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:
- Date Issued: 2014
- 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:
- Date Issued: 2014
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:
- Date Issued: 2014
- 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:
- Date Issued: 2014
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:
- Date Issued: 2014
- 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:
- Date Issued: 2014
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