An ethnographic study of beginner mathematics teachers’ classroom practices in the first three years of their employment: Shaping of a Professional Identity
- Narayanan, Ajayagosh Ettappiriparambil
- Authors: Narayanan, Ajayagosh Ettappiriparambil
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2069 , http://hdl.handle.net/10962/d1020967
- Description: The main theme in this study examines how beginner mathematics teachers (BTs) shape their professional identity in their first three years of classroom practices in Lesotho. This study, which focuses particularly on BTs’ second and third year of employment, gathers data with an understanding that the notion of professional identity is multi-faceted. Professional identity embraces a host of other identities such as personal identity, teacher identity, mathematics identity and community of practice identity. This study is framed by social theories of learning. Learning occurs by active participation and practice. BTs’ peripheral participation assists them in making sense of the activities (situated learning) in which they are engaged, in the classrooms. The sense making processes eventually shape their professional identity. In line with situated meanings that BTs form, the key notion (professional identity) is further categorised into personal identity, teacher identity, mathematics identity and community of practice identity. These identities integrate to become the professional identity of a beginner mathematics teacher. Using a narrative ethnographic approach as the research method, I have made use of extensive classroom observations and interviews to gather data. In this study, six volunteer participant BTs were originally selected. These teachers were from two districts, Berea and Maseru in Lesotho. After being observed in the classrooms, these teachers were interviewed. In the third year of the study, one participant withdrew from the study. I used vertical (descriptive) analysis to narrate their classroom practice followed by horizontal analysis to understand how they shape their professional identity. The analytical model enables the researcher to analyse the data in order to establish how the BTs’ actions, their reflexive stories and their journey in becoming a mathematics teacher shape their professional identity. The recurring themes that emerged from the horizontal analysis are the ways BTs approach the classroom practice which is dominated by teacher-centred learning. This involves demonstrating an example and then students following this model to practice more examples. In this sense, their approach is the same though these BTs started understanding how their classroom approaches can bring changes in the learning of mathematics. I analysed the utterances from the BTs’ classroom activities by separating these into mathematizing and subjectifying. The subjectifying utterances were further analysed to understand how these created meaning. These, in my view, are also central features of a teacher’s practice that need interpretation in order to understand the shaping of a professional identity. The key finding is that their narrative helped them to understand how they shape their professional identity. The study highlights the importance of listening to BTs’ stories of how they become mathematics teachers. Their narratives can be the benchmark for stake-holders, policy makers and potential researchers as the study on BTs’ professional identity is relatively new in Lesotho.
- Full Text:
- Authors: Narayanan, Ajayagosh Ettappiriparambil
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2069 , http://hdl.handle.net/10962/d1020967
- Description: The main theme in this study examines how beginner mathematics teachers (BTs) shape their professional identity in their first three years of classroom practices in Lesotho. This study, which focuses particularly on BTs’ second and third year of employment, gathers data with an understanding that the notion of professional identity is multi-faceted. Professional identity embraces a host of other identities such as personal identity, teacher identity, mathematics identity and community of practice identity. This study is framed by social theories of learning. Learning occurs by active participation and practice. BTs’ peripheral participation assists them in making sense of the activities (situated learning) in which they are engaged, in the classrooms. The sense making processes eventually shape their professional identity. In line with situated meanings that BTs form, the key notion (professional identity) is further categorised into personal identity, teacher identity, mathematics identity and community of practice identity. These identities integrate to become the professional identity of a beginner mathematics teacher. Using a narrative ethnographic approach as the research method, I have made use of extensive classroom observations and interviews to gather data. In this study, six volunteer participant BTs were originally selected. These teachers were from two districts, Berea and Maseru in Lesotho. After being observed in the classrooms, these teachers were interviewed. In the third year of the study, one participant withdrew from the study. I used vertical (descriptive) analysis to narrate their classroom practice followed by horizontal analysis to understand how they shape their professional identity. The analytical model enables the researcher to analyse the data in order to establish how the BTs’ actions, their reflexive stories and their journey in becoming a mathematics teacher shape their professional identity. The recurring themes that emerged from the horizontal analysis are the ways BTs approach the classroom practice which is dominated by teacher-centred learning. This involves demonstrating an example and then students following this model to practice more examples. In this sense, their approach is the same though these BTs started understanding how their classroom approaches can bring changes in the learning of mathematics. I analysed the utterances from the BTs’ classroom activities by separating these into mathematizing and subjectifying. The subjectifying utterances were further analysed to understand how these created meaning. These, in my view, are also central features of a teacher’s practice that need interpretation in order to understand the shaping of a professional identity. The key finding is that their narrative helped them to understand how they shape their professional identity. The study highlights the importance of listening to BTs’ stories of how they become mathematics teachers. Their narratives can be the benchmark for stake-holders, policy makers and potential researchers as the study on BTs’ professional identity is relatively new in Lesotho.
- Full Text:
An exploration of how consistently and precisely mathematics teachers code-switch in multilingual classrooms
- Authors: Chikiwa, Clemence
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2076 , http://hdl.handle.net/10962/d1021304
- Description: Many education research studies conducted in and outside South Africa encourage teachers to take advantage of the presence of multilingualism in their classrooms and to use it to the advancement of students’ conceptual learning. This study adopts the notion that code switching is a potential resource that teachers can use when teaching multilingual mathematics classes. The aim of this study is to determine how precisely and consistently selected teachers of multilingual mathematics classes code switched during teaching of trigonometry and geometry at secondary school. This study is informed by socio-cultural theory in general and Vygotsky’s work in particular. It focussed specifically on the critical role that language plays in the teaching and cognitive development of mathematics. My study situated within an interpretivist paradigm, used a case study research design and a mixed method research approach. Data were obtained through document collection, observing and interviewing three Grade 11 Mathematics teachers purposively selected from three secondary schools in Grahamstown and King Williamstown education districts of the Eastern Cape Province, South Africa. Data were quantitatively and qualitatively analysed. Findings from this study revealed that the frequency of code switching was not consistent across teachers, topics and lessons. Teachers taught predominantly in the public domain exposing students to compromised mathematical content through their code switching practices. Borrowing code switching was prevalently employed consistently across the participating teachers. Very little transparent code switching, from mainly those mathematical terms commonly used in the foundation and the intermediate phases, was evident in teacher language. No Grade 11 trigonometry and geometry terms in isiXhosa were transparently and consistently code switched. The data suggested that while precision was observed in some cases, it was not consistent. Inconsistencies were caused by lack of planning for code switching, lack of teaching materials in indigenous languages, selective code switching, and ‘safe mode’ code switching strategies which affected teachers’ pedagogical practices. Overall results in this study illustrate that the lack of planning for code switching and the lack of explicit policies and clear-cut official positions on code switching for teaching has contributed to inconsistent and imprecise code switching by the participating teachers. This study concludes that the development of supporting mechanisms, identifying and documenting best practices to encourage transparent, meaningful and beneficial code switching is urgently required to aid and promote conceptual understanding of strongly bounded sub-registers of secondary school mathematics such as trigonometry and geometry. It is anticipated that this study will contribute significantly to the ongoing debate on language use in education and to the institution of best practices for judicious, consistent and precise use of students’ home language during the teaching of mathematics in South Africa.
- Full Text:
- Authors: Chikiwa, Clemence
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2076 , http://hdl.handle.net/10962/d1021304
- Description: Many education research studies conducted in and outside South Africa encourage teachers to take advantage of the presence of multilingualism in their classrooms and to use it to the advancement of students’ conceptual learning. This study adopts the notion that code switching is a potential resource that teachers can use when teaching multilingual mathematics classes. The aim of this study is to determine how precisely and consistently selected teachers of multilingual mathematics classes code switched during teaching of trigonometry and geometry at secondary school. This study is informed by socio-cultural theory in general and Vygotsky’s work in particular. It focussed specifically on the critical role that language plays in the teaching and cognitive development of mathematics. My study situated within an interpretivist paradigm, used a case study research design and a mixed method research approach. Data were obtained through document collection, observing and interviewing three Grade 11 Mathematics teachers purposively selected from three secondary schools in Grahamstown and King Williamstown education districts of the Eastern Cape Province, South Africa. Data were quantitatively and qualitatively analysed. Findings from this study revealed that the frequency of code switching was not consistent across teachers, topics and lessons. Teachers taught predominantly in the public domain exposing students to compromised mathematical content through their code switching practices. Borrowing code switching was prevalently employed consistently across the participating teachers. Very little transparent code switching, from mainly those mathematical terms commonly used in the foundation and the intermediate phases, was evident in teacher language. No Grade 11 trigonometry and geometry terms in isiXhosa were transparently and consistently code switched. The data suggested that while precision was observed in some cases, it was not consistent. Inconsistencies were caused by lack of planning for code switching, lack of teaching materials in indigenous languages, selective code switching, and ‘safe mode’ code switching strategies which affected teachers’ pedagogical practices. Overall results in this study illustrate that the lack of planning for code switching and the lack of explicit policies and clear-cut official positions on code switching for teaching has contributed to inconsistent and imprecise code switching by the participating teachers. This study concludes that the development of supporting mechanisms, identifying and documenting best practices to encourage transparent, meaningful and beneficial code switching is urgently required to aid and promote conceptual understanding of strongly bounded sub-registers of secondary school mathematics such as trigonometry and geometry. It is anticipated that this study will contribute significantly to the ongoing debate on language use in education and to the institution of best practices for judicious, consistent and precise use of students’ home language during the teaching of mathematics in South Africa.
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A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: 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.
- Full Text:
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: 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.
- Full Text:
Exploring teaching proficiency in geometry of selected effective mathematics teachers in Namibia
- Stephanus, Gervasius Hivengwa
- Authors: Stephanus, Gervasius Hivengwa
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia , Effective teaching -- Namibia , Mathematics teachers -- Education (Secondary) -- Namibia , Education, Secondary -- Namibia , Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1976 , http://hdl.handle.net/10962/d1013012
- Description: Quality mathematics education relies on effective pedagogy which offers students appropriate and rich opportunities to develop their mathematical proficiency (MP) and intellectual autonomy in learning mathematics. This qualitative case study aimed to explore and analyse selected effective mathematics teachers' proficiency in the area of geometry in five secondary schools in five different Namibia educational regions. The sample was purposefully selected and comprised five mathematics teachers, identified locally as being effective practitioners by their peers, Education Ministry officials and the staff of the University of Namibia (UNAM). The schools where the selected teachers taught were all high performing Namibian schools in terms of students' mathematics performance in the annual national examinations. The general picture of students' poor performance in mathematics in Namibia is no different to other sub-Saharan countries and it is the teachers who unfortunately bear the brunt of the criticism. There are, however, beacons of excellence in Namibia and these often go unnoticed and are seldom written about. It is the purpose of this study to focus on these high achievers and analyse the practices of these teachers so that the rest of Namibia can learn from their practices and experience what is possible in the Namibian context. The mathematical content and context focus of this study was geometry. This qualitative study adopted a multiple case study approach and was framed within an interpretive paradigm. The data were collected through individual questionnaires, classroom lesson observations and in-depth open-ended and semi-structured interviews with the participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions. An adapted framework based on the Kilpatrick, Swafford and Findell's (2001) five strands of teaching for MP was developed as a conceptual and analytical lens to analyse the selected teachers' practice. The developed coding and the descriptive narrative vignettes of their teaching enabled a qualitative analysis of what teachers said contributed to their effectiveness and how they developed MP in students. An enactivist theoretical lens was used to complement the Kilpatrick et al.'s (2001) analytical framework. This enabled a deeper analysis of teacher teaching practice in terms of their embodied mathematical knowledge, actions and interactions with students. procedural fluency (PF) and productive disposition (PD), were addressed regularly by all five participating teachers. Evidence of addressing either the development of students' strategic competence (SC) or adaptive reasoning (AR) appeared rarely. Of particular interest in this study was that the strand of PD was the glue that held the other four strands of MP together. PD was manifested in many different ways in varying degrees. PD was characterised by a high level of content knowledge, rich personal experience, sustained commitment, effective and careful preparation for lessons, high expectations of themselves and learners, collegiality, passion for mathematics and an excellent work ethic. In addition, the teachers' geometry teaching practices were characterised by making use of real-world connections, manipulatives and representations, encouraging a collaborative approach and working together to show that geometry constituted a bridge between the concrete and abstract. The findings of the study have led me, the author, to suggest a ten (10) principles framework and seven (7) key interrelated factors for effective teaching, as a practical guide for teachers. This study argues that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick et al.'s (2001) model and the four concepts of autopoesis, co-emergence, structural determinism and embodiment of the enactivist approach. The study concludes with recommendations for effective pedagogical practices in the teaching of geometry, and opportunities for further research.
- Full Text:
- Authors: Stephanus, Gervasius Hivengwa
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia , Effective teaching -- Namibia , Mathematics teachers -- Education (Secondary) -- Namibia , Education, Secondary -- Namibia , Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1976 , http://hdl.handle.net/10962/d1013012
- Description: Quality mathematics education relies on effective pedagogy which offers students appropriate and rich opportunities to develop their mathematical proficiency (MP) and intellectual autonomy in learning mathematics. This qualitative case study aimed to explore and analyse selected effective mathematics teachers' proficiency in the area of geometry in five secondary schools in five different Namibia educational regions. The sample was purposefully selected and comprised five mathematics teachers, identified locally as being effective practitioners by their peers, Education Ministry officials and the staff of the University of Namibia (UNAM). The schools where the selected teachers taught were all high performing Namibian schools in terms of students' mathematics performance in the annual national examinations. The general picture of students' poor performance in mathematics in Namibia is no different to other sub-Saharan countries and it is the teachers who unfortunately bear the brunt of the criticism. There are, however, beacons of excellence in Namibia and these often go unnoticed and are seldom written about. It is the purpose of this study to focus on these high achievers and analyse the practices of these teachers so that the rest of Namibia can learn from their practices and experience what is possible in the Namibian context. The mathematical content and context focus of this study was geometry. This qualitative study adopted a multiple case study approach and was framed within an interpretive paradigm. The data were collected through individual questionnaires, classroom lesson observations and in-depth open-ended and semi-structured interviews with the participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions. An adapted framework based on the Kilpatrick, Swafford and Findell's (2001) five strands of teaching for MP was developed as a conceptual and analytical lens to analyse the selected teachers' practice. The developed coding and the descriptive narrative vignettes of their teaching enabled a qualitative analysis of what teachers said contributed to their effectiveness and how they developed MP in students. An enactivist theoretical lens was used to complement the Kilpatrick et al.'s (2001) analytical framework. This enabled a deeper analysis of teacher teaching practice in terms of their embodied mathematical knowledge, actions and interactions with students. procedural fluency (PF) and productive disposition (PD), were addressed regularly by all five participating teachers. Evidence of addressing either the development of students' strategic competence (SC) or adaptive reasoning (AR) appeared rarely. Of particular interest in this study was that the strand of PD was the glue that held the other four strands of MP together. PD was manifested in many different ways in varying degrees. PD was characterised by a high level of content knowledge, rich personal experience, sustained commitment, effective and careful preparation for lessons, high expectations of themselves and learners, collegiality, passion for mathematics and an excellent work ethic. In addition, the teachers' geometry teaching practices were characterised by making use of real-world connections, manipulatives and representations, encouraging a collaborative approach and working together to show that geometry constituted a bridge between the concrete and abstract. The findings of the study have led me, the author, to suggest a ten (10) principles framework and seven (7) key interrelated factors for effective teaching, as a practical guide for teachers. This study argues that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick et al.'s (2001) model and the four concepts of autopoesis, co-emergence, structural determinism and embodiment of the enactivist approach. The study concludes with recommendations for effective pedagogical practices in the teaching of geometry, and opportunities for further research.
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Narratives that shape the professional identities of mathematics teachers
- Felix, Clyde Benedict Aurelius
- Authors: Felix, Clyde Benedict Aurelius
- Date: 2014
- Subjects: Mathematics teachers -- South Africa -- Port Elizabeth , Mathematics teachers -- South Africa -- Grahamstown , Mathematics teachers -- Professional relationships , Mathematics teachers -- Training of , Mathematics -- Study and teaching -- South Africa -- Eastern Cape , Education -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1995 , http://hdl.handle.net/10962/d1013547
- Description: The central position in this study is that the professional identities, and consequently the classroom practices, of mathematics teachers are continuously being shaped by their narratives of past and present experiences. The primary research question explores the narratives that shape the professional identities of seven mathematics teachers; and the secondary research question, how their narratives shape their professional identities. Furthermore, the potential implications of this study for the design and implementation of pre-service teacher education programmes and in-service teacher development initiatives are considered. This study is framed by Socioculturalism; a theoretical perspective of human thinking as social in origin and of learning as participation in social practices. Futhermore, in line with Situated Learning Theory, the key theoretical notions are: identity (or learning as becoming); community (or learning as belonging); practice (or learning as doing); and meaning (or learning as experience). Identity is construed here as a conceptual bridge between learning and its cultural settings; and also between the individual and the social. In this study, the identity-shaping narratives of seven mathematics teachers, all purposively sampled from schools in the Port Elizabeth and Grahamstown education districts of the Eastern Cape Province of South Africa, were accessed via a narrative inquiry; followed by a horizontal analysis to identify common patterns or recurring themes in the narratives of all seven participants; and, a vertical analysis of the narratives of four of the participants to determine how their narratives shape their professional identities. Recurring themes that emerged during the horizontal analysis include the influence of: family support; role models; changing work environments; continuous professional development; professional recognition; religion; and, micro-politics. The vertical analysis demonstrated how, through a process of interpreting the narratives and restorying them into a meaningful core narrative; it is possible to gain insights into how personal narratives shape a professional identity. This study highlights the importance of listening to the narratives of mathematics teachers; because their professional identities, and consequently their teaching practices, are continuously being shaped by their narratives. It is anticipated that this research will be of interest and benefit to researchers, policy-makers, and teachers; especially in the area of Mathematics Education, where both narrative inquiry as a research method and research into teachers’ professional identities are relatively new.
- Full Text:
- Authors: Felix, Clyde Benedict Aurelius
- Date: 2014
- Subjects: Mathematics teachers -- South Africa -- Port Elizabeth , Mathematics teachers -- South Africa -- Grahamstown , Mathematics teachers -- Professional relationships , Mathematics teachers -- Training of , Mathematics -- Study and teaching -- South Africa -- Eastern Cape , Education -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1995 , http://hdl.handle.net/10962/d1013547
- Description: The central position in this study is that the professional identities, and consequently the classroom practices, of mathematics teachers are continuously being shaped by their narratives of past and present experiences. The primary research question explores the narratives that shape the professional identities of seven mathematics teachers; and the secondary research question, how their narratives shape their professional identities. Furthermore, the potential implications of this study for the design and implementation of pre-service teacher education programmes and in-service teacher development initiatives are considered. This study is framed by Socioculturalism; a theoretical perspective of human thinking as social in origin and of learning as participation in social practices. Futhermore, in line with Situated Learning Theory, the key theoretical notions are: identity (or learning as becoming); community (or learning as belonging); practice (or learning as doing); and meaning (or learning as experience). Identity is construed here as a conceptual bridge between learning and its cultural settings; and also between the individual and the social. In this study, the identity-shaping narratives of seven mathematics teachers, all purposively sampled from schools in the Port Elizabeth and Grahamstown education districts of the Eastern Cape Province of South Africa, were accessed via a narrative inquiry; followed by a horizontal analysis to identify common patterns or recurring themes in the narratives of all seven participants; and, a vertical analysis of the narratives of four of the participants to determine how their narratives shape their professional identities. Recurring themes that emerged during the horizontal analysis include the influence of: family support; role models; changing work environments; continuous professional development; professional recognition; religion; and, micro-politics. The vertical analysis demonstrated how, through a process of interpreting the narratives and restorying them into a meaningful core narrative; it is possible to gain insights into how personal narratives shape a professional identity. This study highlights the importance of listening to the narratives of mathematics teachers; because their professional identities, and consequently their teaching practices, are continuously being shaped by their narratives. It is anticipated that this research will be of interest and benefit to researchers, policy-makers, and teachers; especially in the area of Mathematics Education, where both narrative inquiry as a research method and research into teachers’ professional identities are relatively new.
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An investigation into how cell phones can be used in the teaching of mathematics using VITALmaths video clips: a case study of 2 schools in Grahamstown, South Africa
- Authors: Ndafenongo, Gerhard
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown Educational innovations -- South Africa -- Grahamstown Telecommunication in education -- South Africa -- Grahamstown Teaching -- Aids and devices -- South Africa -- Grahamstown Mathematics Software -- South Africa -- Grahamstown Mobile communication systems in education -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1596 , http://hdl.handle.net/10962/d1003478
- Description: Cell phones have become a ubiquitous part of daily life for both teachers and learners alike. The educational potential afforded by cell phones is diverse. The challenge for teachers is to capitalise on this ubiquity and make use of cell phones for educational purposes. This study investigates how cell phones can be used in the teaching of Mathematics using VITALmaths video clips. Five VITALmaths video clips were uploaded onto cell phones which were used in the classroom to explore the Theorem of Pythagoras in a visually appealing way that supported a conceptual understanding of the basis of the theorem. The study was conducted in two high schools in Grahamstown, South Africa. It involved two teachers from each school and a total number of 47 Grade 10 Mathematics students. The participating teachers were chosen from a group of Mathematics teachers taking part in the Mathematics Teacher Enrichment Programme (MTEP) of the FirstRand Foundation Mathematics Education Chair hosted by Rhodes University. This study is framed as a case study and is grounded within the interpretive paradigm. The study captures teachers’ and learners’ experiences in using cell phones as instructional aids within the pedagogical context of the classroom. This research suggests that cell phones can be a useful resource to support teaching and learning in the classroom, particularly in under-resourced schools. The use of VITALmaths video clips as mathematical content, and cell phones as a vehicle of delivery, enhanced active participation and concentration, sped up lessons, encouraged collaboration as well as interaction and hands-on exploration, and promoted both student autonomy as well as teacher enrichment.
- Full Text:
- Authors: Ndafenongo, Gerhard
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown Educational innovations -- South Africa -- Grahamstown Telecommunication in education -- South Africa -- Grahamstown Teaching -- Aids and devices -- South Africa -- Grahamstown Mathematics Software -- South Africa -- Grahamstown Mobile communication systems in education -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1596 , http://hdl.handle.net/10962/d1003478
- Description: Cell phones have become a ubiquitous part of daily life for both teachers and learners alike. The educational potential afforded by cell phones is diverse. The challenge for teachers is to capitalise on this ubiquity and make use of cell phones for educational purposes. This study investigates how cell phones can be used in the teaching of Mathematics using VITALmaths video clips. Five VITALmaths video clips were uploaded onto cell phones which were used in the classroom to explore the Theorem of Pythagoras in a visually appealing way that supported a conceptual understanding of the basis of the theorem. The study was conducted in two high schools in Grahamstown, South Africa. It involved two teachers from each school and a total number of 47 Grade 10 Mathematics students. The participating teachers were chosen from a group of Mathematics teachers taking part in the Mathematics Teacher Enrichment Programme (MTEP) of the FirstRand Foundation Mathematics Education Chair hosted by Rhodes University. This study is framed as a case study and is grounded within the interpretive paradigm. The study captures teachers’ and learners’ experiences in using cell phones as instructional aids within the pedagogical context of the classroom. This research suggests that cell phones can be a useful resource to support teaching and learning in the classroom, particularly in under-resourced schools. The use of VITALmaths video clips as mathematical content, and cell phones as a vehicle of delivery, enhanced active participation and concentration, sped up lessons, encouraged collaboration as well as interaction and hands-on exploration, and promoted both student autonomy as well as teacher enrichment.
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An investigation into the use of traditional Xhosa dance to teach mathematics: a case study in a Grade 7 class
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
- Full Text:
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
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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
- Authors: Hyde, Janet Catherine
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Educational innovations -- South Africa Telecommunication in education -- South Africa Teaching -- South Africa -- Aids and devices
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1618 , http://hdl.handle.net/10962/d1003500
- Description: 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.
- Full Text:
- Authors: Hyde, Janet Catherine
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa Educational innovations -- South Africa Telecommunication in education -- South Africa Teaching -- South Africa -- Aids and devices
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1618 , http://hdl.handle.net/10962/d1003500
- Description: 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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An investigation of the role of physical manipulatives in the teaching and learning of measurement in Grade 8 : a case study using surface area and volume
- Authors: Chiphambo, Shakespear M E K
- Date: 2012
- Subjects: Measurement -- Study and teaching -- Research Mathematics -- Education (Secondary) -- Study and teaching Teaching -- Aids and devices -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1657 , http://hdl.handle.net/10962/d1003540
- Description: The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.
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- Authors: Chiphambo, Shakespear M E K
- Date: 2012
- Subjects: Measurement -- Study and teaching -- Research Mathematics -- Education (Secondary) -- Study and teaching Teaching -- Aids and devices -- Research
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1657 , http://hdl.handle.net/10962/d1003540
- Description: The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.
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The heuristic significance of enacted visualisation
- Authors: Samson, Duncan Alistair
- Date: 2012
- Subjects: Heuristic Visualization Problem solving Pattern perception Problem solving -- Ability testing Mathematics -- Study and teaching Education -- Research Interdisciplinary approach to knowledge
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1552 , http://hdl.handle.net/10962/d1003434
- Description: This study is centred on an analysis of pupils' lived experience while engaged in the generalisation of linear sequences/progressions presented in a pictorial context. The study is oriented within the conceptual framework of qualitative research, and is anchored within an interpretive paradigm. A case study methodological strategy was adopted, the research participants being the members of a mixed gender, high ability Grade 9 class of 23 pupils at an independent school in South Africa. The analytical framework is structured around a combination of complementary multiple perspectives provided by three theoretical ideas, enactivism, figural apprehension, and knowledge objectification. An important aspect of this analytical framework is the sensitivity it shows to the visual, phenomenological and semiotic aspects of figural pattern generalisation. It is the central thesis of this study that the combined complementary multiple perspectives of enactivism, figural apprehension and knowledge objectification provide a powerful depth of analysis to the exploration of the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. The richly textured tapestry of activity captured through a multi-systemic semiotic analysis of participants' generalisation activity stands testament to this central thesis. Insights gleaned from this study are presented as practical strategies which support and encourage a multiple representational approach to pattern generalisation in the pedagogical context of the classroom.
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- Authors: Samson, Duncan Alistair
- Date: 2012
- Subjects: Heuristic Visualization Problem solving Pattern perception Problem solving -- Ability testing Mathematics -- Study and teaching Education -- Research Interdisciplinary approach to knowledge
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:1552 , http://hdl.handle.net/10962/d1003434
- Description: This study is centred on an analysis of pupils' lived experience while engaged in the generalisation of linear sequences/progressions presented in a pictorial context. The study is oriented within the conceptual framework of qualitative research, and is anchored within an interpretive paradigm. A case study methodological strategy was adopted, the research participants being the members of a mixed gender, high ability Grade 9 class of 23 pupils at an independent school in South Africa. The analytical framework is structured around a combination of complementary multiple perspectives provided by three theoretical ideas, enactivism, figural apprehension, and knowledge objectification. An important aspect of this analytical framework is the sensitivity it shows to the visual, phenomenological and semiotic aspects of figural pattern generalisation. It is the central thesis of this study that the combined complementary multiple perspectives of enactivism, figural apprehension and knowledge objectification provide a powerful depth of analysis to the exploration of the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. The richly textured tapestry of activity captured through a multi-systemic semiotic analysis of participants' generalisation activity stands testament to this central thesis. Insights gleaned from this study are presented as practical strategies which support and encourage a multiple representational approach to pattern generalisation in the pedagogical context of the classroom.
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An investigation into parental involvements in the learning of mathematics : a case study involving grade 5 San learners and their parents
- Hamukwaya, Shemunyenge Taleiko
- Authors: Hamukwaya, Shemunyenge Taleiko
- Date: 2010
- Subjects: Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1598 , http://hdl.handle.net/10962/d1003480 , Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Description: The purpose of this study was to investigate and document parental involvement in a San community in Namibia over a period of two months. The emphasis was to investigate whether San parents in the Omusati region were involved in the learning of mathematics of their children. The learner participants were selected according to those who were open to sharing their ideas. An interpretive approach was used to collect and analyse data. The collected data was gathered from 9 participants (4 learners in grade 5 together with their parents, plus their mathematics teacher). Semi-structured interviews, parental contributions and home visit observations were the three tools that I used to collect data. The selected school is located in a rural area in the Omusati region of northern Namibia. The interviews were conducted in Oshiwambo (the participants‟ mother tongue) and translated into English and then analyzed. I discovered that the selected San parents were involved in some but limited school activities. The findings of this study emphasizes that illiteracy may be one of the contributing factors of low or non-involvement of parents among the San community. Other factors which I found caused parents not to assist their children with homework was parents spending much of their time at the local cuca shops during the day until late in the evenings. The study also highlights possible strategies that can be carried out by teachers to encourage parental involvement in school activities.
- Full Text:
- Authors: Hamukwaya, Shemunyenge Taleiko
- Date: 2010
- Subjects: Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1598 , http://hdl.handle.net/10962/d1003480 , Mathematics (Elementary) -- Study and teaching -- Namibia , Mathematics (Elementary) -- Study and teaching -- Activity programs -- Namibia , Mathematics (Elementary) -- Study and teaching -- Parent participation -- Namibia , Parent-teacher relationships -- Namibia , Marginality, Social -- Namibia , Literacy -- Social aspects -- Namibia , Khoisan (African people) -- Namibia
- Description: The purpose of this study was to investigate and document parental involvement in a San community in Namibia over a period of two months. The emphasis was to investigate whether San parents in the Omusati region were involved in the learning of mathematics of their children. The learner participants were selected according to those who were open to sharing their ideas. An interpretive approach was used to collect and analyse data. The collected data was gathered from 9 participants (4 learners in grade 5 together with their parents, plus their mathematics teacher). Semi-structured interviews, parental contributions and home visit observations were the three tools that I used to collect data. The selected school is located in a rural area in the Omusati region of northern Namibia. The interviews were conducted in Oshiwambo (the participants‟ mother tongue) and translated into English and then analyzed. I discovered that the selected San parents were involved in some but limited school activities. The findings of this study emphasizes that illiteracy may be one of the contributing factors of low or non-involvement of parents among the San community. Other factors which I found caused parents not to assist their children with homework was parents spending much of their time at the local cuca shops during the day until late in the evenings. The study also highlights possible strategies that can be carried out by teachers to encourage parental involvement in school activities.
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The use of the van Hiele theory in investigating teaching strategies used by grade 10 geometry teachers in Namibia
- Authors: Muyeghu, Augustinus
- Date: 2009
- Subjects: Hiele, Pierre M. van Kilpatrick, Jeremy Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1817 , http://hdl.handle.net/10962/d1003703
- Description: This study reports on the extent to which selected mathematics teachers facilitate the teaching and learning of geometry at the van Hiele levels 1 and 2 at a Grade 10 level in selected schools in Namibia. It also addresses and explores the teaching strategies teachers employ in their classrooms. Kilpatrick et al.’s model for proficient teaching and the van Hiele model of geometric thinking were used to explore the type of teaching strategies employed by selected mathematics teachers. These two models served as guidelines from which interview and classroom observation protocols were developed. Given the continuing debate across the world about the learning and teaching of geometry, my thesis aims to contribute to a wider understanding of the teaching of geometry with regard to the van Hiele levels 1 and 2. There are no similar studies on the teaching of geometry in Namibia. My study concentrates on selected Grade 10 mathematics teachers and how they teach geometry using the van Hiele theory and the five Kilpatrick components of proficient teaching. As my research looks at teaching practice it was important to deconstruct teaching proficiency with a view to understanding what makes good teachers effective. The results from this study indicated that the selected Grade 10 mathematics teachers have a good conceptual understanding of geometry as all of them involved in this study were able to facilitate the learning and teaching of geometry that is consistent with the van Hiele levels 1 and 2.
- Full Text:
- Authors: Muyeghu, Augustinus
- Date: 2009
- Subjects: Hiele, Pierre M. van Kilpatrick, Jeremy Geometry -- Study and teaching (Secondary) -- Namibia Mathematics -- Study and teaching (Secondary) -- Namibia Mathematics teachers -- Training of -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1817 , http://hdl.handle.net/10962/d1003703
- Description: This study reports on the extent to which selected mathematics teachers facilitate the teaching and learning of geometry at the van Hiele levels 1 and 2 at a Grade 10 level in selected schools in Namibia. It also addresses and explores the teaching strategies teachers employ in their classrooms. Kilpatrick et al.’s model for proficient teaching and the van Hiele model of geometric thinking were used to explore the type of teaching strategies employed by selected mathematics teachers. These two models served as guidelines from which interview and classroom observation protocols were developed. Given the continuing debate across the world about the learning and teaching of geometry, my thesis aims to contribute to a wider understanding of the teaching of geometry with regard to the van Hiele levels 1 and 2. There are no similar studies on the teaching of geometry in Namibia. My study concentrates on selected Grade 10 mathematics teachers and how they teach geometry using the van Hiele theory and the five Kilpatrick components of proficient teaching. As my research looks at teaching practice it was important to deconstruct teaching proficiency with a view to understanding what makes good teachers effective. The results from this study indicated that the selected Grade 10 mathematics teachers have a good conceptual understanding of geometry as all of them involved in this study were able to facilitate the learning and teaching of geometry that is consistent with the van Hiele levels 1 and 2.
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Understanding the differences in marking performance of JSC mathematics markers in Namibia : a case study
- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
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- Authors: Mutuku, Elizabeth
- Date: 2009
- Subjects: Educational change -- Namibia , Mathematics -- Namibia -- Examinations -- Case studies , Mathematics -- Study and teaching -- Namibia -- Case studies , Grading and marking (Students) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1999 , http://hdl.handle.net/10962/d1015223
- Description: Education reform in Namibia brought about changes to mathematics education since independence. This has put pressure on the government to provide both resources and qualified mathematics teachers to help drive the reform process in all teaching and learning activities. This included availing reliable and valid national examination results which is a measure of whether the newly introduced programmes are working or not. For the Ministry of Education this meant training more mathematics teachers and ensuring that competent and reliable teachers are appointed for marking national examination every year. The teachers' training process however, has not been going as fast as it was expected and year after year the Directorate of National Examinations and Assessment experienced problems in obtaining competent teachers for the marking of national examination. The purpose of the study was to understand the differences in marking performances of the JSC mathematics national examination markers. Particularly the study was to create a clear and detailed understanding of different factors that could possibly affect the marking performance of different markers. In addition, the study was to investigate the effect the mathematical content knowledge of the markers has on their marking performance. It was evident from the findings that their mathematical content knowledge had influenced their marking performance. Moreover the research findings also gave a strong indication that there are other factors that were influencing the markers marking performance. These were the markers' knowledge of the assessment and marking process, the markers' marking experience, the markers' socioeconomic background. The difference in their moderators' input has emerged as the other factors that have influenced their performance in marking and consequently contributed to the differences in their marking performances.
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The initial grounding of rational numbers : an investigation
- Authors: Brown, Bruce John Lindsay
- Date: 2007
- Subjects: Number theory Numbers, Rational -- Study and teaching (Elementary) Numeracy -- Study and teaching (Elementary) Mathematics -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1904 , http://hdl.handle.net/10962/d1006351
- Description: This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.
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- Authors: Brown, Bruce John Lindsay
- Date: 2007
- Subjects: Number theory Numbers, Rational -- Study and teaching (Elementary) Numeracy -- Study and teaching (Elementary) Mathematics -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1904 , http://hdl.handle.net/10962/d1006351
- Description: This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of interviews that were transcribed and then analysed in detail, interspersed with periods of reading and reflection. The pilot cycle involved a single grade three teacher, the second cycle involved 2 grade three teachers and the third cycle involved 2 grade three children. The research identified a number of different perspectives that were all important for the development of a fundamental intuitive understanding that could be considered personally meaningful to the individual concerned and relevant to the development of rational number concepts. Firstly in order to motivate and engage the child on a personal level the grounding situation needed to be seen as personally significant by the child. Secondly, coordinating operations provided a means of developing a fundamental intuitive understanding, through coordination with affording structures of the situation that are relevant to rational numbers. Finally, goal directed actions that are deliberately structured to achieve explicit goals in a situation are important for the development of more explicit concepts and skills fundamental for rational number understanding. Different explicit structures give rise to different interpretations of rational numbers in grounding situations. In addition to these perspectives, it became evident that building and learning representations was important for developing a more particularly mathematical understanding, based on the fundamental understanding derived from the child's grounded experience. The conclusion drawn in this research as a result of this complexity, is that to achieve a comprehensive and meaningful grounding, children's learning of rational numbers will not follow a simple linear trajectory. Rather this process forms a web of learning, threading coordinating operations for intuitive development, interpretations for explicit grounding and representations to develop more formal mathematical conceptions.
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The use of Van Hiele's theory to explore problems encountered in circle geometry: a grade 11 case study
- Authors: Siyepu, Sibawu Witness
- Date: 2005
- Subjects: Geometry -- Study and teaching (Secondary) -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa Mathematical ability -- Testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1871 , http://hdl.handle.net/10962/d1004777
- Description: 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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- Authors: Siyepu, Sibawu Witness
- Date: 2005
- Subjects: Geometry -- Study and teaching (Secondary) -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa Mathematical ability -- Testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1871 , http://hdl.handle.net/10962/d1004777
- Description: 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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Project 1 - Student teachers' exploration of beadwork : cultural heritage as a resource for mathematical concepts
- Authors: Dabula, Nomonde Patience
- Date: 2001
- Subjects: Ethnomathematics , Beadwork -- South Africa -- Eastern Cape , Beadwork , Mathematics -- Study and teaching , Culture -- Study and teaching
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:1415 , http://hdl.handle.net/10962/d1003292
- Description: This portfolio consists of three research projects that predominantly lie within the socio-cultural strand. The first project is a qualitative ethnomathematical study that links students' knowledge of mathematics to their cultural heritage. The study was conducted with a group of final year student teachers at a College of Education in Umtata, Eastern Cape. These students visited a city museum where mathematics concepts were identified from beadwork artifacts. Mathematics concepts that were identified consisted of symmetry, tessellation and number patterns. Students' views about the nature of mathematics shifted radically after their own explorations. Initially students did not perceive mathematics as relating to socio-cultural practices. But now, they have reviewed their position and see mathematics as inextricably interwoven in everyday activities and as such, a product of all cultures. They also pride themselves of their own cultural heritage to have mathematical connections. A more positive attitude towards studying mathematics in this approach was noticed. Data was collected by means of interviews, reflective journal entries and photographs. The second project is a survey with a group of practising teachers who have already implemented Curriculum 2005, and a group which is about to implement it in 2001. The study sought teachers' understanding of connections between mathematics and socio-cultural issues. The new mathematics curriculum in South Africa calls for teachers to grapple well with these issues. About a third of the articulated specific outcomes specifically relate to socio-cultural issues. If teachers' understanding of these issues is poor, implementation of the new curriculum will remain a mere dream. The findings of the survey revealed that the majority of teachers could not identify the culture related specific outcomes in the new mathematics curriculum. Complicated language used in the OBE policy documents was found to inhibit meaning to these teachers. Although, all teachers showed a positive attitude towards the inclusion of socio-cultural issues in the mathematics classroom, the implementation of these outcomes was found to be very problematic. In this survey data was collected by means of questionnaires. The third project is a literature review on the need to popularise mathematics to students in particular, and to the broader public in general. The 21 st century places great technological demands. Mathematics underpins most thinking behind technological development. The role played by mathematics in advancing other fields is largely hidden to the majority of people. There is, therefore, a need to bring forth the vital role that mathematics plays in these fields. The number of students participating in mathematics is decreasing. Mathematics, as a field, is experiencing competition from other science fields. There is a need to bring some incentives to attract more students into this field and retain those mathematicians already involved. Also important, is the need to change the negative image that the public often holds about mathematics. Many people are mathematically illiterate and do not see mathematics as an everyday activity that relates to their needs. There is, therefore, a need to change the face of mathematics.
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- Authors: Dabula, Nomonde Patience
- Date: 2001
- Subjects: Ethnomathematics , Beadwork -- South Africa -- Eastern Cape , Beadwork , Mathematics -- Study and teaching , Culture -- Study and teaching
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:1415 , http://hdl.handle.net/10962/d1003292
- Description: This portfolio consists of three research projects that predominantly lie within the socio-cultural strand. The first project is a qualitative ethnomathematical study that links students' knowledge of mathematics to their cultural heritage. The study was conducted with a group of final year student teachers at a College of Education in Umtata, Eastern Cape. These students visited a city museum where mathematics concepts were identified from beadwork artifacts. Mathematics concepts that were identified consisted of symmetry, tessellation and number patterns. Students' views about the nature of mathematics shifted radically after their own explorations. Initially students did not perceive mathematics as relating to socio-cultural practices. But now, they have reviewed their position and see mathematics as inextricably interwoven in everyday activities and as such, a product of all cultures. They also pride themselves of their own cultural heritage to have mathematical connections. A more positive attitude towards studying mathematics in this approach was noticed. Data was collected by means of interviews, reflective journal entries and photographs. The second project is a survey with a group of practising teachers who have already implemented Curriculum 2005, and a group which is about to implement it in 2001. The study sought teachers' understanding of connections between mathematics and socio-cultural issues. The new mathematics curriculum in South Africa calls for teachers to grapple well with these issues. About a third of the articulated specific outcomes specifically relate to socio-cultural issues. If teachers' understanding of these issues is poor, implementation of the new curriculum will remain a mere dream. The findings of the survey revealed that the majority of teachers could not identify the culture related specific outcomes in the new mathematics curriculum. Complicated language used in the OBE policy documents was found to inhibit meaning to these teachers. Although, all teachers showed a positive attitude towards the inclusion of socio-cultural issues in the mathematics classroom, the implementation of these outcomes was found to be very problematic. In this survey data was collected by means of questionnaires. The third project is a literature review on the need to popularise mathematics to students in particular, and to the broader public in general. The 21 st century places great technological demands. Mathematics underpins most thinking behind technological development. The role played by mathematics in advancing other fields is largely hidden to the majority of people. There is, therefore, a need to bring forth the vital role that mathematics plays in these fields. The number of students participating in mathematics is decreasing. Mathematics, as a field, is experiencing competition from other science fields. There is a need to bring some incentives to attract more students into this field and retain those mathematicians already involved. Also important, is the need to change the negative image that the public often holds about mathematics. Many people are mathematically illiterate and do not see mathematics as an everyday activity that relates to their needs. There is, therefore, a need to change the face of mathematics.
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