The mathematical and pedagogical content knowledge that Namibian senior primary teachers draw on to develop their learners’ computational estimation
- Authors: Shigwedha, Emilia Ndilimeke
- Date: 2023-10-13
- Subjects: Mathematics Study and teaching (Primary) Namibia , Approximation theory , Pedagogical content knowledge , Mathematics teachers In-service training Namibia , Mathematics Namibia Outlines, syllabi, etc
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424108 , vital:72124
- Description: Computational estimation is important in the development of learners’ number sense. It is through the process of finding an approximate (but satisfactory) that learners can check the reasonableness of their answers to calculations, develop an understanding of place value and by implication the four number operations. It is the role of teachers to develop the computational estimation skills of learners. To do this, teachers need to have a sound knowledge of computational estimation, its value and how to teach it. This study thus seeks to explore and understand Namibian senior primary teachers’ mathematical and pedagogical content knowledge to develop their learners’ computation estimation knowledge. The research is guided by the following question: What mathematical and pedagogical content knowledge do senior primary mathematics teachers draw on to develop their learners’ computational estimation skills? The research is a qualitative interpretivist case study. Eight senior primary teachers of Mathematics from the Ohangwena region in Namibia participated in the study. Data was generated through questionnaires, a focus group interview and lesson observations. The Mathematics Knowledge for Teaching (Ball et al., 2008) and the Knowledge Quartet (Rowland, 2005) frameworks were used as both analytic and explanatory tools for the study. Key findings from the research are that teachers have knowledge of and use a variety of strategies for estimation, however, they only use the ‘rounding off’ strategy when teaching learners computational estimation. The teachers appear to teach computational estimation by first focusing on place value before moving on to ‘rounding off’ to the nearest 10s, 100s, 1000s and so forth. My research recommends that the National Institute of Educational Development together with the Ministry of Education, Art and Culture in Namibia, provide teachers with professional development opportunities on how to develop learners’ computational estimation. Such professional development will further develop teachers’ mathematical and pedagogical content knowledge. Furthermore, the Namibian syllabus should include a variety of strategies for computational estimation. , Thesis (MEd) -- Faculty of Education, Primary and Early Childhood Education, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Shigwedha, Emilia Ndilimeke
- Date: 2023-10-13
- Subjects: Mathematics Study and teaching (Primary) Namibia , Approximation theory , Pedagogical content knowledge , Mathematics teachers In-service training Namibia , Mathematics Namibia Outlines, syllabi, etc
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424108 , vital:72124
- Description: Computational estimation is important in the development of learners’ number sense. It is through the process of finding an approximate (but satisfactory) that learners can check the reasonableness of their answers to calculations, develop an understanding of place value and by implication the four number operations. It is the role of teachers to develop the computational estimation skills of learners. To do this, teachers need to have a sound knowledge of computational estimation, its value and how to teach it. This study thus seeks to explore and understand Namibian senior primary teachers’ mathematical and pedagogical content knowledge to develop their learners’ computation estimation knowledge. The research is guided by the following question: What mathematical and pedagogical content knowledge do senior primary mathematics teachers draw on to develop their learners’ computational estimation skills? The research is a qualitative interpretivist case study. Eight senior primary teachers of Mathematics from the Ohangwena region in Namibia participated in the study. Data was generated through questionnaires, a focus group interview and lesson observations. The Mathematics Knowledge for Teaching (Ball et al., 2008) and the Knowledge Quartet (Rowland, 2005) frameworks were used as both analytic and explanatory tools for the study. Key findings from the research are that teachers have knowledge of and use a variety of strategies for estimation, however, they only use the ‘rounding off’ strategy when teaching learners computational estimation. The teachers appear to teach computational estimation by first focusing on place value before moving on to ‘rounding off’ to the nearest 10s, 100s, 1000s and so forth. My research recommends that the National Institute of Educational Development together with the Ministry of Education, Art and Culture in Namibia, provide teachers with professional development opportunities on how to develop learners’ computational estimation. Such professional development will further develop teachers’ mathematical and pedagogical content knowledge. Furthermore, the Namibian syllabus should include a variety of strategies for computational estimation. , Thesis (MEd) -- Faculty of Education, Primary and Early Childhood Education, 2023
- Full Text:
- Date Issued: 2023-10-13
The nature of Visual Representations of multiplication and division exercises in nine Grades 1 to 3 South African textbooks
- Authors: Booysen, Tammy Irene
- Date: 2023-03-29
- Subjects: Mathematics Textbooks , Mathematics Study and teaching (Elementary) South Africa , Visual learning , Multiplication Study and teaching (Elementary) South Africa , Division Study and teaching (Elementary) South Africa , Constructivism (Education)
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422579 , vital:71959
- Description: Mathematics is a language that is rich in visual representations (Mudaly & Rampersad, 2010). Visual Representations assist us in developing our reasoning skills when solving a problem and our understanding of the relationships between concepts (Ozkan et al., 2018). This thesis focuses on the different visual representations (VR) in South African Foundation Phase mathematics textbooks and workbooks. Textbooks and workbooks play an important role in developing an understanding of mathematical concepts for both teachers and learners (Harries & Spooner, 2000). While teachers generally rely heavily on textbooks, they were a key resource while schools were closed due to COVID-19 lockdown regulations. The theory of Constructivism forms part of the theoretical framework for this study. Constructivism advocates that learners actively construct knowledge through experiences rather than passively receiving knowledge from the outside (Von Glaserfeld, 2001). Vygotsky believed that social interactions create experiences that facilitate the learning and meaning-making process (Vygotsky, 1978). This case study is underpinned by an interpretivist paradigm as it sought to examine the nature of VRs in three Grades 1 - 3 textbooks/workbooks. My research approach is primarily qualitative with descriptive statistics to assist in developing a more comprehensive understanding of the research questions. The study was guided by the analytic tool designed by Fotakopoulou and Spiliotopoulou (2008) which I adapted for Foundation Phase mathematics use. The framework provides insight on the type of VR, VRs relation to content, VRs relation to reality, the function of the VR and dimensionality of a VR. While the workbooks had many more VRs than textbooks, the dominant type of VR in textbooks and workbooks are images. The VRs mostly have a strong relation to content with a realistic relation to reality as they were predominantly 2D representation of a 3D object that had an exemplifying function (type b). , Thesis (MEd) -- Faculty of Education, Education, 2023
- Full Text:
- Date Issued: 2023-03-29
- Authors: Booysen, Tammy Irene
- Date: 2023-03-29
- Subjects: Mathematics Textbooks , Mathematics Study and teaching (Elementary) South Africa , Visual learning , Multiplication Study and teaching (Elementary) South Africa , Division Study and teaching (Elementary) South Africa , Constructivism (Education)
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422579 , vital:71959
- Description: Mathematics is a language that is rich in visual representations (Mudaly & Rampersad, 2010). Visual Representations assist us in developing our reasoning skills when solving a problem and our understanding of the relationships between concepts (Ozkan et al., 2018). This thesis focuses on the different visual representations (VR) in South African Foundation Phase mathematics textbooks and workbooks. Textbooks and workbooks play an important role in developing an understanding of mathematical concepts for both teachers and learners (Harries & Spooner, 2000). While teachers generally rely heavily on textbooks, they were a key resource while schools were closed due to COVID-19 lockdown regulations. The theory of Constructivism forms part of the theoretical framework for this study. Constructivism advocates that learners actively construct knowledge through experiences rather than passively receiving knowledge from the outside (Von Glaserfeld, 2001). Vygotsky believed that social interactions create experiences that facilitate the learning and meaning-making process (Vygotsky, 1978). This case study is underpinned by an interpretivist paradigm as it sought to examine the nature of VRs in three Grades 1 - 3 textbooks/workbooks. My research approach is primarily qualitative with descriptive statistics to assist in developing a more comprehensive understanding of the research questions. The study was guided by the analytic tool designed by Fotakopoulou and Spiliotopoulou (2008) which I adapted for Foundation Phase mathematics use. The framework provides insight on the type of VR, VRs relation to content, VRs relation to reality, the function of the VR and dimensionality of a VR. While the workbooks had many more VRs than textbooks, the dominant type of VR in textbooks and workbooks are images. The VRs mostly have a strong relation to content with a realistic relation to reality as they were predominantly 2D representation of a 3D object that had an exemplifying function (type b). , Thesis (MEd) -- Faculty of Education, Education, 2023
- Full Text:
- Date Issued: 2023-03-29
The use of lesson study to support grade 2 teachers in implementing differentiated instruction to develop learners’ reading comprehension skills
- Authors: Shipanga, Elizabeth Magano
- Date: 2022-10-14
- Subjects: Reading comprehension Study and teaching (Elementary) Namibia , Lesson study , Differentiated instruction , Teaching Social aspects Namibia
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/405390 , vital:70167
- Description: Research has found that learners in Namibia have poor reading comprehension (UNESCO, 2017). The Ministry of Education Arts and Culture (MoEAC) is concerned that teachers do not have the required pedagogical content knowledge to teach reading, and particularly reading comprehension in English Second Language. In addition, the MoEAC (2015) advocates for Differentiated Instruction (DI) to accommodate the needs of all learners in the classroom. Despite, numerous Continuous Professional Development programs, there has not been much change in the way teachers teach reading. The Lesson Study (LS) approach is viewed as a means to support teachers’ professional development. It provides teachers with the agency to take responsibility for their own professional development. It is against this background that an interpretivist action research was utilised to ascertain how LS can be used to support Grade 2 teachers in implementing DI to develop learners’ reading comprehension skill. This study asked the question: How can Lesson Study be used to support Grade 2 teachers in implementing Differentiated Instruction to develop the learners’ reading comprehension? Data was generated through observations, document analysis and interviews. The Theory of Practice Architectures was used to analyse data. As teachers we began this study with knowledge of the goals and terminology of DI but lacked the competence to implement it. The LS process used in the study enhanced teamwork as we planned, taught, observed each other, and reflected on the lessons taught during the intervention. We shared diverse insights in a supportive environment. Despite still novices with LS and DI we worked on redesigning lessons to become more intentional in catering for the needs of all learners in developing their reading comprehension in English Second Language. The emerging evidence from this and other studies is that LS is a very useful vehicle for Continuous Professional Development (CPD), but it is time consuming and in this study planning and reflecting on the lessons had to occur after hours. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Shipanga, Elizabeth Magano
- Date: 2022-10-14
- Subjects: Reading comprehension Study and teaching (Elementary) Namibia , Lesson study , Differentiated instruction , Teaching Social aspects Namibia
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/405390 , vital:70167
- Description: Research has found that learners in Namibia have poor reading comprehension (UNESCO, 2017). The Ministry of Education Arts and Culture (MoEAC) is concerned that teachers do not have the required pedagogical content knowledge to teach reading, and particularly reading comprehension in English Second Language. In addition, the MoEAC (2015) advocates for Differentiated Instruction (DI) to accommodate the needs of all learners in the classroom. Despite, numerous Continuous Professional Development programs, there has not been much change in the way teachers teach reading. The Lesson Study (LS) approach is viewed as a means to support teachers’ professional development. It provides teachers with the agency to take responsibility for their own professional development. It is against this background that an interpretivist action research was utilised to ascertain how LS can be used to support Grade 2 teachers in implementing DI to develop learners’ reading comprehension skill. This study asked the question: How can Lesson Study be used to support Grade 2 teachers in implementing Differentiated Instruction to develop the learners’ reading comprehension? Data was generated through observations, document analysis and interviews. The Theory of Practice Architectures was used to analyse data. As teachers we began this study with knowledge of the goals and terminology of DI but lacked the competence to implement it. The LS process used in the study enhanced teamwork as we planned, taught, observed each other, and reflected on the lessons taught during the intervention. We shared diverse insights in a supportive environment. Despite still novices with LS and DI we worked on redesigning lessons to become more intentional in catering for the needs of all learners in developing their reading comprehension in English Second Language. The emerging evidence from this and other studies is that LS is a very useful vehicle for Continuous Professional Development (CPD), but it is time consuming and in this study planning and reflecting on the lessons had to occur after hours. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
An investigation into the role of lesson study in developing teachers’ mathematics content and pedagogical content knowledge
- Authors: Kgothego, Naomi Ntsae
- Date: 2021-04
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Bojanala Platinum District Municipality , Pedagogical content knowledge , Lesson planning -- South Africa -- Bojanala Platinum District Municipality , Mathematics teachers -- Training of -- South Africa -- Bojanala Platinum District Municipality , South Africa. Department of Basic Education , Kokusai Kyōryoku Jigyōdan
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/178019 , vital:42899
- Description: Results of international assessments conducted with South African learners, both in primary and secondary schools, suggest that South African learners underperform in mathematics (Spaull, 2013). While there are numerous explanations for this, one of the key explanations is that teachers are deemed to have inadequate knowledge of both mathematics content and pedagogy. Poor content and pedagogical knowledge are indications that teachers are not adequately trained to teach mathematics (Green, 2011). To improve teachers' content and pedagogical knowledge, well-planned and researched professional development programmes need to be put in place. Current professional development opportunities that centre on workshops are not working as they provide little opportunity for teachers to connect the workshop content to the contexts in which they teach. Through a collaboration between the Department of Basic Education (DBE) and Japan International Corporation Agency (JICA), the Lesson Study approach is being introduced to support teachers' professional development. This research seeks to research this approach within the context of Foundation Phase mathematics education. The research asks: How does Lesson Study contribute to the development of teachers' mathematics content and pedagogical content knowledge? Two sub-questions were developed to support the main question: • What mathematics content knowledge do teachers develop as the engage in LS? • What pedagogical content knowledge do teachers develop as they engage in LS? Using a qualitative interpretivist case study approach, I worked collaboratively with four Grade 1 teachers from two schools. Data was generated through observations, semi-structured interviews and document analysis as we engaged in the Lesson Study process. The Mathematics Knowledge for Teaching (Ball, Thames & Phelps, 2008) and the Knowledge Quartet (Rowland, Turner, Thwaites & Huckstep, 2009) frameworks were used as analytic and explanatory tools in this research. This study's findings showed that participation in the interactive cycles of Lesson Study developed the teachers’ confidence, their pedagogical content knowledge and skills and provided them with the opportunity to collaborate and reflect on their knowledge. The study's findings suggest that lesson study can be used as a strategy for improving teacher professional development. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Kgothego, Naomi Ntsae
- Date: 2021-04
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Bojanala Platinum District Municipality , Pedagogical content knowledge , Lesson planning -- South Africa -- Bojanala Platinum District Municipality , Mathematics teachers -- Training of -- South Africa -- Bojanala Platinum District Municipality , South Africa. Department of Basic Education , Kokusai Kyōryoku Jigyōdan
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/178019 , vital:42899
- Description: Results of international assessments conducted with South African learners, both in primary and secondary schools, suggest that South African learners underperform in mathematics (Spaull, 2013). While there are numerous explanations for this, one of the key explanations is that teachers are deemed to have inadequate knowledge of both mathematics content and pedagogy. Poor content and pedagogical knowledge are indications that teachers are not adequately trained to teach mathematics (Green, 2011). To improve teachers' content and pedagogical knowledge, well-planned and researched professional development programmes need to be put in place. Current professional development opportunities that centre on workshops are not working as they provide little opportunity for teachers to connect the workshop content to the contexts in which they teach. Through a collaboration between the Department of Basic Education (DBE) and Japan International Corporation Agency (JICA), the Lesson Study approach is being introduced to support teachers' professional development. This research seeks to research this approach within the context of Foundation Phase mathematics education. The research asks: How does Lesson Study contribute to the development of teachers' mathematics content and pedagogical content knowledge? Two sub-questions were developed to support the main question: • What mathematics content knowledge do teachers develop as the engage in LS? • What pedagogical content knowledge do teachers develop as they engage in LS? Using a qualitative interpretivist case study approach, I worked collaboratively with four Grade 1 teachers from two schools. Data was generated through observations, semi-structured interviews and document analysis as we engaged in the Lesson Study process. The Mathematics Knowledge for Teaching (Ball, Thames & Phelps, 2008) and the Knowledge Quartet (Rowland, Turner, Thwaites & Huckstep, 2009) frameworks were used as analytic and explanatory tools in this research. This study's findings showed that participation in the interactive cycles of Lesson Study developed the teachers’ confidence, their pedagogical content knowledge and skills and provided them with the opportunity to collaborate and reflect on their knowledge. The study's findings suggest that lesson study can be used as a strategy for improving teacher professional development. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
The development of grade one teachers’ mathematics and pedagogical content knowledge through participation in a collaborative intervention
- Authors: Mutlane, Kedisaletse Stella
- Date: 2021-04
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Northern Cape , Pedagogical content knowledge , Mathematics teachers -- Training of -- South Africa -- Northern Cape , Lesson planning -- South Africa -- Northern Cape , Teaching teams -- South Africa -- Northern Cape , Cultural Historical Activity Theory (CHAT)
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/177370 , vital:42815
- Description: The “South African education system is grossly inefficient, severely underperforming and egregiously unfair” (Spaull, 2013, p.3). In particular, grave concerns with learner performance in mathematics in South Africa are well documented (e.g., Taylor, 2008; Spaull, 2013; Venkat & Spaull, 2015). There are various explanations for the poor state of learner performance in mathematics in South Africa. Two of the explanations that relate closely to my research interest are teachers’ insufficient mathematics content and pedagogical knowledge, and inappropriate professional development. This study aims to ascertain how a collaborative intervention can develop teachers’ mathematics and pedagogical content knowledge as they focus on developing learners’ foundational number sense. Cultural Historical Activity Theory, together with Mathematics Knowledge for Teaching (Ball et al., 2008) and the Knowledge Quartet (Rowlands & Turner, 2007) frameworks, provide the explanatory and analytic tools for the research. The research is a qualitative case study underpinned by an interpretivist orientation. The study was conducted at a township public primary school in the Northern Cape. Three Grade One teachers participated in the research. Data was collected through interviews, classroom observations, and videos of collaborative lesson planning and reflection sessions. A key finding emerging from this research is that the teachers had the necessary mathematics content knowledge to teach Grade One mathematics. Despite this and in contrast to it, they lacked adequate pedagogical content knowledge required to develop learners’ number sense. To develop their pedagogical content knowledge, they required the intervention of a ‘more knowledgable other’ (Vygotsky, 2008). Several contradictions and tensions emerged from the research. For example, the teachers expressed that the opportunity to work collaboratively was beneficial, but it was evident that they were familiar with and accomplished in planning and working together. The contradictions emerging from this research provide an opportunity and basis for expansive learning for future collaborative teacher endeavours. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Mutlane, Kedisaletse Stella
- Date: 2021-04
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Northern Cape , Pedagogical content knowledge , Mathematics teachers -- Training of -- South Africa -- Northern Cape , Lesson planning -- South Africa -- Northern Cape , Teaching teams -- South Africa -- Northern Cape , Cultural Historical Activity Theory (CHAT)
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/177370 , vital:42815
- Description: The “South African education system is grossly inefficient, severely underperforming and egregiously unfair” (Spaull, 2013, p.3). In particular, grave concerns with learner performance in mathematics in South Africa are well documented (e.g., Taylor, 2008; Spaull, 2013; Venkat & Spaull, 2015). There are various explanations for the poor state of learner performance in mathematics in South Africa. Two of the explanations that relate closely to my research interest are teachers’ insufficient mathematics content and pedagogical knowledge, and inappropriate professional development. This study aims to ascertain how a collaborative intervention can develop teachers’ mathematics and pedagogical content knowledge as they focus on developing learners’ foundational number sense. Cultural Historical Activity Theory, together with Mathematics Knowledge for Teaching (Ball et al., 2008) and the Knowledge Quartet (Rowlands & Turner, 2007) frameworks, provide the explanatory and analytic tools for the research. The research is a qualitative case study underpinned by an interpretivist orientation. The study was conducted at a township public primary school in the Northern Cape. Three Grade One teachers participated in the research. Data was collected through interviews, classroom observations, and videos of collaborative lesson planning and reflection sessions. A key finding emerging from this research is that the teachers had the necessary mathematics content knowledge to teach Grade One mathematics. Despite this and in contrast to it, they lacked adequate pedagogical content knowledge required to develop learners’ number sense. To develop their pedagogical content knowledge, they required the intervention of a ‘more knowledgable other’ (Vygotsky, 2008). Several contradictions and tensions emerged from the research. For example, the teachers expressed that the opportunity to work collaboratively was beneficial, but it was evident that they were familiar with and accomplished in planning and working together. The contradictions emerging from this research provide an opportunity and basis for expansive learning for future collaborative teacher endeavours. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
An investigation into the knowledge a Grade one teacher uses to develop the number sense of learners with mathematics learning difficulties
- Authors: Fleming, Kirsty Ann
- Date: 2020
- Subjects: Learning disabled children -- Education -- South Africa , Mathematics -- Study and teching (Elementary) -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/141533 , vital:37983
- Description: Learners in South Africa continue to underperform in the international and national mathematics benchmarking tests. In the primary school, poor performance in mathematics is viewed as an indicator of limited number sense. Since the end of Apartheid, there has been a proliferation of classroom-based research that attempts to explain why learners are underperforming and find solutions to the problem. Research that seeks to explain learner underperformance attributes poor learner performance to social-economic issues, teachers’ poor content and pedagogical knowledge, the complexity of the Language of Learning and Teaching, and insufficient support for learners with Mathematics Learning Difficulties (MLD). With regards to the latter, research suggests that Foundation Phase teachers are not equipped to assist learners with MLD develop their number sense. This qualitative case study aims to investigate the knowledge that an expert Foundation Phase teacher draws on, in the process of teaching, to assist learners with MLD develop their number sense. Data generated from observations and interviews with a Grade One teacher was analysed using Rowland, Turner and Thwaites’ (2013) Knowledge Quartet. The study found that the participant Grade One teacher employed all four categories of the Knowledge Quartet when developing her learners’ number sense. In particular, she placed strong emphasis on vocabulary development as a means of circumnavigating MLD when developing number sense in a Grade One mathematics lesson. She demonstrated knowledge of: the importance of vocabulary in learning mathematics; how to develop the learners’ understanding of mathematics vocabulary (and concepts); and how to adapt her approach to support the number sense development of learners with MLD. This research has value for teacher education programmes, both pre- and in-service, as it highlights the knowledge that a Grade One teacher draws on as she develops the number sense of all her learners, including those with MLD.
- Full Text:
- Date Issued: 2020
- Authors: Fleming, Kirsty Ann
- Date: 2020
- Subjects: Learning disabled children -- Education -- South Africa , Mathematics -- Study and teching (Elementary) -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/141533 , vital:37983
- Description: Learners in South Africa continue to underperform in the international and national mathematics benchmarking tests. In the primary school, poor performance in mathematics is viewed as an indicator of limited number sense. Since the end of Apartheid, there has been a proliferation of classroom-based research that attempts to explain why learners are underperforming and find solutions to the problem. Research that seeks to explain learner underperformance attributes poor learner performance to social-economic issues, teachers’ poor content and pedagogical knowledge, the complexity of the Language of Learning and Teaching, and insufficient support for learners with Mathematics Learning Difficulties (MLD). With regards to the latter, research suggests that Foundation Phase teachers are not equipped to assist learners with MLD develop their number sense. This qualitative case study aims to investigate the knowledge that an expert Foundation Phase teacher draws on, in the process of teaching, to assist learners with MLD develop their number sense. Data generated from observations and interviews with a Grade One teacher was analysed using Rowland, Turner and Thwaites’ (2013) Knowledge Quartet. The study found that the participant Grade One teacher employed all four categories of the Knowledge Quartet when developing her learners’ number sense. In particular, she placed strong emphasis on vocabulary development as a means of circumnavigating MLD when developing number sense in a Grade One mathematics lesson. She demonstrated knowledge of: the importance of vocabulary in learning mathematics; how to develop the learners’ understanding of mathematics vocabulary (and concepts); and how to adapt her approach to support the number sense development of learners with MLD. This research has value for teacher education programmes, both pre- and in-service, as it highlights the knowledge that a Grade One teacher draws on as she develops the number sense of all her learners, including those with MLD.
- Full Text:
- Date Issued: 2020
The teaching practice component of initial teacher education: a social justice approach
- Authors: Long, Kelly Ann
- Date: 2018
- Subjects: Educational change -- South Africa , Teachers -- Training of -- South Africa , Education -- South Africa -- History , Education – South Africa -- Evaluation , Education -- Standards -- South Africa , Teacher effectiveness -- South Africa , Social justice and education , Education -- Study and teaching (Higher) -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/60200 , vital:27746
- Description: Research asserts that learner performance in South African schools is in a state of crisis. While many more learners’ post-1994 in South Africa have physical access to education, very few have epistemological access. The quality of the education learners receive is polarised along socio economic lines. This crisis has its roots in the legacy of colonialism and apartheid, and as such, there is a need to transform the education system to ensure equal opportunity for all learners, and ultimately economic growth and security for the country. One of the explanations offered for the crisis in learner performance is the poor teacher education system. However, there is a paucity of research in teacher education generally in South Africa, and specifically in relation to pre-service teachers. Furthermore, little attention has been given to how initial teacher education could contribute to the promotion of a social justice agenda with the intention of transforming the South African schooling system. This research seeks to understand how the expectations, scaffolding and assessment of preservice teachers’ teaching practices can be utilised to promote social justice during the Teaching Practice (TP) component of initial teacher education. In answering the research question, I analyse data and literature to identify a set of key valued functionings of quality praxis that preservice teachers ought to be provided the capability to realise, at the level of achieved functioning. This is a qualitative case study located in the interpretive paradigm. The case under study is: quality teaching practices of pre-service teachers. This case is bound by context (initial teacher education in South Africa) and setting (the pre-service teacher in the classroom). Two South African Higher Education Institutions (HEIs) were selected through purposive sampling and their respective Teaching Practice (TP) documentation was analysed. Focus group interviews were conducted with five lecturers involved in TP at one of the HEIs. The theoretical framework of the study used to guide the analysis of the data was underpinned by a social justice perspective on quality education. Given that a social justice perspective does not have analytic tools, I view quality pre-service teachers’ teaching practices as praxis and utilise the capability approach as a mechanism for identification and description of valued functionings and capabilities that contribute to quality praxis. There are four significant findings in my research. Firstly, there is consistency with regards to the valued functionings and capabilities across the TP documentation of the two participating HEIs. In other words, the conceptions of a capable pre-service teacher are similar. Secondly, if social justice goals are to be realised, greater clarity of the valued functionings needs to be evident in the TP documentation. Thirdly, the valued functionings can be categorised into those that are foundational and those that promote a social justice agenda. Finally, in promoting a social justice agenda, there are functionings that ought to be valued by the HEIs that are seemingly not currently valued.
- Full Text:
- Date Issued: 2018
- Authors: Long, Kelly Ann
- Date: 2018
- Subjects: Educational change -- South Africa , Teachers -- Training of -- South Africa , Education -- South Africa -- History , Education – South Africa -- Evaluation , Education -- Standards -- South Africa , Teacher effectiveness -- South Africa , Social justice and education , Education -- Study and teaching (Higher) -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/60200 , vital:27746
- Description: Research asserts that learner performance in South African schools is in a state of crisis. While many more learners’ post-1994 in South Africa have physical access to education, very few have epistemological access. The quality of the education learners receive is polarised along socio economic lines. This crisis has its roots in the legacy of colonialism and apartheid, and as such, there is a need to transform the education system to ensure equal opportunity for all learners, and ultimately economic growth and security for the country. One of the explanations offered for the crisis in learner performance is the poor teacher education system. However, there is a paucity of research in teacher education generally in South Africa, and specifically in relation to pre-service teachers. Furthermore, little attention has been given to how initial teacher education could contribute to the promotion of a social justice agenda with the intention of transforming the South African schooling system. This research seeks to understand how the expectations, scaffolding and assessment of preservice teachers’ teaching practices can be utilised to promote social justice during the Teaching Practice (TP) component of initial teacher education. In answering the research question, I analyse data and literature to identify a set of key valued functionings of quality praxis that preservice teachers ought to be provided the capability to realise, at the level of achieved functioning. This is a qualitative case study located in the interpretive paradigm. The case under study is: quality teaching practices of pre-service teachers. This case is bound by context (initial teacher education in South Africa) and setting (the pre-service teacher in the classroom). Two South African Higher Education Institutions (HEIs) were selected through purposive sampling and their respective Teaching Practice (TP) documentation was analysed. Focus group interviews were conducted with five lecturers involved in TP at one of the HEIs. The theoretical framework of the study used to guide the analysis of the data was underpinned by a social justice perspective on quality education. Given that a social justice perspective does not have analytic tools, I view quality pre-service teachers’ teaching practices as praxis and utilise the capability approach as a mechanism for identification and description of valued functionings and capabilities that contribute to quality praxis. There are four significant findings in my research. Firstly, there is consistency with regards to the valued functionings and capabilities across the TP documentation of the two participating HEIs. In other words, the conceptions of a capable pre-service teacher are similar. Secondly, if social justice goals are to be realised, greater clarity of the valued functionings needs to be evident in the TP documentation. Thirdly, the valued functionings can be categorised into those that are foundational and those that promote a social justice agenda. Finally, in promoting a social justice agenda, there are functionings that ought to be valued by the HEIs that are seemingly not currently valued.
- Full Text:
- Date Issued: 2018
An investigation into the mathematics knowledge for teaching required to develop grade 2 learners’ number sense through counting
- Authors: Chikiwa, Samukeliso
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Number concept in children -- South Africa , Number concept -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6042 , vital:21019
- Description: Poor learner performance in mathematics has a long-standing record in South Africa. More than two decades after attainment of democracy South Africa is still seeking ways of addressing this crisis. Research around poor mathematics points to a number of factors, however, the dominant being that South African teachers lack both mathematics content and the pedagogical knowledge to teach it effectively. Ball, Thames and Phelps (2008) refer to the knowledge to teach mathematics effectively as Mathematics Knowledge for Teaching [MKfT]. MKfT combines the knowledge of both the content with the pedagogical skills. Mathematics teachers in South Africa are said to lack MKfT to teach mathematics in ways that enhance conceptual understanding and the effect of this deficiency is felt as far back in the education system as Foundation Phase. Research suggests Foundation Phase teachers do not develop the learners’ number sense well enough to equip them with essential mathematical strategies and proficiency that would help them learn mathematics with ease and understanding. This deficit expands as learners move up the grades. My qualitative research, case study approach was employed to investigate MKfT enacted in the teaching of an expert Foundation Phase teacher, which she used while developing number sense in her Grade Two learners. A key aim is to inform fellow Foundation Phase teachers and Foundation Phase teacher educators, both in-service and in-training, of the key aspects of MKfT required in developing number sense. The study found that Foundation Phase teaching requires employment of all the domains of the MKfT to develop number sense to Grade 2 learners. These domains are complexly interconnected and interdependent and the research shows that while one needs the full set to be able to teach effectively, the expertise becomes visible in the seamless and somewhat automated interweaving of these domains. Furthermore, the research will illuminate how such seamless and automated interweaving can render the individual domains difficult to discern.
- Full Text:
- Date Issued: 2017
- Authors: Chikiwa, Samukeliso
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Number concept in children -- South Africa , Number concept -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6042 , vital:21019
- Description: Poor learner performance in mathematics has a long-standing record in South Africa. More than two decades after attainment of democracy South Africa is still seeking ways of addressing this crisis. Research around poor mathematics points to a number of factors, however, the dominant being that South African teachers lack both mathematics content and the pedagogical knowledge to teach it effectively. Ball, Thames and Phelps (2008) refer to the knowledge to teach mathematics effectively as Mathematics Knowledge for Teaching [MKfT]. MKfT combines the knowledge of both the content with the pedagogical skills. Mathematics teachers in South Africa are said to lack MKfT to teach mathematics in ways that enhance conceptual understanding and the effect of this deficiency is felt as far back in the education system as Foundation Phase. Research suggests Foundation Phase teachers do not develop the learners’ number sense well enough to equip them with essential mathematical strategies and proficiency that would help them learn mathematics with ease and understanding. This deficit expands as learners move up the grades. My qualitative research, case study approach was employed to investigate MKfT enacted in the teaching of an expert Foundation Phase teacher, which she used while developing number sense in her Grade Two learners. A key aim is to inform fellow Foundation Phase teachers and Foundation Phase teacher educators, both in-service and in-training, of the key aspects of MKfT required in developing number sense. The study found that Foundation Phase teaching requires employment of all the domains of the MKfT to develop number sense to Grade 2 learners. These domains are complexly interconnected and interdependent and the research shows that while one needs the full set to be able to teach effectively, the expertise becomes visible in the seamless and somewhat automated interweaving of these domains. Furthermore, the research will illuminate how such seamless and automated interweaving can render the individual domains difficult to discern.
- Full Text:
- Date Issued: 2017
Why do learners and teachers experience problems with the concept of zero?
- Authors: Jooste, Zonia
- Date: 2012
- Subjects: Numbers, Divisibility of -- Study and teaching (Primary) -- South Africa Numbers, Divisibility of -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa -- Eastern Cape Mathematics teachers -- Training of -- South Africa -- Western Cape Education, Primary -- Curricula -- South Africa Education, Secondary -- Curricula -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1906 , http://hdl.handle.net/10962/d1006764
- Description: The controversy around the inclusion of zero in the number system has been widely documented. Influential mathematicians in various ancient cultures did not accept zero as a number. The idea of the empty set was too abstract and they could not conceptualise division by zero. Surprisingly, understanding of the concept is still a matter of concern today. In spite of expansive reports on and recommendations for developing conceptualisation of the concept, learners and teachers still experience problems similar to those that ancient mathematicians struggled with. The study was initiated by an observation of Grade 7 learners' inability to solve the problems 4 × 0 and 0 ÷ 7 effectively or at all. I investigated why Grade 3 to 6 learners and mathematics teachers on a BEd (in-service) course and an accredited ACE course experience problems with the concept of zero. I was especially interested in the understanding of multiplication and division by zero. I investigated teachers' knowledge of zero's characteristics as a number, the history of zero and how they teach the concept, in order to support my assumptions. The data production process was performed over a period of two years. It involved a multi-case opportunity sample approach embedded in the empirical field that formed the backdrop of my involvement as mathematics education specialist in schools in the Western and Eastern Cape. The interpretative orientation of the study allowed me to conduct inquiries that served to confirm or challenge my assumptions and enabled me to construct generalisations that depict learners' and teachers' knowledge construction. The qualitative data analysis informed the presentation and discussion of the findings. The single most important message conveyed to readers of this study is that the value of zero as a number, its importance in the number system, its properties and its behaviour in calculations, should not be underrated. Teaching of this abstract concept requires competent teachers who are able to mediate understanding in the most effective and innovative manner. Professional development programmes should orchestrate this competence and curriculum developers and textbook authors should acknowledge the significance of learning and teaching the concept of zero.
- Full Text:
- Date Issued: 2012
- Authors: Jooste, Zonia
- Date: 2012
- Subjects: Numbers, Divisibility of -- Study and teaching (Primary) -- South Africa Numbers, Divisibility of -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa -- Eastern Cape Mathematics teachers -- Training of -- South Africa -- Western Cape Education, Primary -- Curricula -- South Africa Education, Secondary -- Curricula -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1906 , http://hdl.handle.net/10962/d1006764
- Description: The controversy around the inclusion of zero in the number system has been widely documented. Influential mathematicians in various ancient cultures did not accept zero as a number. The idea of the empty set was too abstract and they could not conceptualise division by zero. Surprisingly, understanding of the concept is still a matter of concern today. In spite of expansive reports on and recommendations for developing conceptualisation of the concept, learners and teachers still experience problems similar to those that ancient mathematicians struggled with. The study was initiated by an observation of Grade 7 learners' inability to solve the problems 4 × 0 and 0 ÷ 7 effectively or at all. I investigated why Grade 3 to 6 learners and mathematics teachers on a BEd (in-service) course and an accredited ACE course experience problems with the concept of zero. I was especially interested in the understanding of multiplication and division by zero. I investigated teachers' knowledge of zero's characteristics as a number, the history of zero and how they teach the concept, in order to support my assumptions. The data production process was performed over a period of two years. It involved a multi-case opportunity sample approach embedded in the empirical field that formed the backdrop of my involvement as mathematics education specialist in schools in the Western and Eastern Cape. The interpretative orientation of the study allowed me to conduct inquiries that served to confirm or challenge my assumptions and enabled me to construct generalisations that depict learners' and teachers' knowledge construction. The qualitative data analysis informed the presentation and discussion of the findings. The single most important message conveyed to readers of this study is that the value of zero as a number, its importance in the number system, its properties and its behaviour in calculations, should not be underrated. Teaching of this abstract concept requires competent teachers who are able to mediate understanding in the most effective and innovative manner. Professional development programmes should orchestrate this competence and curriculum developers and textbook authors should acknowledge the significance of learning and teaching the concept of zero.
- Full Text:
- Date Issued: 2012
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