature survey examines other research in the areas of content selection, content control and content expression. Content selection refers to choices and omissions, content control refers to sequencing, pacing and authority in the pedagogic relationship, and content expression includes verbal and textual modes of expressing content. Theoretical ideas are drawn from Bernstein (1976, 1991, 1993) and Dowling (1993). Although these works are methodologically different, they both describe aspects of regulation and control. Of particular interest are Bernstein's notions of classification and framing, and Dowling's ideas on discourse and procedure. The hypothesis is put forward here that there is a dialectical relationship involving the positioning of teacher and textbook. The teacher recruits the textbook to regulate pupils and knowledge, but s/he is at the same time constrained by strategies implicit in the textbook. In other words the teacher both positions and is positioned by the textbook. Both in tum are positioned by school mathematics. The data analysis examines the 'how', 'what' and 'who' of control. It considers the regulation of speech, silence, working and listening, as well as the sequencing, pacing, selecting, presenting and authorising of content. It argues that the teacher both recruits and is 'recruited' by the textbook, and that although the framing is strong and the teacher has a high degree of control in the pedagogic relationship, the classification is also strong and the teacher lacks control over what she can teach and the relationship between contents. The research concludes by suggesting that the transformative role sometimes attributed to the textbook is problematic. The strategies of regulation and control operating in the classroom, implicit in the textbook and in school mathematics, limit the possibilities of how textbooks can be used by the teacher and constrain transformation to a significant degree.

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Mampane, Marungwane Batseba. "Exploring concept maps for meaningful teaching and learning of mathematics in grade 6." Thesis, University of Limpopo (Turfloop Campus), 2013. http://hdl.handle.net/10386/1123.

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Thesis ( M.ED. (Mathematics)) --University of Limpopo, 2013
This study used case study design to explore concept maps for meaningful teaching and learning of mathematics in Grade 6 class. The purpose of the study was to reflect on the usage of concept maps to promote meaningful teaching and learning of mathematics in Grade 6. Eighty seven (87) learners participated in the study. Data were collected through transcripts of learners’ work and interviews. Interviews were conducted to get more information on learners’ concept maps. Learners drew concept maps on three different sessions on different topics namely: fractions, measurement and angles. A list of concepts was supplied for each topic. 10 learners’ concept maps and 2 interview transcripts were analysed. Mark schedules were also used to check learners’ performance. Results showed that learners used varied number of links to connect concepts and that there was an increase in the number and quality of propositions made. Concept maps proved to be useful in enhancing meaningful teaching and learning of mathematics in Grade 6 class.

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Cherub, Fauzia. "An exploration of understandings and expectations around differentiation in mathematics, science and technology education." Thesis, Rhodes University, 2005. http://hdl.handle.net/10962/d1008179.

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The exploratory study presented in this thesis is a case study, interpretive in nature and located in the qualitative paradigm. The conceptual focus is on differentiation, recognizing that learners vary from one another and so will need educators to consider a wide range of factors to enable learners to learn. The objectives of the study are: • To identify what Whole School Evaluation (WSE) supervisors understand by the term differentiation (conceptual) • To identify how WSE supervisors expect differentiation to be achieved by educators (conceptual). [n order to contextualise this research, a further objective was considered necessary: • To identify the roles of WSE supervisors (contextual) This was set in the context of mathematics, science and technology education. The study was carried out with a group of ten WSE supervisors who were involved in evaluating Mathematics, Science and or Technology education in the GET (General Education and Training) Band. Analysis of questionnaires and documents led to the identification of supervisory roles, while analysis of semi-structured interviews revealed a range of dimensions related to differentiation understandings and expectations. These dimensions have been developed into a typology which is then drawn upon in the development of a new conceptual model of differentiation, particularly relevant to the South African context. Findings presented in the study represent an attempt to understand and make recommendations related to policy, practice, research, curriculum and learning support material (LSM) development, training and evaluation. Textual layering in the form of reflective footnotes and issue boxes. plus specific reflective sections in the main text e.g. limitations and assumptions, help the text to achieve this goal. While the study was focused on the context of mathematics, science and technology education, it became apparent that the findings could be applied across all the learning areas.

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Ngoepe, Mapula Gertrude. "Secondary mathematics teachers' classroom practices : a case study of three township schools in Gauteng Province, South Africa /." Curtin University of Technology, Science and Mathematics Education Centre, 2003. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=14369.

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While there have been enormous changes in the South African system of education since 1994, the legacy of apartheid and the different education of Black teachers is still evident in township schools. This study examined the practices of mathematics teaching in three township secondary schools by conducting a detailed investigation of eight teachers in three schools. Classroom observations and video recordings of teachers of Grades 10 to 12 served as the main data collection method. A sample of 12 lessons was analysed using the Secondary Teaching Analysis Matrix-Mathematics (STAM-Mathematics) (Gallagher & Parker, 1995) instrument. The researcher used STAM to categorise teachers' classroom practices along a three pronged continuum, namely didactic, transitional and conceptual teaching for the purpose of answering research questions about the content, the teaching, the assessment practices, the interactions between the teacher and the student, and the resource availability. Analysis of the data collected using the 22 STAM descriptors showed that the practices of teaching mathematics in township secondary schools was primarily didactic, with only minimal characteristics of transitional teaching and fewer attributes of conceptual teaching. Identifying the gaps between the teachers' practice and the descriptors for transitional and conceptual teaching with respect to the content, the teaching, the approaches to assessment, interactions between teacher and students, and resources availability has provided insight and a baseline for teacher inservice. Consequently, this study has provided research-based evidence for appropriate intervention to improve mathematics teaching and learning as prioritised by the Department of Education since the creation of the democratic government in 1994.
It is recommended that mathematics teachers in township schools use the STAM instrument in pairs or groups to observe and analyse each other's lessons with particular focus on the 22 descriptors and to use this framework as a guideline for daily lesson preparations and to help guide the teachers from teacher-centred instruction to conceptual instruction. Further, the STAM could be incorporated into teacher education and professional development programs and thereby lead to more conceptual forms of teaching that could contribute towards a greater understanding of mathematics and ultimately raise the pass rate of learners in external examinations at Grade 12.

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Coetzee, Johanna. "Reform-based approaches in the learning and teaching for conceptual understanding of calculus for diploma studies at south african university." Thesis, University of Fort Hare, 2017. http://hdl.handle.net/10353/4959.

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This research tested whether Reform-Based Approaches (RBAs) in the learning and teaching of calculus could lead to improved conceptual understanding. The study adopted positivistic paradigm, quantitative approach and pre- and post-test in a quasi-experimental design. The theoretical framework was Constructivism. The interventions were grounded on learner-centred RBAs including Interactive Engagement (IE), Peer Discussion (PD) and Good Questions (GQ). The experimental group comprised 119 volunteering students from a population of 461 registered for Mathematics as a service subject for the National Diploma (ND) in science or engineering at a South African university. Those not in the experimental group were taught through teacher-centred traditional approaches which have been the norm. However, only 71 out of those in the traditionally taught cohort volunteered to write both Pre- and Post-tests. As such, the total number of subjects in the study was 190, i.e., 119 from the Reform-Based cohort and 71 from the Traditional cohort. The instrument, the Calculus Concept Inventory for Technicians (CCIT), consisted of 19 questions on functions, differentiation and integration. Based on a pilot test, the instrument was improved. The Reform-Based cohort did not receive any participation reward and test scores did not contribute to promotion scores. The students wrote Pre-tests in the second week after commencement of lectures and Post-tests during the last week of lectures. The data were analysed using various statistical tools, tests and measures such as Chi-squares, Student t-tests, Pearson’s Product Moment correlation, Cronbach alpha, KR-20, the Difficulty Index, and Item Discrimination Point Biserial Index (PBI). The raw gain and normalised gains were also employed in data analyses. The main finding of this study was that RBA made a significant impact on the conceptual understanding of calculus of the experimental group. The gain achieved by the experimental group was in a low range and corresponded to the low use of IE (25% of contact time). A combination of RBA with Traditional teaching is recommended. Also, RBA will be most successfully introduced if supplemented and complemented through supportive environments.

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Santhanam, Elizabeth. "Investigation and innovation of teaching and learning genetics at the introductory level in the University of Adelaide /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phs2338.pdf.

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Mnqatu, Fiola Wayne. "Educators’ perceptions of foundation phase mathematics Curriculum Assessment Policy Statements (CAPS)." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/1358.

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The aim of the study was to investigate the educators’ perceptions of the Foundation Phase Mathematics Curriculum Assessment Policy Statements (CAPS). This was a case study of eight educators in two primary schools based in Cradock in the Eastern Cape Province of South Africa. There were six main findings. First, all participants displayed a good general knowledge of CAPS. They saw CAPS as different from NCS in that the former is content driven as opposed to outcomes driven in the latter. Second, all participants were happy that CAPS specifies what is to be taught grade by grade as opposed to NCS which specified outcomes and required educators to construct the content. Third, a feature which participants liked was the weighting of different components of the subjects taught. This was seen as an important guideline that indicates how much time should be spent on each component. Fourth, participants understood that CAPS is not a new curriculum; it is an amendment of the NCS. As such educators used the same teaching strategies and methods. Fifth, participants had reservations about the CAPS assessment guidelines as they were the same as those of the NCS and felt that the guidelines which require educators to discuss assessment criteria with children were not suitable for children in Foundation Phase. Sixth, participants were happy with the CAPS programme of assessment and workbooks .They felt the programme guides their teaching while the workbooks complement their teaching. It can be concluded that educators, on the whole, held positive perceptions about CAPS. They saw it as explicit about the content that is to be taught, and it has clear guidelines about assessment procedures. For this reason it can be seen as an improvement on the NCS. Given the findings, it can be recommended that further research be carried out on how educators’ understanding of CAPS is translated into practical teaching and learning in the classroom. To improve the delivery of CAPS, the Education Department must devise strategies aimed at educator empowerment activities that will enhance their work performance.

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Walton, Marguerite. "Mathematical requirements for first-year BCOM students at NMMU." Thesis, Nelson Mandela Metropolitan University, 2009. http://hdl.handle.net/10948/886.

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These studies have focused on identifying the mathematical requirements of first-year BCom students at Nelson Mandela Metropolitan University. The research methodology used in this quantitative study was to make use of interviewing, questionnaire investigation, and document analysis in the form of textbook, test and examination analysis. These methods provided data that fitted into a grounded theory approach. The study concluded by identifying the list of mathematical topics required for the first year of the core subjects in the BCom degree programme. In addition, the study found that learners who study Mathematics in the National Senior Certificate should be able to cope with the mathematical content included in their BCom degree programme, while learners studying Mathematical Literacy would probably need support in some of the areas of mathematics, especially algebra, in order to cope with the mathematical content included in their BCom degree programme. It makes a valuable contribution towards elucidating the mathematical requirements needed to improve the chances of successful BCom degree programme studies at South African universities. It also draws the contours for starting to design an efficient support course for future “at-risk” students who enter higher education studies.

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23

Lau, Ching-heung, and 劉清香. "A comparison of formative assessment practices in primary mathematics classroom in Guangzhou, Hong Kong and Melbourne." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2014. http://hdl.handle.net/10722/208791.

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This study compares formative assessment practices in primary mathematics classrooms in Guangzhou, Hong Kong and Melbourne. Nine schools (three in each research location) were studied to examine the similarities in and differences between formative assessment practices for mathematics, and to identity underlying factors that may account for these similarities and differences. Videotaped classroom observations and face-to-face semi-structured teacher interview were the main data collection methods employed. The study identifies several similarities and differences in formative assessment practices by reviewing a total of 1140minutes of videotaped classroom observations (380 minutes from each city). Four similarities were noted: (a)a common structure of formative assessment practice; (b) providing feedback on what students had done well and what they needed to improve; (c) encouraging students to engage actively in the feedback process; and, (d) infrequent use of practical assessments. In addition, six differences were found: (a) interpreting, judging and suggesting on students’ work; (b) forms of assessment (including self and peer assessment); (c) assessment items; (d) effective feedback;(e) specific format for presenting mathematics; and, (f) ways of receiving feedback. Three key factors have been suggested to account for the similarities in and differences between formative assessment practices in primary mathematics classrooms in the three research locations: (a) cultural influences on mathematics learning and examinations; (b) assessment reform initiatives; and, (c) teachers’ conceptions about formative assessment. This study contributes to the understanding of formative assessment practices in the classrooms by proposing a theoretical framework for comparing formative assessment practices that takes into account cultural, social, school and classroom factors. Potential directions for future research are suggested, including further comparisons of mathematics formative assessment practices at other schools in Guangzhou, Hong Kong and Melbourne, and in other countries with similar cultural backgrounds.
published_or_final_version
Education
Doctoral
Doctor of Philosophy

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Matsolo, Matjala Lydia. "Perceived experiences that grade seven learners have in learning algebra." Thesis, University of the Western Cape, 2006. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_9454_1181559574.

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This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.

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Deliwe, Mawonga Christopher Columbus. "Syllabus differentiation in mathematics in Ciskei : the reality as against intention." Thesis, Rhodes University, 1989. http://hdl.handle.net/10962/d1001436.

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The topic of this half-thesis was conceived after the author had noted with interest, that an alarmingly high number of pupils in the Mdantsane Central District of the Ciskei were registering for Higher Grade (HG) mathematics for their final (Standard 10) year. What mattered most was that the failure rate was abnormally high. As a teacher of the subject for 14 years as at the end of 1988, the author had seen very weak pupils passing through his hands who had nevertheless insisted on registering for the examination in HG mathematics. A look through the Human Sciences Research Council (HSRC) Report of 1971 which recommended the syllabus differentiation, revealed that the intention of the relevant HSRC Committee was to offer a subject at a level in accordance with a pupil's interest, aptitude and ability. In a survey undertaken by the author, samples of teachers, pupils and parents indeed confirmed the existence of a very high number of HG candidates, as suspected. The survey also revealed an aversion to the standard grade (SG) course by some pupils, teachers and even principals. A desire for university education was shown to be in the minds of most pupil respondents. Well sourced registration statistics clearly showed that the Department of Education and Training (DET) in the Republic of South Africa and the Department of Education in the Ciskei had by far the greatest proportion of pupils on the HG in mathematics in comparison with the other race groups.Standard 10 (Std 10) results for two years taken separately confirmed the author's suspicion that aptitude and/or ability were not taken into consideration by most pupils, in the choice of grade. The results were not good at all. In most cases the uninformed pupil was acting alone in taking the important decision, perhaps with only peer group pressure to contend with. Three independent opinions suggested that there was probably a general feeling that Black education was already inferior, even without the syllabus differentiation hence the reluctance to register for the SG option. Furthermore, the investigation indicated that there was no adequate provision for technical education for Blacks in either the RSA or Ciskei which would provide the alternative to a university career for a pupiL Amongst other things, a mild form of pupil screening and a well structured careers guidance programme are suggested in the concluding chapters

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Van, Jaarsveld Pieter Paul. "Hermeneutic and empirical analyses of graphically inspired metamathematics that reflect critical consciousness within perspectives of personal and social justice." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1004376.

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My involvement with mathematics education amongst township educators and learners over the past seven years has highlighted the absence of sustained meaning and meaning making of mathematical concepts. It appears though that this instrumental rather than relational understanding of FET mathematics is not unique to township learners but is encountered amongst learners of all socio-economic classes and is representative of many FET mathematics learners. Given that the language of learning and teaching is a major contributory factor in the South African education system, it appears that the language of mathematics itself is a greater exacerbating factor for many learners of mathematics. The exclusive algorithmic approach to classroom mathematics further seems to alienate many learners from the essence of the meaning of mathematical tasks. This research undertakes to determine whether metateaching and metalearning as forerunners to metacognition facilitates the acquisition of the sustained meaning of mathematical concepts. Metateaching and metalearning refer to the acute and deliberate awareness by educator and learner as to what constitutes concepts. Teaching and learning therefore presupposes the deconstruction of concepts into its subsumed derivative roots. It also assumes an awareness of the tacit degrees of abstraction that characterise tasks and the content of tasks. This in turn has implications for the educator's adopted sequence of topics for instruction. Metacognition implies awareness on the part of the learner (and educator) as to how material is learned and a further awareness as to how that learning can be sustained. Whether we ascribe meaningful learning to radical or social constructivism, or to associationist didactive approaches, or a combination of these, we are making assumptions about how learners acquire and sustain mathematical meaning because mathematics is, by and large a symbolic language often devoid of affective connotation. Furthermore our assessments of learners' tasks amount to clinical corrections of austere formulae wrapped in algorithmic procedures which manifest nothing of a learner's experience of mathematics or the deeper understanding (or misunderstandings) which characterise a learning and/or assessment episode. To this end the research design of this interpretive case study requires learners to expound in textual accounts their thoughts as they describe the evolution of a mathematical process as they approach a solution and eventually interpret it. The textual account exposes the concept definition for what it really is in a learner's understanding of it and it is the expressiveness of language that indicates whether the understanding of a learner is approaching the concept image. The textual accounts vary in richness in terms of mathematical register and this in turn reflects the conceptual depth. The mechanism which seems to promote the conversion from concept definition to concept image is the graphical representation of the mathematical task or procedure, possibly because of its greater concreteness as opposed to the abstraction of its algebraic form.

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Mbelani, Xoliswa Lydia. "An investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms : a case study." Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1017351.

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This research report focuses on an investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms in the Grahamstown region, South Africa. Boredom seems to be strongly evident in our classrooms. Quantitative data was derived from an initial survey questionnaire while semi-structured interviews were used to elicit qualitative data. The data from the survey was analysed quantitatively using descriptive statistics. The quantitative data was categorised according to the structure of the survey. The data was represented in bar graphs and then discussed accordingly. In the final narrative I infused extracts from the interviews with my quantitative analysis. The qualitative data was analysed and coded according to different categories and themes that emerged through repeated engagement with the interview transcripts. The findings revealed that boredom is a common problem in the 8 Grade 10 Mathematics schools in the Grahamstown region and this finding answered my first research question. To answer my second research question, the results showed that learners were bored due to many factors, such as; lack of understanding, repetition and the teacher’s actions and many more. My findings align with what is highlighted by Nett, Goetz, & Hall. (2011) that many learners from particularly the senior secondary schools frequently report episodes of boredom. The study recommends that teachers make their teaching more interesting, much use of concrete teaching materials and make mathematics tasks to be relevant and real.

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Brown, Roger George, and rogergbrown@mac com. "The impact of the introduction of the graphics calculator on system wide 'high stakes' end of secondary school mathematics examinations." Swinburne University of Technology, 2005. http://adt.lib.swin.edu.au./public/adt-VSWT20051117.121210.

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There has been widespread interest in the potential impact of the graphics calculator on system wide 'high stakes' end of secondary school mathematics examinations. This thesis has focused on one aspect, the way in which examiners have gone about writing examination questions in a graphics calculator assumed environment. Two aspects of this issue have been investigated. The first concerns the types of questions that can be asked in a graphics calculator assumed environment and their frequency of use. The second addresses the level of skills assessed and whether with the introduction of the graphics calculator has been associated with an increase in difficulty as has been frequently suggested. A descriptive case study methodology was used with three examination boards, the Danish Ministry of Education, Victorian Curriculum and Assessment Authority and the International Baccalaureate Organization. Four distinct categories of questions were identified which differed according to the potential for the graphics calculator to contribute to the solution of the question and the freedom the student was then given to make use of this potential. While all examination boards made use of the full range of questions, the tendency was to under use questions in which required the use of the calculator for their solution. In respect to the level of skills assessed, it was found that both prior to and after the introduction of the graphics calculator, all three examination boards used question types that primarily tested the use of lower level mathematical skills. With exceptions, where graphics calculator active questions have been used, the tendency has been to continue to ask routine mechanistic questions. In this regard, there is no evidence of the introduction of the graphics calculator being associated with either lowering or raising of the level of the mathematical skills assessed. For all cases studied, the graphics calculator was introduced with minimal change to the curriculum and examination policies. The role of the graphics calculator in the enacted curriculum was left implicit. The resulting examinations were consistent with the stated policies. However, the inexperience of some examiners and a general policy of containment or minimal change enabled examiners to minimise the impact of the introduction of the graphics calculators on assessment.

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Van, Hille Gilles Ernst Willem. "A preliminary investigation into the use of computers in the teaching of mathematics." Thesis, Rhodes University, 1986. http://hdl.handle.net/10962/d1004382.

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Like many South African high school mathematics teachers I have followed the development of computers with interest and I have tried wherever possible to gain some experience on them. Thus when microcomputers became more readily available the mathematics department at our school, Graeme College in Grahamstown, motivated for the school to acquire this powerful new tool. The eventual outcome was that the Old Boys' Association donated to the school 3 BBC B microcomputers with monitors, a disc drive, a printer and two tape recorders. These have now been in the school for three years. The acquisition prompted this research project which takes the following form:- 1) An investigation into some of the uses of microcomputers in schools and, in particular, in the mathematics classroom. 2) A statement on the present position adopted by the Cape Education Department on the use of computers in schools. 3) A study of what the experience has been in other countries, particularly in Britain and the United States of America. 4) A description of an investigation which was undertaken at our school using the method of Action Research and Triangulation. Its aim was to investigate the feasibility of using a microcomputer to aid in the teaching of mathematics and the reaction of the pupils to this innovation. Three different approaches were implemented. a) The algorithmic approach: In this investigation a class of standard eight pupils were required, with the help of the teacher, to write, enter and test a short computer program which would solve any pair of simultaneous linear equations of the form, ax + by = c. Their reaction to this form of instruction was noted by myself and a non-participant observer. The pupils themselves were also asked to express their reactions, both verbally and by filling in a prepared questionnaire. Examples of worksheets, exam questions and analysed questionnaires are given in the appendix. Short programs which examine various other mathematical concepts are also listed and discussed. b) The audio-visual approach: In this case use was made of a graphs software package in which the computer would draw either a straight line, circle, parabola or hyperbola when the appropriate variables were entered. This package also includes a graph game facility where participants are required to find the equation of the graph which will pass through three given points. Points are awarded if the correct type of graph is chosen and the variables are entered within a certain time interval. The pupils involved in this investigation were standard eight higher grade mathematics pupils and their reaction to this form of instruction was again noted using the methods described in (a) above. c) Computer Aided Instruction: Here I was most fortunate to be able to make use of the Rhodes University PLATO Centre. This allowed me to take a class of eighteen standard eight higher grade mathematics pupils to the Centre. Here during four sessions, each of just over an hour, the pupils interacted with the software on the computer terminal. The software used was a set of five lessons written by Barbara Lederman of the Community College Maths Group, of the University of Illinois in 1976. The lessons give instruction and require the pupils to transform, plot and draw the graphs of linear equations of the form, ax + by + c = 0, x = c and y = b. They are also taught and required to find the equations of given straight lines. Their reactions to this form of instruction are discussed after each session. 5) In conclusion some thoughts are given on how computers can best be utilised in the school situation, with particular reference to the teaching of mathematics.

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Stewart, Joyce. "Investigating relationships between mathematics teachers' content knowledge, their pedagogical knowledge and their learnes' achievement in terms of functions and graphs." Thesis, Nelson Mandela Metropolitan University, 2009. http://hdl.handle.net/10948/1100.

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This study used diagnostic tests, questionnaires and interviews to investigate explore teachers’ subject content knowledge (SCK) and pedagogical subject knowledge (PCK). It also explored teachers’ and learners’ misconceptions within the topic of graphicacy and how teachers’ SCK and PCK possibly affect learner achievement. A small sample of teachers were drawn from the Keiskammahoek region; a deep rural area of the Eastern Cape. These teachers were part of the Nelson Mandela Metropolitan University (NMMU) Amathole Cluster Schools Project who were registered for a three-year BEd (FET) in-service programme in mathematics education. As part of the programme they studied mathematics 1 and 2 at university level and received quarterly non-formal workshops on teaching mathematics at FET level. The findings of this study suggest that teachers with insufficient SCK will probably have limited PCK, although the two are not entirely dependent on each other. In cases where teachers’ displayed low levels of SCK and PCK, their learners were more likely to perform poorly and their results often indicated similar misconceptions as displayed by their teachers. This implies that we have to look at what teachers know and what they need to know in terms of SCK and PCK if we are to plan effectively for effective teacher development aimed at improving learner performance.

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Hyde, Janet Catherine. "An investigation into the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips through the medium of cell phones in the teaching of mathematics in selected South African Grade 9 classes: a case study." Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1003500.

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This qualitative study examines the use of Visual Technology for the Autonomous Learning of mathematics (VITALmaths) video clips in three Grade 9 classrooms in the Eastern Cape, South Africa, two of which are in well-resourced ex-Model C schools and one in a semi-rural township school. The rapid development of mobile technology, especially in Africa, has opened up previously unexplored avenues in economy, communication and education (Aker & Mbiti, 2010), with a number of mobile learning initiatives being launched in South Africa (Botha & Ford, 2007; Vosloo & Botha, 2009). The VITALmaths project was developed collaboratively between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa (Linneweber-Lammerskitten, Schäfer and Samson, 2010). As the main platform for dissemination of the video clips is the cell phone, the study looked at the various aspects involved in the use of cell phones by learners in the classroom, as well as the incorporation of the clips into the teaching of three teachers. Consideration was given to whether or not the clips assisted the teachers in teaching, as well as whether or not they encouraged further exploration. The study was divided into six stages during which data was collected and analysed using an interpretive approach throughout. Data collection methods included semistructured interviews, questionnaires, observation, journals and reflective essays. The study revealed the participating teachers, having incorporated the clips into several lessons, found that these had a meaningful effect on their teaching practice, as well as on the engagement of the learners in the lessons. The majority of the learners involved in the study had access to cell phones, either their own or borrowed, and were able to download the video clips onto their phones from the website (www.ru.ac.za/vitalmaths). A number of learners found that the clips helped them find examples of specific mathematical concepts outside of the classroom, thus leading to further enquiry and exploration, while several learners downloaded and viewed additional clips. Overall findings showed that the VITALmaths video clips could be incorporated into teaching with relative ease.

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Sebela, Mokgoko Petrus. "The use of investigative methods in teaching and learning primary mathematics in Lebowa schools : a case study." Thesis, Rhodes University, 1999. http://hdl.handle.net/10962/d1003700.

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This is a report on research conducted in Lebowa (Northern Province) Primary Mathematics Project schools. In view of the high failure rate of matric students, the researcher believes that it is necessary that ways should be devised to improve mathematics understanding from the first level of schooling. A research study was made of constructivist and investigative teaching and learning methods as employed by teachers in a number of primary schools in the area. The researcher believes that investigative and constructivist teaching approaches produce better results than the traditional approach. He further believes that children learn better in a co-operative non-threatening classroom environment. A pilot study was made with two experimental schools and two control schools. The schools were selected from both urban and rural areas. The experimental schools are operating under the PMP and the control schools are not. The experimental schools are also supported by expert teachers called key teachers. Many of these key teachers have attended courses at Leeds University, while others have been trained locally in the theory and practice of constructivist and investigative teaching and learning. Chapter 3 illustrates clearly what is done in the Project schools. The methodology employed in the research included qUestionnaire responses from 174 teachers. Written tests by four schools (350 pupils), and interviews with 55 people, including directors of education, inspectors, principals, teachers and parents. Observations in classes were also done. Another questionnaire was given to 484 pupils. The tests were mitten on two occasions: an initial test was written during November 1993, the second year of the PMP project, while a second test was written the following year. Data collected was analysed and positive results obtained. The results from the tests indicated that pupils in experimental schools where constructivist and investigative approaches are used, perform better than those from schools where the traditional approach is still used. They indicated that children in PMP schools develop a better understanding of mathematics. This would seem to indicate that the constructivist and investigative approach to teaching produces better results than the traditional approaches. The reader will find graphs indicating the results and their analysis in Chapters 4 and 5. It is recommended by the researcher that: - Constructivist and investigative teaching and learning methods be introduced to all schools. - The services of key teachers be supported by the Department - The Department should equip all schools with the necessary materials for proper teaching and learning, or provide materials for schools to make their own teaching aids. - Teachers be involved with materials production where they are given guidance on how teaching aids can be made. - The curriculum for primary school mathematics be revised and changed, especially in view of the fact that at present it does not cater for local needs. It was planned by whites and it caters mainly for those with an European cultural background.

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Elgie, Brian James. "Computer-based remediation in Cape Senior Certificate standard grade mathematics." Thesis, Rhodes University, 1991. http://hdl.handle.net/10962/d1003339.

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This dissertation begins by reviewing the difficulties experienced in teaching mathematics to pupiis, weak in mathematics, in the Senior Secondary phase of Cape Education Department schools. The possible use of computer-aided instruction (CAl) in improving the examination performance of such pupils is considered. A suitable CAl software program, viz. the SERGO system, is identified and its operation is described in detail. The researcher investigates, both from a quantitative and a qualitative aspect, the change in mathematics examination performance of a number of weak in mathematics pupils, as a result of receiving an extended period of extra tuition on the SERGO system. It needs to be noted that these pupils are passing candidates in other subjects, and have above average intelligence. They are not slow learners. The researcher identifies three categories of pupils who are weak in mathematics. Different programmes of remediation are recommended for each category. The possible use of the SERGO system as a stand-alone instrument of remediation , for pupils working in pairs, and the possible use by H.G. pupils in combined H.G./S.G. classes are also investigated.

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Knoetze, Susanna. "An investigation into the mathematics teaching practices of non-isiXhosa-speaking teachers teaching isiXhosa-speaking 3rd Graders through the medium of Afrikaans." Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1018910.

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There is a considerable body of literature on the challenges faced by learners who speak an African language at home but who are taught through the medium of English. Less research has focused, however, on contexts where isiXhosa-speaking learners have Afrikaans as their Language of Learning and Teaching (LoLT), especially in Foundation Phase classrooms where teachers may not speak their learners’ home language. Such learners face the triple challenge of simultaneously learning a second language, learning to read in that language, and also learning new content and concepts through it. Using a multiple case study design, this investigation explores the mathematics teaching practices of Afrikaans-speaking Grade 3 teachers teaching isiXhosa-speaking learners through the medium of Afrikaans. Separate contextual profiles of the teaching practices of the participating teachers at the three schools are presented. Data were derived from school, classroom, and lesson observations (at least five complete mathematics lessons of each teacher), plus interviews with the teachers and with their school principals. By drawing on Vygotskian sociocultural theory and the interactive model of second language acquisition, this study highlighted the teaching practices of the three teachers as they mediated their learners’ mathematical conceptual development. An inductive data analysis approach was used to isolate recurring themes and patterns. Four main themes were identified: structuring of teaching and learning, facilitating of interaction, language use and implementation of mediating strategies. Analysis of the data shows that all three teachers’ language use displayed high levels of modified input, and high levels of context-embedded support. The levels of scaffolded learner talk were, however, found to be much lower than the levels of teacher talk, especially as far as academic registers were concerned. The teachers’ mediation strategies also displayed high levels of teacher-directed input which, on the whole, did not provide optimal opportunities for learners to develop independent levels of academic discourse. The study highlights the need for further research to inform teacher education and development with regard to more effective support structures to assist teachers with the sorts of challenges outlined above.

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Mostert, Ingrid Elizabeth. "Research for the learning and teaching of mathematics : an emergent design /." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/687.

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36

Alummoottil, Joseph Michael. "The spiral curriculum, integrated teaching and structured learning of mathematics at the secondary level." Thesis, Rhodes University, 1990. http://hdl.handle.net/10962/d1003654.

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The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.

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Stott, Deborah Ann. "Learners' numeracy progression and the role of mediation in the context of two after school mathematics clubs." Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1017181.

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National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.

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Austin, Pamela Winifred. "The family maths programme: facilitators' ability to implement inquiry-based teaching and learning with learners and parents." Thesis, Nelson Mandela Metropolitan University, 2007. http://hdl.handle.net/10948/471.

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Despite the fact that the facilitation of inquiry learning is a core methodology in the General Education and Training (GET) band of the South African National Curriculum Statement, rote learning and memorization of algorithms remains common practice in many mathematics classrooms. The inquiry-based Family Maths professional development programme, offered by the Nelson Mandela Metropolitan University, attempts not only to support the transformative education practices targeted by the South African National Department of Education, but also to extend them beyond the school walls to the community at large. This study investigates the extent to which the Family Maths professional development programme develops facilitators’ ability to implement inquiry-based learning. It also seeks to explore which aspects of the programme are effective in developing an inquiry-based approach. The research undertaken is an empirical study of 39 facilitators and uses both qualitative and quantitative methods. The facilitators’ inquiry beliefs and ability to implement inquiry learning was measured by means of questionnaires, observation schedules and interviews. As the ‘teacher as facilitator of inquiry-based teaching and learning’ is a requirement of all South African teachers, the findings of this research should make a meaningful contribution to the field of mathematics teacher education in the South African context.

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Raghavan, Prasannakumary. "Social constructivist mathematics education in a Ciskeian secondary school classroom." Thesis, Rhodes University, 1994. http://hdl.handle.net/10962/d1003652.

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The researcher's experience as a high school mathematics teacher in several African countries convinced her that a good number of mathematics learners exhibit serious difficulties in conceptualising mathematics properly. Her experience in teaching the subject in the Ciskei since 1990 reinforced this conviction. The researcher's natural curiosity to probe into the causes of the poor state of mathematics education in the region served as the springboard into her investigation. Her thoughts developed in line with the emerging educational theories of social constructivism. This provided a conceptual framework for the solution of the problem, the feasibility of which was put to test practically in a Ciskeian classroom. She explicates that the difficulties experienced by the pupils in conceptualising mathematics are philosophically deep rooted and latent in the present system of mathematics education itself, which, in Ciskei, impedes the learners' conceptualisation owing to numerous problems related to their linguistic and cultural situatedness. In the analysis of the present system of mathematics education in the Ciskei she reviews a few recently published mathematics text books in the context of the topics chosen for her research study. The results of her classroom investigation establish that a possible solution to the problem lies in the social constructivist teaching approaches.

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Siyepu, Sibawu Witness. "The use of Van Hiele's theory to explore problems encountered in circle geometry: a grade 11 case study." Thesis, Rhodes University, 2005. http://hdl.handle.net/10962/d1004777.

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The research presented in this thesis is a case study located in the interpretive paradigm of qualitative research. The focus is on the use of van Hiele's theory to explore problems encountered in circle geometry by grade 11 learners and making some policy recommendations concerning the curriculum structure and teaching of the geometry at all grades. The interpretation is based to the learners' background in geometry i.e. their prior knowledge and experience of learning geometry. The study was carried out over a period of three years. The data collection process took a period of two months (April and May 2003) with a group of 21 grade 11 mathematics learners in a rural senior secondary school in the Eastern Cape. The researcher used document analysis, worksheets, participants' observation, van Hiele tests, a questionnaire and semi-structured interviews to collect data. The study showed that the structure of the South African geometry syllabus consists of a some what disorganized mixture of concepts. It is not sequential and hierarchical and it sequences concepts in a seemingly unrelated manner. The study revealed that the South African high school geometry curriculum is presented at a higher van Hiele level than what the learners can attain. The findings of the study showed that many of the grade 11 learners were under-prepared for the study of more sophisticated geometry concepts and proofs. Three categories of reasons could be ascribed to this: Firstly, there was insufficient preparation of learners during the primary and senior phases. Secondly the study indicated that there is overload of geometry at the high school level in the South African mathematics curriculum. Thirdly, the over-reliance on the traditional approach to teaching geometry, poor presentation of mathematical technical concepts and language problems, were identified as possible additional reasons for the poor learner understanding of geometry in general and circle geometry in particular. The study recommends that the structure of the South African geometry curriculum should be revisited and redesigned. Teachers should be empowered and developed to be more effective in teaching geometry through further studies in mathematics and in-service workshops. They should also be engaged in the process of implementing the van Hiele's theory in the teaching of geometry in their classrooms.

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Ngudle, N. G. "Learner perceptions on feedback received on performance tasks in mathematics in selected schools from the East London district in the Eastern Cape." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/d1016499.

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Feedback has an important role to play in the performance of learners. This study looks to identify the challenges that the learners are faced with when the teachers provide them with feedback and the ways they would like like it to be used in order to see feedback assisting them in their learning and improve their performance. Feedback contributes a lot to assessment and has a close link with performance. The study used the qualitative approach to identify the challenges the learners experience when they receive the feedback from their teachers. The participants were sampled from grade 12 learners in the form of a focus group (seven to ten per school) and individual respondents. The method used semi-structured interviews and portfolio observations to collect the data from two high schools in East London (EL) district to look at the nature of the feedback provided to learners. The data was later analysed and interpreted. It has been identified that for both schools feedback conveyed certain messages to learners such motivation to do better, a need to do better and, lastly, affirmation that the learners are on the right track or they are neglected and left to figure out how to do the tasks. The study discovered that, according to Hattie and Timperley (2007)’ there are four levels of feedback. It was found that for the task level learners from school A mainly received oral feedback which was often seen as denigrating them; however, in school B learners received both the oral and written feedback. They felt that the feedback assisted them to understand the task at hand. They also saw this as a way of building up their confidence in all the tasks they come across. Secondly, in the process level, learners in school A did not report receiving feedback at this level but only oral feedback which does not show their mistakes step by step in the task, yet in school B they reported that they got feedback from their teacher individually to help them understand the task. Thirdly, for the self regulation level, in school A there was no data to confirm this. Regarding school B, learners were being assisted by the feedback they received from their teacher and this caused them to monitor their progress. The fourth and last level is the self or personal evaluation where in school A learners were not able to evaluate themselves because they did not receive written feedback, whereas in school B learners could do that freely referring to the written comments from their teacher. The research therefore concluded that in one of the schools the four levels that the study was looking at were not all addressed and thus no meaningful feedback was given. For school B the teacher gave them the feedback which has contributed a lot in their learning. The study recommends that feedback should not be used for right or wrong answers but it must also state clearly why the learner has obtained such mark or grade and what to do to correct the wrongs. Teachers should consider that learner errors also assist them to have a broader picture on what more they need to do in their subjects. It is also recommended that teachers should consider various strategies in giving feedback and the learners’ work has to be monitored timeously for the purpose of the learning process. Lastly, a good approach when feedback is provided is also important because it builds high self-esteem and develops the teacher-learner approach accordingly.

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Mofu, Zanele Abegail. "An investigation of a mathematics recovery programme for multiplicative reasoning to a group of learners in the South African context : a case study approach." Thesis, Rhodes University, 2014. http://hdl.handle.net/10962/d1013333.

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This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.

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Kaulinge, Penehafo Olivia. "Examining the nature of learning within an afterschool mathematics club : a case study of four learners." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1001835.

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This study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. The study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. The study made use of a variety of data collection techniques, including one-to-one assessment interviews, task-based interviews and observations. In line with the case study approach adopted, four learners were selected for interviews. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. Even though they were found to have advanced in their Strategies for Early Arithmetic Learning (SEAL), some of them were observed still using their fingers to support their counting. Such strategies were likely to mirror the teaching approaches used in their usual school mathematical lessons. The overall findings in terms of learners’ proficiency and progress give rise to concerns about current number teaching practices in their school, which emphasize the standard written algorithm in the lower primary grades. The study also made use of Vygotsky’s notion of the ZPD to analyse the nature of mentor-peer mediation. Witnessing the learners’ use of trial and error strategies during the task-based interview allowed both mentors to support learners through understanding their thinking, prompting them and encouraging them to reflect on their answers and develop more effective strategies. Learners progressed through the ZPD at different paces and in different ways, with ‘aha’ moments happening at different points for individual learners. Their progression in the ZPD seemed to depend on interaction among all participants, which varied according to what was contributed and what requested by each participant. The findings revealed that although there was evidence of learners achieving success at the tasks in task based interviews there were also there were also some learners who experienced difficulties. Additionally, in order to argue that learning was fully realised within the ZPD would have required follow up task based interviews to assess the extent to which learners were able to complete the tasks independently without the scaffolding of mentors. This was not possible within the scope of this research but would be useful in future research.

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Marsh, Terence Anthony. "The computer in secondary school mathematics : an analysis and classification of possible modes of application, with suggested implications for the mathematics curriculum in South Africa." Thesis, Rhodes University, 1991. http://hdl.handle.net/10962/d1003340.

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There is a variety of possible ways in which computers can be used to enhance mathematics education. This thesis attempts to identify, analyse and classify these possibilities, particularly at the secondary school level. It describes and exemplifies applications ranging from drill-and-practice through games and simulations to problem solving by computer programming. Software evaluation procedures are considered in some depth. Illuminative evaluations of various items of software and there classroom use are reported. The underlying methodology is small-scale action research. Insights gained during the process of investigating each class of software lead to the eventual formulation of a scheme for classifying mathematics education software by means of 'multidimensional attributes'. It is contended that this scheme will help mathematics teachers to make well informed and sound professional judgements regarding the evaluation and use of computer programs for teaching/learning purposes. Also, it is hoped that this scheme and the thesis as a whole will contribute towards the establishment of well founded standards and procedures for software development in the field of mathematics education. Several implications of the computer for the mathematics curriculum in South Africa are suggested. A note of caution is sounded regarding possible detrimental effects of the computer and several questions requiring further research are posed. A recommendation arising from the thesis is that in-service training courses concerning computer applications in mathematics education should be run for secondary school teachers.

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Truran, John Maxwell. "The Teaching and Learning of Probability, with Special Reference to South Australian Schools from 1959-1994." 2001. http://hdl.handle.net/2440/37837.

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The teaching of probability in schools provides a good opportunity for examining how a new topic is integrated into a school curriculum. Furthermore, because probabilistic thinking is quite different from the deterministic thinking traditionally found in mathematics classrooms, such an examination is particularly able to highlight significant forces operating within educational practice. After six chapters which describe relevant aspects of the philosophical, cultural, and intellectual environment within which probability has been taught, a 'Broad-Spectrum Ecological Model' is developed to examine the forces which operate on a school system. The Model sees school systems and their various participants as operating according to general ecological principles, where and interprets actions as responses to situations in ways which minimise energy expenditure and maximise chances of survival. The Model posits three principal forces-Physical, Social and Intellectual-as providing an adequate structure. The value of the Model as an interpretative framework is then assessed by examining three separate aspects of the teaching of probability. The first is a general survey of the history of the teaching of the topic from 1959 to 1994, paying particular attention to South Australia, but making some comparisons with other countries and other states of Australia. The second examines in detail attempts which have been made throughout the world to assess the understanding of probabilistic ideas. The third addresses the influence on classroom practice of research into the teaching and learning of probabilistic ideas. In all three situations the Model is shown to be a helpful way of interpreting the data, but to need some refinements. This involves the uniting of the Social and Physical forces, the division of the Intellectual force into Mathematics and Mathematics Education forces, and the addition of Pedagogical and Charismatic forces. A diagrammatic form of the Model is constructed which provides a way of indicating the relative strengths of these forces. The initial form is used throughout the thesis for interpreting the events described. The revised form is then defined and assessed, particularly against alternative explanations of the events described, and also used for drawing some comparisons with medical education. The Model appears to be effective in highlighting uneven forces and in predicting outcomes which are likely to arise from such asymmetries, and this potential predictive power is assessed for one small case study. All Models have limitations, but this one seems to explain far more than the other models used for mathematics curriculum development in Australia which have tended to see our practice as an imitation of that in other countries.
Thesis (Ph.D.)--Graduate School of Education and Department of Pure Mathematics, 2001.

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Truran, J. M. (John M. ). "The teaching and learning of probability, with special reference to South Australian schools from 1959-1994." 2001. http://web4.library.adelaide.edu.au/theses/09PH/09pht872.pdf.

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47

Pournara, Craig. "Mathematics-for-teaching in pre-service mathematics teacher education: the case of financial mathematics." Thesis, 2013. http://hdl.handle.net/10539/18836.

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Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Humanities, School of Education, 2013
Mathematics-for-teaching (MfT) is complex, multi-faceted and topic-specific. In this study, a Financial Mathematics course for pre-service secondary mathematics teachers provides a revelatory case for investigating MfT. The course was designed and taught by the author to a class of forty-two students at a university in South Africa. Eight students, forming a purposive sample, participated as members of two focus tutorial groups and took part in individual and group interviews. As an instance of insider research, the study makes use of a qualitative methodology that draws on a variety of data sources including lecture sessions and group tutorials, group and individual interviews, students’ journals, a test and a questionnaire. The thesis is structured in two parts. The first part explores revisiting of school mathematics with particular focus on compound interest and the related aspects of percentage change and exponential growth. Four cases are presented, in the form of analytic narrative vignettes which structure the analysis and provide insight into opportunities for learning MfT of compound interest. The evidence shows that opportunities may be provided to learn a range of aspects of MfT through revisiting school mathematics. The second part focuses on obstacles experienced by students in learning annuities, their time-related talk, as well as their use of mathematical resources such as timelines and spreadsheets. A range of obstacles are identified. Evidence shows that students use timelines in a range of non-standard ways but that this does not necessarily determine or reflect their success in solving annuities problems. Students’ use of spreadsheets reveals that spreadsheets are a powerful tool for working with annuities. A key finding with regard to teachers’ mathematical knowledge, and which cuts across both parts of the thesis, is the importance of being able to move between compressed and decompressed forms of mathematics. The study makes three key contributions. Firstly, a framework for MfT is proposed, building on existing frameworks in the literature. This framework is used as a conceptual tool to frame the study, and as an analytic tool to explore opportunities to learn MfT as well as the obstacles experienced by. A second contribution is the theoretical and empirical elaboration of the notion of revisiting. Thirdly, a range of theoretical constructs related to teaching and learning introductory financial mathematics are introduced. These include separate reference landscapes for the concepts of compound interest and annuities

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Molefe, Sarah Motlalepule. "The teaching of mathematics in the Kagiso area." Thesis, 2012. http://hdl.handle.net/10210/5988.

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M.Ed.
Our world is becoming more mathematical. We are constantly surrounded by mathematical situations and are regularly required to make mathematical decisions. These decisions require number sense, estimation skills, ability to analyse data intelligently, knowledge of two and three-dimensional geometry and many other abilities not often taught in school. Halpern (1992:1) states: "...as a nation we not only need competent scientists and engineers, we also need a citizenry that is literate in mathematics issues." Reyes and Stannic (1998:26) support this view as they state: "Knowledge of mathematics is essential for all members of our society. To participate in our democratic processes and to be unrestricted in career choice and advancement, people must be able to apply mathematical ideas." Learners leaving school need to be able to use available technology and to reason mathematically, be confident of their abilities, be able to communicate mathematically and be problem solvers. The introduction of technology into the lives of many people has called upon their background of mathematics to cope with mathematical problems and manipulating technological instruments. The relationship between mathematics and technology is emphasised by Dowling and Noss (1990:24) when they say: "New technology is a powerful tool which opens up new areas of mathematics and changes the way in which society makes use of mathematics in the factory, office and home". The Cockcroft Committee (1982), in their report on an inquiry into the teaching of Mathematics in schools, sees the main task of mathematics teachers as: "Enabling each learner to develop within his own capabilities the mathematical understanding and skills required for adult life, for employment and further study". The most important contribution for the purpose of this study, was the emphasis placed on cognitive aims to equip learners with numerical understanding and skills. Other contributions were to develop logical thinking and to expand their ability to look for patterns and explain them and to develop an awareness of the link between mathematics and everyday situations. This report (1982) motivated the researcher to review how teachers are teaching. This means that there will be an investigation into how children learn mathematics and not just what should be taught. Naidoo, Smit and Van Heerden (1995:7) also emphasise this by stating that "...the advance in technology at this time changed educational thinking more, making it even more important to further investigate how children actually learn." Yildirim (1994:28) argues that "... improving student's thinking ability is accepted as an important goal of education, and schools are considered places where thinking skills can be promoted. However, ways in which this should be done is a matter of controversy among educators." He further postulates that the best way to improve student thinking involves deep and thoughtful subject matter instruction in which students are encouraged to think reflectively rather than to merely cite the facts. The central characteristics of mathematical thinking are the determination of relationship and their application. It includes the ability to analyse a given situation or experience; to distinguish between applicable data and those which are not applicable; to classify and arrange these data; to abstract relationships from them, and finally to symbolize them for future use and application in new situations. Therefore it is important and essential for students to be taught how to approach the problems. This is one way of encouraging inquisitive and creative mathematics. Well-developed thinking skills are useful in almost every life situation, therefore there is a need to design instructional programmes that focus on the acquisition and uses thinking skills that are needed to find and solve mathematical problems.

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Manyatshe, Salome Makgoshi. "Media usage in the teaching of mathematics." Thesis, 2014. http://hdl.handle.net/10210/10993.

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Анотація:

M.Ed. (Media Studies)
The subject mathematics is for one reason or another regarded as a necessary prerequisite for various job directions by many countries (Del;we, 1988:1). This subject is also valuable as preparation for the contingency that the child in future may take up an occupation requiring knowledge of the subject in question (Young, 1927:14). What matters most is that·a large number of pupils fail mathematics every year in their examination in primary and secondary schools. This is a clear indication that there are problems in the teaching and learning of mathematics which need special attention. Mathematics is a sequential learning subject (Larcombe, 1985:12). By this is meant that new learning content cannot be grasped unless there is insight into and understanding of the previous learning content. This is true because the growth of mathematical understanding develops step by· step with each forward move depending upon the consolidation of previous experience. In the light of the evidence that primary school children are in the concrete reasoning state, most mathematics educators believe that it is desirable to use large amounts of manipulative materials with young children. The understanding of the nature of mathematics is more important in teaching, as the teaching of the subject is influenced and determined by the teacher's understanding of the nature of the subject. The theory, most prevalent among teachers is that mathematics affords the best training for the reasoning powers, and this is its traditional form (Young, 1927:15).

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Rampa, Seake Harry. "Teaching of mathematics in Soshanguve schools : a situation analysis." Thesis, 2014. http://hdl.handle.net/10210/11688.

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M.Ed. (Subject Didactics)
Research shows that "the aims of secondary school's teaching of mathematics are often not realized with many pupils leaving the school with passive knowledge of mathematics" (H.S.R.C. 1981:8). This means that knowledge of mathematical facts are reproduced on demand, instead of active mathematical knowledge " which is congruent with the aims of teaching secondary mathematics" (Crooks, 1988 : 6/7). Active knowledge of mathematics implies and characterised by the understanding of concepts, principles that underlie facts and ideas and principles and concepts that are connected to each other" (Entwistle & Entwistle, 1992 : 2). Active knowledge also enables pupils to act intellectually independently. One reason for the previously mentioned predicament is that "teaching often encourage passive knowledge because the teaching practice of mathematics teachers are often not in accordance with their educational aims" (Gravett, 1994 :6). Thus, a discrepancy exists between teacher's intentions of teaching mathematics and their conduct during teaching. It can be argued also that teachers teach mathematics in the classroom but that the pupils not always effectively learn. It is from the perception above that a constructivistic view of learning as a conceptual change underlies the idea that teaching "as the creation of a classroom context conducive to learning" (Strike & Posner, 1985:117). Biggs (1993 : 74) thus argues that "if knowledge is constructed, rather than recorded as received, it does not make sense to think of teaching as imparting knowledge, but rather as creating learning environments that enhance the process of mathematical knowledge construction". Russell (1969: 14) mentions that "mathematics is a subject in which we never know what we are talking about, nor whether what we are saying is true". The views, amongst others Oosthuizen, Swart and Gildenhuys (1992:2) see mathematics as "an essential language of a creative but deductive process which has its origins in the problems of the physical world", In the light of this, the origin of mathematics in the real world, it can be argued that from a "constructivistic perspective, mathematical learning is an active process by which pupils construct their own mathematical knowledge in the light of their existing knowledge and through interaction with the world around them" (Gravett, 1994 : 6/7). "Construction, not absorption or unfocused discovery, enables learning" (Leder, 1993 : 13). Mathematics is not something discovered by mankind, mathematics is a creation of mankind and is transmitted and changed from one generation to the next.

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