Integrating music and mathematics for connecting across multiple constructs of fractional understanding: an RME task design journey
- Authors: Lovemore, Tarryn Shirley
- Date: 2023-03-29
- Subjects: Communities of practice , Interdisciplinary approach in education , Fractions , Mathematics Study and teaching , Music in mathematics education , Number line
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/366200 , vital:65842 , DOI https://doi.org/10.21504/10962/366200
- Description: Two South African curricular aims: appreciating creativity in mathematics and developing conceptual understanding, motivated this study. Negative views towards mathematics and challenges in teaching and learning fractions at primary school level are reported in literature, with the part-whole construct of fractions often the sole teaching focus. Despite challenges in curriculum integration (high demands on teachers and diluting disciplines), benefits, such as motivation and creative thinking, are noted. I recognised music-mathematics integration as an opportune context for designing tasks to support learners in moving flexibly between the fraction as ratio, fraction as measure and part-whole constructs. Guided by Realistic Mathematics Education principles, I embarked on a participatory dual-design experiment in task design, grappling within three micro-Communities of Practice (micro-CoPs) and across two planes: the Design-Theorising Plane and the Grounded-Practice Plane. In the Design-Theorising Plane, I worked with my two doctoral supervisors, grappling with design obstacles and finding resolutions. COVID-19 restrictions shifted our meetings to online platforms, allowing documentation and analysis of the task design process through recording functions. In the Grounded-Practice Plane, I worked within two separate micro-CoPs, both at independent schools (eight and two participating teachers respectively). Data on the teachers’ interrogation and implementation of the designed tasks were obtained via formal and informal interviews. Their reflections informed ongoing adaptations to the task design. Data were analysed in a matrix I designed and via NVivo coding. Findings include both the product of the task design journey (eight music-mathematics lessons, resources, and representations) and the process (ten groupings of Obstacle-Resolution Cycles). Three key questions (relating to music-mathematics fidelity; to task simplification for implementation; and to appropriate music-mathematics representation) were used in addressing each Obstacle-Resolution Cycle. Designing tasks to teach the part-whole construct of fractions was relatively straightforward, but designing tasks to teach the fraction as ratio and fraction as measure constructs was more challenging. These constructs could not be conflated by superimposing the music and mathematical linear representations. Aligning them, however, allowed for moving flexibly between the constructs. The teachers reported that the integrated music-mathematics tasks and supporting resources enhanced their learners’ fractional problem-solving abilities, simultaneously promoting more positive learner dispositions towards mathematics. , Thesis (PhD) -- Faculty of Education, Education, 2023
- Full Text:
- Authors: Lovemore, Tarryn Shirley
- Date: 2023-03-29
- Subjects: Communities of practice , Interdisciplinary approach in education , Fractions , Mathematics Study and teaching , Music in mathematics education , Number line
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/366200 , vital:65842 , DOI https://doi.org/10.21504/10962/366200
- Description: Two South African curricular aims: appreciating creativity in mathematics and developing conceptual understanding, motivated this study. Negative views towards mathematics and challenges in teaching and learning fractions at primary school level are reported in literature, with the part-whole construct of fractions often the sole teaching focus. Despite challenges in curriculum integration (high demands on teachers and diluting disciplines), benefits, such as motivation and creative thinking, are noted. I recognised music-mathematics integration as an opportune context for designing tasks to support learners in moving flexibly between the fraction as ratio, fraction as measure and part-whole constructs. Guided by Realistic Mathematics Education principles, I embarked on a participatory dual-design experiment in task design, grappling within three micro-Communities of Practice (micro-CoPs) and across two planes: the Design-Theorising Plane and the Grounded-Practice Plane. In the Design-Theorising Plane, I worked with my two doctoral supervisors, grappling with design obstacles and finding resolutions. COVID-19 restrictions shifted our meetings to online platforms, allowing documentation and analysis of the task design process through recording functions. In the Grounded-Practice Plane, I worked within two separate micro-CoPs, both at independent schools (eight and two participating teachers respectively). Data on the teachers’ interrogation and implementation of the designed tasks were obtained via formal and informal interviews. Their reflections informed ongoing adaptations to the task design. Data were analysed in a matrix I designed and via NVivo coding. Findings include both the product of the task design journey (eight music-mathematics lessons, resources, and representations) and the process (ten groupings of Obstacle-Resolution Cycles). Three key questions (relating to music-mathematics fidelity; to task simplification for implementation; and to appropriate music-mathematics representation) were used in addressing each Obstacle-Resolution Cycle. Designing tasks to teach the part-whole construct of fractions was relatively straightforward, but designing tasks to teach the fraction as ratio and fraction as measure constructs was more challenging. These constructs could not be conflated by superimposing the music and mathematical linear representations. Aligning them, however, allowed for moving flexibly between the constructs. The teachers reported that the integrated music-mathematics tasks and supporting resources enhanced their learners’ fractional problem-solving abilities, simultaneously promoting more positive learner dispositions towards mathematics. , Thesis (PhD) -- Faculty of Education, Education, 2023
- Full Text:
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:
- 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:
An exploration of the mathematical learner identities of high school learners who participated in after school mathematics clubs in primary school
- Authors: Hokonya, Wellington Munetsi
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) South Africa , Mathematics Study and teaching (Elementary) Activity programs South Africa , Identity (Psychology) in children , After-school programs South Africa , School children Attitudes , Mathematics Study and teaching Psychological aspects South Africa , South African Numeracy Chair Project (SANCP)
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/189985 , vital:44953 , 10.21504/10962/189985
- Description: This study focuses on understanding mathematics learner identities of high school learners who participated in the South African Numeracy Chair Project after school mathematics clubs, an environment that afforded different mathematics identities from the traditional South African classroom. Mathematics learner identities feature prominently in current research on mathematics education because they affect whether and how learners engage in mathematics. They play a critical role in enhancing (or detracting from) learners’ attitudes, dispositions, emotional development, and general sense of self as they learn mathematics. Development of positive learner mathematical identity is therefore useful in making learners commit to their mathematics work. South African primary mathematics education is described as being in a state of crisis, and various programmes are being implemented to develop intervention models to improve quality and ensure the effective teaching and learning of primary mathematics. The South African Numeracy Chair Project initiative at Rhodes University provides for longitudinal research and development programmes with primary mathematics teachers and learners from previously disadvantaged schools, in order to find ways of mitigating the crisis. The after school mathematics clubs provide extra-curricular activities focused on developing a supportive learning community where learners’ active mathematical participation, engagement, enjoyment, and sense making are the focus. The clubs provide a supportive learning environment that is different to the traditional classroom and in which learners can participate actively and freely in mathematical activities. The study explores the nature of mathematics learner identities as learning trajectories that connect the past and future in negotiation of the present. It also seeks to discover how primary school club participation and experiences feature in the learners’ mathematical identities. The study employs two theoretical frameworks to analyse qualitative data that was gathered in the form of spoken and written stories, by 14 learners who participated in the after school mathematics clubs in primary school. The stories covered learners’ engagement in mathematics in different landscapes of practice that promoted the construction of different learner mathematical identities. A close analysis of the qualitative data revealed that learners’ mathematical identities are heavily influenced by the values that were foregrounded in the after school mathematics clubs. The clubs valued hard work and encouraged learners to ask for assistance when in doubt. In line with the club ethos, the learners storied resilience and hard work in their narratives. In addition, although many learners storied Mathematics as difficult in high school, they chose to continue taking the subject. , Thesis (PhD) -- Faculty of Education, Education, 2021
- Full Text:
- Authors: Hokonya, Wellington Munetsi
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) South Africa , Mathematics Study and teaching (Elementary) Activity programs South Africa , Identity (Psychology) in children , After-school programs South Africa , School children Attitudes , Mathematics Study and teaching Psychological aspects South Africa , South African Numeracy Chair Project (SANCP)
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/189985 , vital:44953 , 10.21504/10962/189985
- Description: This study focuses on understanding mathematics learner identities of high school learners who participated in the South African Numeracy Chair Project after school mathematics clubs, an environment that afforded different mathematics identities from the traditional South African classroom. Mathematics learner identities feature prominently in current research on mathematics education because they affect whether and how learners engage in mathematics. They play a critical role in enhancing (or detracting from) learners’ attitudes, dispositions, emotional development, and general sense of self as they learn mathematics. Development of positive learner mathematical identity is therefore useful in making learners commit to their mathematics work. South African primary mathematics education is described as being in a state of crisis, and various programmes are being implemented to develop intervention models to improve quality and ensure the effective teaching and learning of primary mathematics. The South African Numeracy Chair Project initiative at Rhodes University provides for longitudinal research and development programmes with primary mathematics teachers and learners from previously disadvantaged schools, in order to find ways of mitigating the crisis. The after school mathematics clubs provide extra-curricular activities focused on developing a supportive learning community where learners’ active mathematical participation, engagement, enjoyment, and sense making are the focus. The clubs provide a supportive learning environment that is different to the traditional classroom and in which learners can participate actively and freely in mathematical activities. The study explores the nature of mathematics learner identities as learning trajectories that connect the past and future in negotiation of the present. It also seeks to discover how primary school club participation and experiences feature in the learners’ mathematical identities. The study employs two theoretical frameworks to analyse qualitative data that was gathered in the form of spoken and written stories, by 14 learners who participated in the after school mathematics clubs in primary school. The stories covered learners’ engagement in mathematics in different landscapes of practice that promoted the construction of different learner mathematical identities. A close analysis of the qualitative data revealed that learners’ mathematical identities are heavily influenced by the values that were foregrounded in the after school mathematics clubs. The clubs valued hard work and encouraged learners to ask for assistance when in doubt. In line with the club ethos, the learners storied resilience and hard work in their narratives. In addition, although many learners storied Mathematics as difficult in high school, they chose to continue taking the subject. , Thesis (PhD) -- Faculty of Education, Education, 2021
- Full Text:
Investigating grade R teacher institutional identity presented in policy and expressed through narrative in a time of transition
- Authors: Long, Roxanne
- Date: 2021
- Subjects: Early childhood education -- South Africa , Early childhood education -- Government policy -- South Africa , Child development -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/171346 , vital:42051 , 10.21504/10962/171346
- Description: This study investigated Grade R (reception year) teacher institutional identity presented in policy and expressed through teacher narratives. The study was conducted in the context of a major national policy transition that involved the physical and contextual shift of Grade R out of the Early Childhood Development sector and into the formal schooling sector. This study highlighted the way in which this shift has resulted in mixed policy messages, which have implications for Grade R teachers’ institutional identities and learning trajectories across their landscapes of practice. The thesis begins by exploring the South African Education context in general as well as the Early Childhood Development context in particular. In order to understand the institutional identities of Grade R teachers as both storied by others (in policy) and by themselves, the study conducted a documentary analysis of policy relating to Grade R teachers and Grade R teacher narrative expressions of their identities. The methodological approach of the study involved a qualitative approach, drawing on grounded theory analytical techniques to closely examine policy documents and teacher generated data gathered through interviews and questionnaires. The study was guided by a sociocultural perspective and drew on three key sociocultural theorists whose work provided complementary perspectives on teacher identity. Sfard and Prusak’s (2005) operationalization of identity as narratives was used to define the unit of analysis for the study (i.e. identities as stories). Gee’s (2000) definition and conceptualization of institutional identity was supplemented with Wenger-Trayner, Fenton-O'Creevy, Hutchinson, Kubiak, and Wenger-Trayner’s (2015) notion of identity as journeying across landscapes of practice. This complementary framing allowed for focused and detailed analysis of policy documents and Grade R teacher identity stories. The study addresses the research gap of an under-representation of identity research in early childhood teacher education and particularly in the South African context. This study is significant as it is the first study of its kind to explore the importance of identity formation for Grade R teachers as newcomers to the formal schooling landscape. Findings from the policy analysis point to mixed messages moving across a spectrum of descriptors from the not yet qualified ‘mothers and ‘caregivers’ to qualified ‘specialised’ educators. These descriptors have implications for the differentiated roles and responsibilities (institutional identity) of Grade R teachers. The findings from teacher identity narratives highlighted tension in the navigation of the policy promoted institutional identities. Teacher narratives pointed to vastly contrasting experiences of teachers with specialised and qualified institutional teacher identities to those with not yet qualified institutional identities. For the former, there were high levels of confidence in their job security and in terms of recognition received from others. For the latter, however, there was vulnerability in terms of the stability of their jobs and remuneration as well as low levels of recognition from others. The study draws on the findings from the analysis to suggest recommendations for Grade R policy, Grade R teacher education (both inservice and pre-service); as well as Grade R professional development initiatives.
- Full Text:
- Authors: Long, Roxanne
- Date: 2021
- Subjects: Early childhood education -- South Africa , Early childhood education -- Government policy -- South Africa , Child development -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/171346 , vital:42051 , 10.21504/10962/171346
- Description: This study investigated Grade R (reception year) teacher institutional identity presented in policy and expressed through teacher narratives. The study was conducted in the context of a major national policy transition that involved the physical and contextual shift of Grade R out of the Early Childhood Development sector and into the formal schooling sector. This study highlighted the way in which this shift has resulted in mixed policy messages, which have implications for Grade R teachers’ institutional identities and learning trajectories across their landscapes of practice. The thesis begins by exploring the South African Education context in general as well as the Early Childhood Development context in particular. In order to understand the institutional identities of Grade R teachers as both storied by others (in policy) and by themselves, the study conducted a documentary analysis of policy relating to Grade R teachers and Grade R teacher narrative expressions of their identities. The methodological approach of the study involved a qualitative approach, drawing on grounded theory analytical techniques to closely examine policy documents and teacher generated data gathered through interviews and questionnaires. The study was guided by a sociocultural perspective and drew on three key sociocultural theorists whose work provided complementary perspectives on teacher identity. Sfard and Prusak’s (2005) operationalization of identity as narratives was used to define the unit of analysis for the study (i.e. identities as stories). Gee’s (2000) definition and conceptualization of institutional identity was supplemented with Wenger-Trayner, Fenton-O'Creevy, Hutchinson, Kubiak, and Wenger-Trayner’s (2015) notion of identity as journeying across landscapes of practice. This complementary framing allowed for focused and detailed analysis of policy documents and Grade R teacher identity stories. The study addresses the research gap of an under-representation of identity research in early childhood teacher education and particularly in the South African context. This study is significant as it is the first study of its kind to explore the importance of identity formation for Grade R teachers as newcomers to the formal schooling landscape. Findings from the policy analysis point to mixed messages moving across a spectrum of descriptors from the not yet qualified ‘mothers and ‘caregivers’ to qualified ‘specialised’ educators. These descriptors have implications for the differentiated roles and responsibilities (institutional identity) of Grade R teachers. The findings from teacher identity narratives highlighted tension in the navigation of the policy promoted institutional identities. Teacher narratives pointed to vastly contrasting experiences of teachers with specialised and qualified institutional teacher identities to those with not yet qualified institutional identities. For the former, there were high levels of confidence in their job security and in terms of recognition received from others. For the latter, however, there was vulnerability in terms of the stability of their jobs and remuneration as well as low levels of recognition from others. The study draws on the findings from the analysis to suggest recommendations for Grade R policy, Grade R teacher education (both inservice and pre-service); as well as Grade R professional development initiatives.
- Full Text:
Exploring pre-service teachers’ reflective practice in the context of video-based lesson analysis
- Authors: Chikiwa, Samukeliso
- Date: 2020-04-30
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/355357 , vital:64492
- Description: This study explored the development of reflective practice in foundation phase pre-service teachers in the context of video-based lesson analysis at a university in South Africa. The study was conducted in the field of mathematics education, responding to the urgent need to equip pre-service South African teachers with the knowledge and skills for effective mathematics teaching. The research is foregrounded by the continuing poor performance of South African learners in mathematics at all levels of education in the country, which has been linked to the inadequate knowledge and skills of mathematics teachers. Pre-service teacher education is putting considerable effort into improving the preparation of mathematics teachers and developing their ability to reflect on their teaching practice is one of the strategies being employed for this purpose. Research has demonstrated the importance of reflective practice (RP) in both developing and extending teachers’ mathematical knowledge for teaching. This study therefore contributes to current research that supports the development of RP as a professional skill for promoting the acquisition of knowledge for teaching in pre-service teacher education. The study adopted a qualitative case study approach with two phases of data collection. In Phase 1 I collected and analysed three sets of 19 pre-service teachers’ written reflections to establish the nature of the reflections that they developed when analysing video-recorded mathematics lessons of experienced teachers’ practice. Phase 2 was conducted with four PSTs who reflected on video-recorded mathematics lessons of their own practice, and similarly sought to investigate the nature of the reflections they developed when reflecting on practice. The four PSTs wrote one set of reflections on their own lessons, went through three sessions of facilitator-guided reflections, then wrote another set of reflections to establish if the support provided in small group facilitator-guided sessions improved their reflections. Iterative content analysis was employed to analyse the PSTs’ written reflections, using an analytic tool that I developed for this purpose through merging Lee’s (2007) and Muir and Beswick’s (2007) levels of reflection frameworks. My model had four levels of reflection: description, explanation, suggestion and reflectivity. The names of each of the levels connect to the key indicator for that level. PSTs’ written reflections were coded and analysed according to these levels. The study found that PSTs’ initial reflections were mostly description of general classroom events with little reflection at the levels of explanation and suggestion, and an absence of reflectivity. Most reflections focused on general events in the lesson rather than mathematical events, even though the six lens framework they were given to guide their reflections prompted them to steer their attention towards mathematical events. The second and third sets of reflections, although mostly still at level 1, showed some shifts towards explanation and suggestion, although an increased focus on mathematical events though reflectivity was still largely absent. No PST reached the fourth level of reflectivity in Phase 1. However, in Phase 2, the PSTs’ reflections after the three small group facilitator-guided sessions included some evidence of reflectivity. The findings suggest the need for pre-service teacher educators to make a concerted effort to teach PSTs what reflection is and how to reflect on their practice. The findings also showed the need for small group facilitator-guided support in the development of PSTs’ reflective practice. , Thesis (PhD) -- Faculty of Education, Education, 2020
- Full Text:
- Authors: Chikiwa, Samukeliso
- Date: 2020-04-30
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/355357 , vital:64492
- Description: This study explored the development of reflective practice in foundation phase pre-service teachers in the context of video-based lesson analysis at a university in South Africa. The study was conducted in the field of mathematics education, responding to the urgent need to equip pre-service South African teachers with the knowledge and skills for effective mathematics teaching. The research is foregrounded by the continuing poor performance of South African learners in mathematics at all levels of education in the country, which has been linked to the inadequate knowledge and skills of mathematics teachers. Pre-service teacher education is putting considerable effort into improving the preparation of mathematics teachers and developing their ability to reflect on their teaching practice is one of the strategies being employed for this purpose. Research has demonstrated the importance of reflective practice (RP) in both developing and extending teachers’ mathematical knowledge for teaching. This study therefore contributes to current research that supports the development of RP as a professional skill for promoting the acquisition of knowledge for teaching in pre-service teacher education. The study adopted a qualitative case study approach with two phases of data collection. In Phase 1 I collected and analysed three sets of 19 pre-service teachers’ written reflections to establish the nature of the reflections that they developed when analysing video-recorded mathematics lessons of experienced teachers’ practice. Phase 2 was conducted with four PSTs who reflected on video-recorded mathematics lessons of their own practice, and similarly sought to investigate the nature of the reflections they developed when reflecting on practice. The four PSTs wrote one set of reflections on their own lessons, went through three sessions of facilitator-guided reflections, then wrote another set of reflections to establish if the support provided in small group facilitator-guided sessions improved their reflections. Iterative content analysis was employed to analyse the PSTs’ written reflections, using an analytic tool that I developed for this purpose through merging Lee’s (2007) and Muir and Beswick’s (2007) levels of reflection frameworks. My model had four levels of reflection: description, explanation, suggestion and reflectivity. The names of each of the levels connect to the key indicator for that level. PSTs’ written reflections were coded and analysed according to these levels. The study found that PSTs’ initial reflections were mostly description of general classroom events with little reflection at the levels of explanation and suggestion, and an absence of reflectivity. Most reflections focused on general events in the lesson rather than mathematical events, even though the six lens framework they were given to guide their reflections prompted them to steer their attention towards mathematical events. The second and third sets of reflections, although mostly still at level 1, showed some shifts towards explanation and suggestion, although an increased focus on mathematical events though reflectivity was still largely absent. No PST reached the fourth level of reflectivity in Phase 1. However, in Phase 2, the PSTs’ reflections after the three small group facilitator-guided sessions included some evidence of reflectivity. The findings suggest the need for pre-service teacher educators to make a concerted effort to teach PSTs what reflection is and how to reflect on their practice. The findings also showed the need for small group facilitator-guided support in the development of PSTs’ reflective practice. , Thesis (PhD) -- Faculty of Education, Education, 2020
- Full Text:
Enriching my teaching around the inverse order relationship in unit fractions at the Grade 5 level through the inclusion of musical activities: an action research case study
- Authors: Lovemore, Tarryn Shirley
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Interdisciplinary approach in education -- South Africa -- Case studies , Music -- Study and teaching (Elementary) -- South Africa -- Case studies , Music -- Mathematics , Musical notation -- Study and teaching (Elementary)
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/142431 , vital:38079
- Description: This research study explored how the use of musical activities, specifically based on note values, might enrich my teaching around the inverse order relation of unit fractions in my Grade 5 mathematics classroom. Much research has identified fractions as a problematic concept to teach in primary schools. Curriculum expectations of mathematics and music, as well as prior research, recognise a link between these two subject areas. Based on these connections between mathematics and music, I make the case for further research into practical ways in which music and mathematics can be integrated to support teaching and learning in the South African context. This study is located within a qualitative and interpretive framework. The concepts of integration, learning style theory, Gardner’s multiple intelligences and Bresler’s styles of arts integration guide the research. I made use of practical and theoretical activities relating to note values in music. I explored these strategies and the use of learning support materials through an action research case study, in which I engaged in cycles of trialing, reflecting, adjusting and re-trialing within the ‘case’ of my own mathematics class. Data sources comprised of my reflective journal, learner feedback, video- and audio-recorded lessons, examples of learners’ work and interviews with critical peers who observed critical moments from the video recordings. I was guided through the analysis phase by two analytical frameworks: Karsenty and Arcavi’s Six Lense Framework (SLF) and Adler and Ronda’s Mathematics Discourse in Instruction (MDI) framework which I adapted. Using three key lessons, I provide detailed descriptions of how the lessons progressed and then identify and discuss some of the key findings and recurring themes in relation to my study’s research question and goals. Through this process, I show that my integration of mathematics and musical activities helped promote active engagement amongst learners and provided them with co-equivalent opportunities to appreciate the importance of note values in music, and relate this back to understandings around the inverse order relation of unit fractions.
- Full Text:
- Authors: Lovemore, Tarryn Shirley
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Interdisciplinary approach in education -- South Africa -- Case studies , Music -- Study and teaching (Elementary) -- South Africa -- Case studies , Music -- Mathematics , Musical notation -- Study and teaching (Elementary)
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/142431 , vital:38079
- Description: This research study explored how the use of musical activities, specifically based on note values, might enrich my teaching around the inverse order relation of unit fractions in my Grade 5 mathematics classroom. Much research has identified fractions as a problematic concept to teach in primary schools. Curriculum expectations of mathematics and music, as well as prior research, recognise a link between these two subject areas. Based on these connections between mathematics and music, I make the case for further research into practical ways in which music and mathematics can be integrated to support teaching and learning in the South African context. This study is located within a qualitative and interpretive framework. The concepts of integration, learning style theory, Gardner’s multiple intelligences and Bresler’s styles of arts integration guide the research. I made use of practical and theoretical activities relating to note values in music. I explored these strategies and the use of learning support materials through an action research case study, in which I engaged in cycles of trialing, reflecting, adjusting and re-trialing within the ‘case’ of my own mathematics class. Data sources comprised of my reflective journal, learner feedback, video- and audio-recorded lessons, examples of learners’ work and interviews with critical peers who observed critical moments from the video recordings. I was guided through the analysis phase by two analytical frameworks: Karsenty and Arcavi’s Six Lense Framework (SLF) and Adler and Ronda’s Mathematics Discourse in Instruction (MDI) framework which I adapted. Using three key lessons, I provide detailed descriptions of how the lessons progressed and then identify and discuss some of the key findings and recurring themes in relation to my study’s research question and goals. Through this process, I show that my integration of mathematics and musical activities helped promote active engagement amongst learners and provided them with co-equivalent opportunities to appreciate the importance of note values in music, and relate this back to understandings around the inverse order relation of unit fractions.
- Full Text:
Investigating the nature of grade six after school mathematics club learners’ shifts in mathematical number sense and procedural fluency
- Authors: Baart, Noluntu Via
- Date: 2019
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Numeracy -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96825 , vital:31326
- Description: A wide range of research locally points to intermediate phase learners having extremely weak basic number sense resulting in the dominance of inefficient strategies for calculations with the four operations, irrespective of the number range. The grade six Annual National Assessments (ANA) diagnostic reports for 2012 to 2014 also point to errors and misconceptions that tend to dominate learners’ computations in the four basic operations; such errors are often attributed to the use of either tallies or incorrectly applied mathematical procedures. Having the above context in mind and following informal conversations with teachers in the Uitenhage Education District, five teachers expressed an interest in running the afterschool mathematics clubs based on the South African Numeracy Chair (SANC) project model. The SANC project team ran workshops in April, May and June 2016 with nine teachers (five as facilitators and four others as co-facilitators in five different club sites) in which teachers were provided with key resources for use in their clubs. Fifteen club sessions ran in each club with grade six learners across the 2nd and 3rd terms. These clubs form the empirical field for this research, which aims to investigate the nature of learners’ evolving number sense, procedural fluency and teachers’ experiences of working with learners in the club space. The unit of analysis in this study is both the shifts evident in learners’ number sense and procedural fluency as a result of participating in the clubs and the teacher’s experiences of working with learners in those clubs as club facilitators. A social constructivist perspective of learning guides this study. Especially Vygotsky’s (1978) notion that cognitive development stems from social interactions and guided learning within the Zone of Proximal Development (ZPD) of children, guided by more knowledgeable others. Furthermore, Kilpatrick et al.’s (2001) strands of mathematical proficiency provide the conceptual frame with a particular focus on procedural fluency and number sense. A mixed method approach to data collection was used. Quantitative data has been drawn from learner’s scores on pre- and post- assessments on four basic operations. Visual progression spectra have been adopted from the Pushing for Progression (PfP) Programme which is an intervention Programme developed by the SANC project for club facilitators. They provide explanations of learner progression trajectories and how to analyse learner methods. Qualitative narratives were drawn from learner progression data, as well as teacher post club questionnaires and one-to-one teacher interviews. The findings of this research suggest that learner workings when used in conjunction with visual progression spectra can provide important clues to researchers and teachers. This in turn contributes to an understanding of where learners are in their mathematical learning and gives ideas for how to support learners to progress using more flexible methods of calculation, particularly for poor performing learners. Included, is the discussion of the effectiveness of the club space to enable such shifts and improve learner flexibility, fluency and performance as displayed in learner methods and scores of the pre- and post- assessments. The teachers’ observations about the relaxed atmosphere in the club space, small sized groups, learning through play with co-members may have enabled the shifts in procedural fluency and number sense in club learners. Additionally, implications of the study are discussed, and tentative recommendations are made for the DBE to consider.
- Full Text:
- Authors: Baart, Noluntu Via
- Date: 2019
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Numeracy -- South Africa
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96825 , vital:31326
- Description: A wide range of research locally points to intermediate phase learners having extremely weak basic number sense resulting in the dominance of inefficient strategies for calculations with the four operations, irrespective of the number range. The grade six Annual National Assessments (ANA) diagnostic reports for 2012 to 2014 also point to errors and misconceptions that tend to dominate learners’ computations in the four basic operations; such errors are often attributed to the use of either tallies or incorrectly applied mathematical procedures. Having the above context in mind and following informal conversations with teachers in the Uitenhage Education District, five teachers expressed an interest in running the afterschool mathematics clubs based on the South African Numeracy Chair (SANC) project model. The SANC project team ran workshops in April, May and June 2016 with nine teachers (five as facilitators and four others as co-facilitators in five different club sites) in which teachers were provided with key resources for use in their clubs. Fifteen club sessions ran in each club with grade six learners across the 2nd and 3rd terms. These clubs form the empirical field for this research, which aims to investigate the nature of learners’ evolving number sense, procedural fluency and teachers’ experiences of working with learners in the club space. The unit of analysis in this study is both the shifts evident in learners’ number sense and procedural fluency as a result of participating in the clubs and the teacher’s experiences of working with learners in those clubs as club facilitators. A social constructivist perspective of learning guides this study. Especially Vygotsky’s (1978) notion that cognitive development stems from social interactions and guided learning within the Zone of Proximal Development (ZPD) of children, guided by more knowledgeable others. Furthermore, Kilpatrick et al.’s (2001) strands of mathematical proficiency provide the conceptual frame with a particular focus on procedural fluency and number sense. A mixed method approach to data collection was used. Quantitative data has been drawn from learner’s scores on pre- and post- assessments on four basic operations. Visual progression spectra have been adopted from the Pushing for Progression (PfP) Programme which is an intervention Programme developed by the SANC project for club facilitators. They provide explanations of learner progression trajectories and how to analyse learner methods. Qualitative narratives were drawn from learner progression data, as well as teacher post club questionnaires and one-to-one teacher interviews. The findings of this research suggest that learner workings when used in conjunction with visual progression spectra can provide important clues to researchers and teachers. This in turn contributes to an understanding of where learners are in their mathematical learning and gives ideas for how to support learners to progress using more flexible methods of calculation, particularly for poor performing learners. Included, is the discussion of the effectiveness of the club space to enable such shifts and improve learner flexibility, fluency and performance as displayed in learner methods and scores of the pre- and post- assessments. The teachers’ observations about the relaxed atmosphere in the club space, small sized groups, learning through play with co-members may have enabled the shifts in procedural fluency and number sense in club learners. Additionally, implications of the study are discussed, and tentative recommendations are made for the DBE to consider.
- Full Text:
Researching the development of a programme that merges mathematics and music in Grade R
- Authors: Stevenson-Milln, Carolyn
- Date: 2018
- Subjects: Mathematics Study and teaching (Elementary) Activity programs , Music and children , Music, Influence of , Music Africa , Action research in education
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/61928 , vital:28084
- Description: This small-scale case study explores the potential for synergy between music and mathematics learning in early childhood education whereby music can be used to help enhance children’s mathematical proficiency. Informal observations of the young learners participating in an Early Number Fun programme initiated by the South African Numeracy Chair Project suggested that many children struggled to exercise executive functioning and self-regulated skills, and struggled also with fluency in basic numeracy concepts such as understanding pattern. This case study was set up to investigate the effect of the development and implementation of a programme in which African music and mathematics learning, (particularly in relation to pattern and sequencing) were blended. The study’s core aim was to contribute to strengthening learners’ executive function and self-regulated learning competencies, both of which are important to learners’ developing agency over their own learning. An Action-Research-embedded-in-Design-Research approach was employed. This allowed an iterative process in developing a new mode of learning through blending music and mathematics. The theory of enactivism provided a theoretical framework to the study. The basic assumptions of an enactive perspective are shared understanding and joint action through engagement (as exemplified through group interaction between learner and teacher, and learning through action). The programme was developed and implemented with ongoing refinements in two Grade R classrooms. Data collected through observation, interviewing, document analysis and the keeping of a reflective research journal, are qualitative in nature. Analysis of the data indicate that the use of African block notation, as a rhythmic medium was well within reach of the participating children, such that at the end of each 16 session intervention programme, learners at both research sites demonstrated their capacity to: • Focus their attention on one activity while a different activity was taking place alongside them. • Watch, listen and only then act. • Practise their numbers through play: to count out and to write up to 16 and beyond. • Notate, read and interpret rhythmic patterns through block notation and instrumentation. The findings suggest the intervention programme could be continued over a longer period for maximum benefit, possibly through following Grade R learners through to Grade 1. The findings further suggest that fun with rhythmic, number-based patterning can assist learners’ development of executive function and self-regulated learning skills.
- Full Text:
- Authors: Stevenson-Milln, Carolyn
- Date: 2018
- Subjects: Mathematics Study and teaching (Elementary) Activity programs , Music and children , Music, Influence of , Music Africa , Action research in education
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/61928 , vital:28084
- Description: This small-scale case study explores the potential for synergy between music and mathematics learning in early childhood education whereby music can be used to help enhance children’s mathematical proficiency. Informal observations of the young learners participating in an Early Number Fun programme initiated by the South African Numeracy Chair Project suggested that many children struggled to exercise executive functioning and self-regulated skills, and struggled also with fluency in basic numeracy concepts such as understanding pattern. This case study was set up to investigate the effect of the development and implementation of a programme in which African music and mathematics learning, (particularly in relation to pattern and sequencing) were blended. The study’s core aim was to contribute to strengthening learners’ executive function and self-regulated learning competencies, both of which are important to learners’ developing agency over their own learning. An Action-Research-embedded-in-Design-Research approach was employed. This allowed an iterative process in developing a new mode of learning through blending music and mathematics. The theory of enactivism provided a theoretical framework to the study. The basic assumptions of an enactive perspective are shared understanding and joint action through engagement (as exemplified through group interaction between learner and teacher, and learning through action). The programme was developed and implemented with ongoing refinements in two Grade R classrooms. Data collected through observation, interviewing, document analysis and the keeping of a reflective research journal, are qualitative in nature. Analysis of the data indicate that the use of African block notation, as a rhythmic medium was well within reach of the participating children, such that at the end of each 16 session intervention programme, learners at both research sites demonstrated their capacity to: • Focus their attention on one activity while a different activity was taking place alongside them. • Watch, listen and only then act. • Practise their numbers through play: to count out and to write up to 16 and beyond. • Notate, read and interpret rhythmic patterns through block notation and instrumentation. The findings suggest the intervention programme could be continued over a longer period for maximum benefit, possibly through following Grade R learners through to Grade 1. The findings further suggest that fun with rhythmic, number-based patterning can assist learners’ development of executive function and self-regulated learning skills.
- Full Text:
The place of language in supporting children’s mathematical development: two Grade 4 teachers’ use of classroom talk
- Authors: Robertson, Sally-Ann, 1952-
- Date: 2018
- Subjects: Mathematics Study and teaching (Elementary) South Africa , Multilingual education South Africa , Language and education South Africa , Translanguaging (Linguistics) , Language policy South Africa
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/62072 , vital:28104
- Description: Measures of mathematics achievement (documented locally, and in internationally comparative terms) have shown that South African learners whose first language (L1) is different from their language of learning and teaching (LoLT) are at a significant disadvantage, most particularly learners from vulnerable or marginalised communities. This transdisciplinary case study looks at two experienced Grade 4 teachers’ mathematics classroom talk practices. It is situated within a second language (L2) teaching/learning context in which teachers and learners share the same first language, but mathematics learning and teaching takes place officially through an L2 (English). The study is located within a qualitative and interpretive framework. It brings together insights from a range of distinct but complementary theoretical disciplines in its analysis of the empirical classroom observation and interview data. Its theoretical framing derives initially from professional literature relating to L2 teaching and learning. This is then embedded within a broader theoretical frame deriving from the work of Vygotsky, Bernstein and Halliday, each of whom has focussed on the centrality of language to the teaching/ learning process, as well as contributed to a heightened appreciation of socio-cultural influences on learners’ meaning-making processes. The study illuminates some of the linguistic challenges to L2 children’s maximal participation in the learning of school mathematics. It points too to the significant challenge many South African mathematics teachers face in trying to meet curriculum coverage and pacing demands, while simultaneously facilitating their learners’ ongoing induction – in and through L2 predominantly – into mathematically-appropriate discourse. Grade 4 is a year in which such challenges are often more acutely felt. Independently of the transition across to an L2 for the majority of South African learners, this is the year also where - relative to the foundation phase years - learners encounter an expansion of knowledge areas and more specialised academic text. Many learners struggle to adjust to these higher conceptual and linguistic demands, often leading to what has been termed a ‘fourth-grade slump’. The study highlights the need for more sustained and proactive challenging of perceptions that English as LoLT is the obvious route to educational - and subsequent economic - opportunity. Recognition of the consequences deriving from the choice of English as the main LoLT for mathematics teaching and learning could help counterbalance deficit discourses implicating poor teaching as a major contributor to South Africa’s poor mathematics education outcomes. The study highlights further that, if language is genuinely to be used as the ‘tool’ for learning it is claimed to be, synergistic opportunities for the dovetailing of insights into L2 learners’ literacy/ numeracy development require further exploration. It points to the need for ongoing professional development support for teachers of mathematics (at both pre- and in-service levels) that focuses on broadening and deepening their understandings around the linguistic, and hence epistemological, consequences of learning mathematics through an L2. Expanding mathematics teachers’ repertoires of strategies for supporting learners’ developing cognitive academic language proficiency (CALP) in mathematics (in both L1 and L2) would involve a conception of ‘academic language’ in mathematics which goes beyond a constrained interpretation of ‘legitimate’ mathematical text as that which is in texts such as curriculum documents and text books. Especially important here are strategies which foreground the value of classroom talk in assisting L2 children towards becoming more confident, competent and explorative bilingual learners, and thereby, more active agents of their own mathematical meaning-making processes. The study argues that such meaning-making processes would be further strengthened were additive bilingualism (in place of current predominantly subtractive practices) to be genuinely taken up as core to any teaching and learning of mathematics in contexts such as those described in this case study.
- Full Text:
- Authors: Robertson, Sally-Ann, 1952-
- Date: 2018
- Subjects: Mathematics Study and teaching (Elementary) South Africa , Multilingual education South Africa , Language and education South Africa , Translanguaging (Linguistics) , Language policy South Africa
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/62072 , vital:28104
- Description: Measures of mathematics achievement (documented locally, and in internationally comparative terms) have shown that South African learners whose first language (L1) is different from their language of learning and teaching (LoLT) are at a significant disadvantage, most particularly learners from vulnerable or marginalised communities. This transdisciplinary case study looks at two experienced Grade 4 teachers’ mathematics classroom talk practices. It is situated within a second language (L2) teaching/learning context in which teachers and learners share the same first language, but mathematics learning and teaching takes place officially through an L2 (English). The study is located within a qualitative and interpretive framework. It brings together insights from a range of distinct but complementary theoretical disciplines in its analysis of the empirical classroom observation and interview data. Its theoretical framing derives initially from professional literature relating to L2 teaching and learning. This is then embedded within a broader theoretical frame deriving from the work of Vygotsky, Bernstein and Halliday, each of whom has focussed on the centrality of language to the teaching/ learning process, as well as contributed to a heightened appreciation of socio-cultural influences on learners’ meaning-making processes. The study illuminates some of the linguistic challenges to L2 children’s maximal participation in the learning of school mathematics. It points too to the significant challenge many South African mathematics teachers face in trying to meet curriculum coverage and pacing demands, while simultaneously facilitating their learners’ ongoing induction – in and through L2 predominantly – into mathematically-appropriate discourse. Grade 4 is a year in which such challenges are often more acutely felt. Independently of the transition across to an L2 for the majority of South African learners, this is the year also where - relative to the foundation phase years - learners encounter an expansion of knowledge areas and more specialised academic text. Many learners struggle to adjust to these higher conceptual and linguistic demands, often leading to what has been termed a ‘fourth-grade slump’. The study highlights the need for more sustained and proactive challenging of perceptions that English as LoLT is the obvious route to educational - and subsequent economic - opportunity. Recognition of the consequences deriving from the choice of English as the main LoLT for mathematics teaching and learning could help counterbalance deficit discourses implicating poor teaching as a major contributor to South Africa’s poor mathematics education outcomes. The study highlights further that, if language is genuinely to be used as the ‘tool’ for learning it is claimed to be, synergistic opportunities for the dovetailing of insights into L2 learners’ literacy/ numeracy development require further exploration. It points to the need for ongoing professional development support for teachers of mathematics (at both pre- and in-service levels) that focuses on broadening and deepening their understandings around the linguistic, and hence epistemological, consequences of learning mathematics through an L2. Expanding mathematics teachers’ repertoires of strategies for supporting learners’ developing cognitive academic language proficiency (CALP) in mathematics (in both L1 and L2) would involve a conception of ‘academic language’ in mathematics which goes beyond a constrained interpretation of ‘legitimate’ mathematical text as that which is in texts such as curriculum documents and text books. Especially important here are strategies which foreground the value of classroom talk in assisting L2 children towards becoming more confident, competent and explorative bilingual learners, and thereby, more active agents of their own mathematical meaning-making processes. The study argues that such meaning-making processes would be further strengthened were additive bilingualism (in place of current predominantly subtractive practices) to be genuinely taken up as core to any teaching and learning of mathematics in contexts such as those described in this case study.
- Full Text:
Adaptation of the mathematics recovery programme to facilitate progression in the early arithmetic strategies of Grade 2 learners in Zambia
- Authors: Young, Catherine
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- Zambia Arithmetic -- Study and teaching (Elementary) -- Zambia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/4977 , vital:20749
- Description: Research indicates that many children finish primary school in Southern Africa still reliant on inefficient counting strategies. This study extends the research of the South African Numeracy Chair project to early mathematics intervention with Grade 2 learners. It investigated the possible adaptation of the Mathematics Recovery programme to facilitate learner progression in early arithmetic strategies. This study aimed to investigate the possibility of adapting the Mathematics Recovery programme for use in a whole class setting, and to research the effectiveness of such an adapted programme. This study also aimed to investigate the extent of the phenomenon of unit counting and other early arithmetic strategies used in the early years in Zambia. This study was conducted from an emergent perspective. A review of the literature indicated that children who become stuck using unit counting face later mathematical difficulties, and that teacher over-emphasis on unit counting in the early years of schooling may be a contributing factor. This study used a qualitative design research methodology that consisted of a preparation phase, teaching experiment and retrospective analysis. The context of this teaching experiment was a seven week after-school intervention with a class of Grade 2 learners aged seven to eight in a rural Zambian primary school. Data collection and analysis focused on video recordings of a sample of 6 learners. The experimental teaching content focused on the Early Arithmetic Strategies aspect of the Mathematics Recovery programme. Although limited by time and research focus, this study found that all learners made some progress in early arithmetic strategies, and indicates that the Mathematics Recovery programme has potential for adaptation for early intervention in whole class teaching to address the mathematical education challenges in Zambia and beyond. This study also found that unit counting predominated in the sample learners, but that strategies were not yet entrenched, indicating this was a suitable age for early intervention. This study makes methodological contributions to a growing body of research into the adaptation of the Mathematics Recovery in Southern African contexts and suggests avenues for possible further research.
- Full Text:
- Authors: Young, Catherine
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- Zambia Arithmetic -- Study and teaching (Elementary) -- Zambia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/4977 , vital:20749
- Description: Research indicates that many children finish primary school in Southern Africa still reliant on inefficient counting strategies. This study extends the research of the South African Numeracy Chair project to early mathematics intervention with Grade 2 learners. It investigated the possible adaptation of the Mathematics Recovery programme to facilitate learner progression in early arithmetic strategies. This study aimed to investigate the possibility of adapting the Mathematics Recovery programme for use in a whole class setting, and to research the effectiveness of such an adapted programme. This study also aimed to investigate the extent of the phenomenon of unit counting and other early arithmetic strategies used in the early years in Zambia. This study was conducted from an emergent perspective. A review of the literature indicated that children who become stuck using unit counting face later mathematical difficulties, and that teacher over-emphasis on unit counting in the early years of schooling may be a contributing factor. This study used a qualitative design research methodology that consisted of a preparation phase, teaching experiment and retrospective analysis. The context of this teaching experiment was a seven week after-school intervention with a class of Grade 2 learners aged seven to eight in a rural Zambian primary school. Data collection and analysis focused on video recordings of a sample of 6 learners. The experimental teaching content focused on the Early Arithmetic Strategies aspect of the Mathematics Recovery programme. Although limited by time and research focus, this study found that all learners made some progress in early arithmetic strategies, and indicates that the Mathematics Recovery programme has potential for adaptation for early intervention in whole class teaching to address the mathematical education challenges in Zambia and beyond. This study also found that unit counting predominated in the sample learners, but that strategies were not yet entrenched, indicating this was a suitable age for early intervention. This study makes methodological contributions to a growing body of research into the adaptation of the Mathematics Recovery in Southern African contexts and suggests avenues for possible further research.
- Full Text:
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:
- 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:
The emergence and expression of teachers’ identities in teaching foundation phase mathematics
- Authors: Westaway, Lise
- Date: 2017
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/7000 , vital:21208
- Description: The assertion that learner performance in South African schools is in crisis may be cliched but it is certainly true. The majority of learners in the schooling system are not achieving the required outcomes, particularly in language and mathematics. I use the underperformance of learners in mathematics as the impetus for my research which seeks to understand how teachers’ identities emerge and are expressed in teaching Foundation Phase mathematics. The research contributes to an emerging scholarship that strives to explain underperformance and quality in mathematics classrooms beyond structuralist theorising. Recently research, particularly in South Africa, has begun to look more closely at who the teacher is and how the teacher is key in understanding what happens in the mathematics classroom. This emerging scholarship focuses on teacher identities. Research that foregrounds teacher identities within the field of mathematics education tends to be situated within a social constructionist orientation, which assumes that our knowledge of self and the world comes from our interactions with people and not some ‘objective’ reality (Berger & Luckman, 1966). Such a perspective appears to conflate questions of how we know something with what is. In other words, it elides structure and agency, thereby making research that seeks to examine the interplay between the two in the formation and expression of teachers’ identities, practically impossible. It is for this reason, as well as the need to move beyond the hermeneutic, that my research draws on Margaret Archer’s (1995, 1996, 2000) social realist framework. Social realism posits a relativist epistemology but a realist ontology. It is underpinned by the notion of a stratified reality with structural mechanisms giving rise to events in the world whether we experience them or not. It is only through the (inter)actions of persons that such mechanisms have the tendential power to constrain or enable the projects of persons. As such, my research seeks to identify the structural and agential mechanisms that give rise to teachers’ identities and how these identities are expressed in teaching Foundation Phase mathematics. In my research, teacher identity refers to the manner in which teachers express their social roles as teachers. In the research I use a case study methodology. I provide rich data on four isiXhosa teachers teaching in low socio-economic status schools. This data is gleaned through interviews and classroom based observations which were recorded as field notes and video transcripts. Analysis of the data occurs through the thought processes of abduction and retroduction (Danermark, Ekstrom, Jakobsen, & Karlsson, 2002). These thought process enable me to (re)describe and (re)contextualise the object of study. Through the process of asking transfactual questions I identify the structural, cultural and agential mechanisms giving rise to teachers’ identities and their expression in teaching foundation phase mathematics. There are three significant findings in my research. Firstly, research that attempts to understand the emergence and expression of teacher identities should consider their broad contextual realities. The historical, economic, social and political contexts in which the teachers are born and live, influences their sense of self, personal identities and social identities (teacher identities) and as such, influences their decision to become teachers and how they express their roles as teachers of Foundation Phase mathematics. Secondly, my research suggests that teachers’ mode of reflexivity is key to understanding the decisions that they make in the classroom and how they deal with the structures that condition the manner in which they express their roles as teachers. Thirdly, collective agency is necessary to bring about change in the way in which teachers express their roles in teaching Foundation Phase mathematics. My research produces new knowledge by examining the interplay of structure, culture and agency in the constitution of foundation phase teachers’ identities and their expression in teaching foundation phase mathematics. I use a social realist orientation to examine this interplay and provide an understanding of the mechanisms giving rise to the phenomenon under consideration. In this way I contribute to the extensive research on learner underperformance by focusing more explicitly on who the teacher is in the classroom.
- Full Text:
- Authors: Westaway, Lise
- Date: 2017
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/7000 , vital:21208
- Description: The assertion that learner performance in South African schools is in crisis may be cliched but it is certainly true. The majority of learners in the schooling system are not achieving the required outcomes, particularly in language and mathematics. I use the underperformance of learners in mathematics as the impetus for my research which seeks to understand how teachers’ identities emerge and are expressed in teaching Foundation Phase mathematics. The research contributes to an emerging scholarship that strives to explain underperformance and quality in mathematics classrooms beyond structuralist theorising. Recently research, particularly in South Africa, has begun to look more closely at who the teacher is and how the teacher is key in understanding what happens in the mathematics classroom. This emerging scholarship focuses on teacher identities. Research that foregrounds teacher identities within the field of mathematics education tends to be situated within a social constructionist orientation, which assumes that our knowledge of self and the world comes from our interactions with people and not some ‘objective’ reality (Berger & Luckman, 1966). Such a perspective appears to conflate questions of how we know something with what is. In other words, it elides structure and agency, thereby making research that seeks to examine the interplay between the two in the formation and expression of teachers’ identities, practically impossible. It is for this reason, as well as the need to move beyond the hermeneutic, that my research draws on Margaret Archer’s (1995, 1996, 2000) social realist framework. Social realism posits a relativist epistemology but a realist ontology. It is underpinned by the notion of a stratified reality with structural mechanisms giving rise to events in the world whether we experience them or not. It is only through the (inter)actions of persons that such mechanisms have the tendential power to constrain or enable the projects of persons. As such, my research seeks to identify the structural and agential mechanisms that give rise to teachers’ identities and how these identities are expressed in teaching Foundation Phase mathematics. In my research, teacher identity refers to the manner in which teachers express their social roles as teachers. In the research I use a case study methodology. I provide rich data on four isiXhosa teachers teaching in low socio-economic status schools. This data is gleaned through interviews and classroom based observations which were recorded as field notes and video transcripts. Analysis of the data occurs through the thought processes of abduction and retroduction (Danermark, Ekstrom, Jakobsen, & Karlsson, 2002). These thought process enable me to (re)describe and (re)contextualise the object of study. Through the process of asking transfactual questions I identify the structural, cultural and agential mechanisms giving rise to teachers’ identities and their expression in teaching foundation phase mathematics. There are three significant findings in my research. Firstly, research that attempts to understand the emergence and expression of teacher identities should consider their broad contextual realities. The historical, economic, social and political contexts in which the teachers are born and live, influences their sense of self, personal identities and social identities (teacher identities) and as such, influences their decision to become teachers and how they express their roles as teachers of Foundation Phase mathematics. Secondly, my research suggests that teachers’ mode of reflexivity is key to understanding the decisions that they make in the classroom and how they deal with the structures that condition the manner in which they express their roles as teachers. Thirdly, collective agency is necessary to bring about change in the way in which teachers express their roles in teaching Foundation Phase mathematics. My research produces new knowledge by examining the interplay of structure, culture and agency in the constitution of foundation phase teachers’ identities and their expression in teaching foundation phase mathematics. I use a social realist orientation to examine this interplay and provide an understanding of the mechanisms giving rise to the phenomenon under consideration. In this way I contribute to the extensive research on learner underperformance by focusing more explicitly on who the teacher is in the classroom.
- Full Text:
Investigating a mathematics recovery program for assessment and intervention with groups of Grade 4 learners
- Authors: Wasserman, Anelia
- Date: 2016
- Subjects: Mathematics -- Study and teaching (Primary) , Mathematics -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2065 , http://hdl.handle.net/10962/d1020340
- Description: This study reports on the findings of my research, which was based on an intervention focused on recovery of early arithmetic strategies with one Grade 4 class of learners in a township school in Port Elizabeth in the Eastern Cape. Learners came from poor socio-economic backgrounds and initial evaluations showed that the majority of learners still relied on concrete methods, like tally counting, to perform addition and subtraction calculations even with numbers less than 10. This is not uncommon in the South African context especially with learners in low Socio-economic Status (SES) schools. The results of numerous assessments including the Department of Education’s Annual National Assessments point to a crisis in primary mathematics education where intermediate phase learners are generally operating several grade levels below the grade they are in. A large drop in mathematics performance is seen in the ANA results in grade 4 learners (the first grade of the transition from foundation phase to intermediate phase). Within this context, and my background in learning support for students, my research aimed to understand the possibilities and constraints of the implementation of a recovery program adapted from the widely implemented work of Wright et al. (2006, 2012). The primary adaptation made to the MR program involved administering the assessments and intervention with groups of (rather than individual) learners. Within the context of the many low SES under-resourced schools in SA, individualised interview based assessments and recovery is not seen as a possible remediation strategy. Drawing on a socio- constructivist perspective, my study used action research with one class of 23 learners and found that adaptation of the MR program for a group, based on eight recovery sessions, was useful for enabling some progress for all learners in terms of their early arithmetic strategies and conceptual place value. Although the need for a longer recovery period is acknowledged, the adapted program enabled some progress in levels and stages of conceptual knowledge (as conceptualized by Wright et al.’s (2006) Learning Framework in Number) for these two domains. The study concludes with some reflections and recommendations for the future.
- Full Text:
- Authors: Wasserman, Anelia
- Date: 2016
- Subjects: Mathematics -- Study and teaching (Primary) , Mathematics -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2065 , http://hdl.handle.net/10962/d1020340
- Description: This study reports on the findings of my research, which was based on an intervention focused on recovery of early arithmetic strategies with one Grade 4 class of learners in a township school in Port Elizabeth in the Eastern Cape. Learners came from poor socio-economic backgrounds and initial evaluations showed that the majority of learners still relied on concrete methods, like tally counting, to perform addition and subtraction calculations even with numbers less than 10. This is not uncommon in the South African context especially with learners in low Socio-economic Status (SES) schools. The results of numerous assessments including the Department of Education’s Annual National Assessments point to a crisis in primary mathematics education where intermediate phase learners are generally operating several grade levels below the grade they are in. A large drop in mathematics performance is seen in the ANA results in grade 4 learners (the first grade of the transition from foundation phase to intermediate phase). Within this context, and my background in learning support for students, my research aimed to understand the possibilities and constraints of the implementation of a recovery program adapted from the widely implemented work of Wright et al. (2006, 2012). The primary adaptation made to the MR program involved administering the assessments and intervention with groups of (rather than individual) learners. Within the context of the many low SES under-resourced schools in SA, individualised interview based assessments and recovery is not seen as a possible remediation strategy. Drawing on a socio- constructivist perspective, my study used action research with one class of 23 learners and found that adaptation of the MR program for a group, based on eight recovery sessions, was useful for enabling some progress for all learners in terms of their early arithmetic strategies and conceptual place value. Although the need for a longer recovery period is acknowledged, the adapted program enabled some progress in levels and stages of conceptual knowledge (as conceptualized by Wright et al.’s (2006) Learning Framework in Number) for these two domains. The study concludes with some reflections and recommendations for the future.
- Full Text:
Investigating the nature of the linguistic challenges of the Department of Basic Education (DBE) 2013 Grade 4 Mathematics ANAs and learners’ and teachers’ experience of them.
- Authors: Sibanda, Lucy
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2079 , http://hdl.handle.net/10962/d1021312
- Description: The underperformance of South African learners in literacy and numeracy is a source of grave concern, especially at the transition from Grade 3 to Grade 4. The challenge that complicates this shift is to some extent linguistic, since at Grade 4 in South Africa the majority of learners begin learning in English, which is an additional language for most. The study adopts a sociocultural view of language and learning. Vygotsky’s influential theoretical work on language and learning, in which language is considered central to learning and learning is a social process embedded in sociocultural settings, informs the study. The introduction of the Annual National Assessments (ANAs) across primary and secondary grades in South Africa in mathematics and literacy in 2011 provides the context for this research. It is against this background that the present study aimed, through a case study approach of three Grade 4 classes of English additional language (EAL) learners, to achieve four things, namely: to investigate the linguistic challenges of the 2013 Grade 4 mathematics ANAs; to analyse the learners’ written responses to the 2013 mathematics ANA items; to explore the 2013 Grade 4 learners’ difficulties and experiences of the 2013 mathematics ANAs, and to investigate the Grade 4 mathematics teachers’ perspectives of the language of the ANAs. In order to achieve these aims, the data was collected in four phases. The first phase of the study addressed the nature of the linguistic challenges of the Department of Basic Education Grade 4 mathematics ANAs. Data collection occurred in two parts: 1) Comparing Grade 4 ANAs to exemplars provided and 2) Analysing the language of the 2013 mathematics ANAs. This was done through content analysis and Shaftel et al.’s (2006) linguistic complexity checklist. Findings for part 1 of the study revealed that there were several inconsistencies in the questioning format and language used in the ANAs and in the exemplars. Findings of the content analysis done on the 2013 mathematics ANA test items using Shaftel et al.’s (2006) linguistic complexity checklist and Vale’s (2013) Linguistic Complexity Index formula point to many linguistic complexities in several test items, particularly in relation to recurrent use of: 7 or more letter words, homophones, prepositional phrases and specific mathematics vocabulary across the majority of questions. In phase 2, the analysis of 106 learners’ written responses for the 2013 mathematics ANA questions revealed that for many of the questions the language used was unfamiliar for Grade 4 learners using English as an additional language. This was aggravated by the inclusion in the ANAs of linguistic forms learners would not have encountered in their workbooks or exemplars intended to prepare the learners for the assessments. Therefore, linguistic complexity of items was a key contributing factor to learners’ poor performance in the test. In the third phase, the quantitative and qualitative analysis of the 26 learners’ interviews revealed that during the task-based interviews, learners experienced difficulties in the following skills: reading, comprehension, transformation, process and encoding. The greatest difficulties were experienced in comprehension and in reading, especially in the two classes where the learners were less proficient in the English language. The fourth phase, in which two Grade 4 mathematics teachers’ perceptions of the linguistic demands of the Grade 4 mathematics ANAs were presented and analysed, the teachers’ perceptions indicated that the mathematical language was mostly too difficult for the Grade 4 learners. Teachers also were of the opinion that learners’ reading skills were poor and they struggled to comprehend what they read. A dilemma regarding whether teachers should assist learners during the ANAs, satisfying the local needs for mediating the language or whether they should comply with the ANA policy which states that they may not assist learners was expressed by one of the teachers. A range of language challenges that teachers managed with various strategies were raised. These included one teacher’s use of code-switching during the teaching of mathematics. The study concludes with implications and recommendations. These include that test designers should minimise the language complexity of test items, especially in the early transition grades of learning in English. Research should be conducted on possibilities for allowing teachers to provide linguistic mediation to ANA questions in these transition years of learners learning in English.
- Full Text:
- Authors: Sibanda, Lucy
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2079 , http://hdl.handle.net/10962/d1021312
- Description: The underperformance of South African learners in literacy and numeracy is a source of grave concern, especially at the transition from Grade 3 to Grade 4. The challenge that complicates this shift is to some extent linguistic, since at Grade 4 in South Africa the majority of learners begin learning in English, which is an additional language for most. The study adopts a sociocultural view of language and learning. Vygotsky’s influential theoretical work on language and learning, in which language is considered central to learning and learning is a social process embedded in sociocultural settings, informs the study. The introduction of the Annual National Assessments (ANAs) across primary and secondary grades in South Africa in mathematics and literacy in 2011 provides the context for this research. It is against this background that the present study aimed, through a case study approach of three Grade 4 classes of English additional language (EAL) learners, to achieve four things, namely: to investigate the linguistic challenges of the 2013 Grade 4 mathematics ANAs; to analyse the learners’ written responses to the 2013 mathematics ANA items; to explore the 2013 Grade 4 learners’ difficulties and experiences of the 2013 mathematics ANAs, and to investigate the Grade 4 mathematics teachers’ perspectives of the language of the ANAs. In order to achieve these aims, the data was collected in four phases. The first phase of the study addressed the nature of the linguistic challenges of the Department of Basic Education Grade 4 mathematics ANAs. Data collection occurred in two parts: 1) Comparing Grade 4 ANAs to exemplars provided and 2) Analysing the language of the 2013 mathematics ANAs. This was done through content analysis and Shaftel et al.’s (2006) linguistic complexity checklist. Findings for part 1 of the study revealed that there were several inconsistencies in the questioning format and language used in the ANAs and in the exemplars. Findings of the content analysis done on the 2013 mathematics ANA test items using Shaftel et al.’s (2006) linguistic complexity checklist and Vale’s (2013) Linguistic Complexity Index formula point to many linguistic complexities in several test items, particularly in relation to recurrent use of: 7 or more letter words, homophones, prepositional phrases and specific mathematics vocabulary across the majority of questions. In phase 2, the analysis of 106 learners’ written responses for the 2013 mathematics ANA questions revealed that for many of the questions the language used was unfamiliar for Grade 4 learners using English as an additional language. This was aggravated by the inclusion in the ANAs of linguistic forms learners would not have encountered in their workbooks or exemplars intended to prepare the learners for the assessments. Therefore, linguistic complexity of items was a key contributing factor to learners’ poor performance in the test. In the third phase, the quantitative and qualitative analysis of the 26 learners’ interviews revealed that during the task-based interviews, learners experienced difficulties in the following skills: reading, comprehension, transformation, process and encoding. The greatest difficulties were experienced in comprehension and in reading, especially in the two classes where the learners were less proficient in the English language. The fourth phase, in which two Grade 4 mathematics teachers’ perceptions of the linguistic demands of the Grade 4 mathematics ANAs were presented and analysed, the teachers’ perceptions indicated that the mathematical language was mostly too difficult for the Grade 4 learners. Teachers also were of the opinion that learners’ reading skills were poor and they struggled to comprehend what they read. A dilemma regarding whether teachers should assist learners during the ANAs, satisfying the local needs for mediating the language or whether they should comply with the ANA policy which states that they may not assist learners was expressed by one of the teachers. A range of language challenges that teachers managed with various strategies were raised. These included one teacher’s use of code-switching during the teaching of mathematics. The study concludes with implications and recommendations. These include that test designers should minimise the language complexity of test items, especially in the early transition grades of learning in English. Research should be conducted on possibilities for allowing teachers to provide linguistic mediation to ANA questions in these transition years of learners learning in English.
- Full Text:
Learners' numeracy progression and the role of mediation in the context of two after school mathematics clubs
- Authors: Stott, Deborah Ann
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , After-school programs -- South Africa , Numeracy -- Study and teaching (Elementary) -- South Africa , Learning, Psychology of , Education -- Research -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2017 , http://hdl.handle.net/10962/d1017181
- Description: National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.
- Full Text:
- Authors: Stott, Deborah Ann
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , After-school programs -- South Africa , Numeracy -- Study and teaching (Elementary) -- South Africa , Learning, Psychology of , Education -- Research -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2017 , http://hdl.handle.net/10962/d1017181
- Description: National and international assessment results, research studies and reports point to South Africa as having educational challenges, specifically with mathematics, science and language. Addressing some of these issues is a key aim for the SANC project at Rhodes University, the context in which this study takes place. Working from a broad Vygotskian perspective of learning and development, this study had a dual focus and investigated how Grade 3 learners’ mathematical proficiency progressed (or not) whilst participating in after school maths clubs over the course of a year, and explored how the mediation offered in the clubs enabled or constrained the emergence of zones of proximal development (ZPD) and thus learning for the club learners. Methodologically, this study works within a largely qualitative, interpretive research paradigm and is designed using a longitudinal case study research strategy. Two after school maths clubs formed the empirical field. The study drew on a range of data collection methods to investigate the dual nature of the research questions for Grade 3 learners. Examples include adapted one-to-one mathematical proficiency interviews and paired task based interviews. The study highlighted the relationship between the multiple roles I played both within the research study and within the SANC project context and emphasises the influence and future implications for these various roles within the SANC project and beyond in terms of my own role as club mentor, for the future design of the SANC project maths club programme and for broader teacher and club facilitator development within and beyond the project. This study has offered insight into how mathematical proficiency may develop in Grade 3 South African learners and as such is an important contribution to the newly developing field of both numeracy and primary educational research in Southern Africa. Additionally, the research findings point to the clubs, as an example of an out-of-school time (OST) programme, providing potentially enabling spaces for both recovery and extension of mathematical proficiency in learners as these spaces are free from several contextual constraints that teachers face in their classrooms. Furthermore, it was found that learners showed development of their conceptual understanding, procedural fluency and adaptive reasoning as proposed by Kilpatrick, Swafford and Findell (2001). The use of various elements of the Maths Recovery (MR) programme (Wright, 2003) in the research process has highlighted various important contributions for broader research. For example, the need to investigate less time consuming approaches to both diagnostic assessment and learner mathematical profiling. Findings from this study support Meira and Lerman’s (2001, 2009) recently developed notion that catching attention is key to the creation or emergence of a ZPD. The study found that a combination of ‘attention catching’ and ‘tuning in’ enabled the creation (emergence) and sustainment of ZPDs in club learners. The study proposed the notion of tuning in where participants in a mathematical interaction continually adjust to each other in order to communicate mathematically. Furthermore, the study found that when attention is not caught or the participants are not tuned in, the learning activity may still be useful in assisting learners to consolidate their existing learning and / or build confidence and as such is particularly relevant to the South African context where fluency in calculating is weak (Hoadley, 2012; Schollar, 2008). This emergent notion of ‘flow’ additionally can play a supporting role in the emergence of a ZPD. The study also found that the manner in which the mediation was offered is important. The results show that the mathematical contributions learners make during interactions captured the mentors’ attention and resulted in mediation that was intentional but spontaneous, flexible, responsive and in-the-moment. This study makes theoretical and methodological contributions to various aspects of mathematics education research particularly with regard to how ZPDs emerge and are sustained and how mediation is offered to facilitate the emergence of ZPDs. Additionally, some aspects of the Learning Framework in Number (LFIN) as part of the Maths Recovery programme have been extended to work in a South African after school club context and to provide useful information for both learner progression over time and for planning of club activities. As such this study thus also contributes to the newly developing field of primary mathematics research in South Africa and to the body of research on primary after school learning programmes both locally and internationally.
- Full Text:
Primary maths teacher learning and identity within a numeracy in-service community of practice
- Authors: Pausigere, Peter
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Teachers -- In-service training -- South Africa , Student-centered learning -- South Africa , Communities of practice -- South Africa , Educational change -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2019 , http://hdl.handle.net/10962/d1017183
- Description: This study focuses on the processes of primary maths teacher learning and how their identities and practices evolve in relation to participation in a primary maths focused in-service teacher education programme, called the Numeracy Inquiry Community of Leader Educators (NICLE).Additionally it investigates activities, relations and forms of participation within the Community of Practice (CoP) which enable or constrain evolving primary maths identities and practices and how these relate to the broader context. The study draws from the situative-participationists (Lave, 1996; Wenger, 1998; Sfard & Prusak, 2005; Wenger et al, 2002) theoretical framework supplemented by Bernstein’s (2000) pedagogic identity model. Using a qualitative educational interpretive approach I sampled 8 primary teachers drawn from NICLE and gathered data through participant observations, interactive interviews, document analysis and reflective journals. Analysing the key data themes that emerged from teacher learning stories, which I have called stelos, the study explains the nature of the primary maths teachers’ learning, transformation and participation experiences in NICLE using the synonyms reinvigoration and remediation and activation and relating these semantics to the teachers’ mathematical identities and histories. The study also explains the processes through which primary maths teacher identities evolve in relation to participation in an in-service CoP as ‘insiding’ and ‘outcropping’. Interpreting qualitative data from the empirical field indicates that teachers participating in NICLE mostly took-up into their maths classrooms key numeracy-domain concepts, resources and issues presented by primary maths experts which are informed by research and theory that link to practices. Teachers collaboratively and actively engaged in a range of activities that relate to classroom practices. Teacher learning was also enabled when teachers engaged in maths overlapping communities of practice, shared classroom experiences in friendly ways with fellow NICLE teachers and engaged with NICLE presenters who mutually respected and regarded them as professionals. Such affordances were said to enable teachers to engage learners in maths classes and improve their understanding of specific primary maths concepts. On the other hand teachers felt challenged by the travelling distance, limited time and also raised the tension of how to scale-up maths professional development initiatives to include schools from their community. The study makes a theoretical contribution by illustrating how Bernstein’s pedagogic identity model and its elaboration by Tyler (1999) provides analytical tools to interrogate macro educational changes and connect these to the micro processes and teacher identities.
- Full Text:
- Authors: Pausigere, Peter
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Teachers -- In-service training -- South Africa , Student-centered learning -- South Africa , Communities of practice -- South Africa , Educational change -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2019 , http://hdl.handle.net/10962/d1017183
- Description: This study focuses on the processes of primary maths teacher learning and how their identities and practices evolve in relation to participation in a primary maths focused in-service teacher education programme, called the Numeracy Inquiry Community of Leader Educators (NICLE).Additionally it investigates activities, relations and forms of participation within the Community of Practice (CoP) which enable or constrain evolving primary maths identities and practices and how these relate to the broader context. The study draws from the situative-participationists (Lave, 1996; Wenger, 1998; Sfard & Prusak, 2005; Wenger et al, 2002) theoretical framework supplemented by Bernstein’s (2000) pedagogic identity model. Using a qualitative educational interpretive approach I sampled 8 primary teachers drawn from NICLE and gathered data through participant observations, interactive interviews, document analysis and reflective journals. Analysing the key data themes that emerged from teacher learning stories, which I have called stelos, the study explains the nature of the primary maths teachers’ learning, transformation and participation experiences in NICLE using the synonyms reinvigoration and remediation and activation and relating these semantics to the teachers’ mathematical identities and histories. The study also explains the processes through which primary maths teacher identities evolve in relation to participation in an in-service CoP as ‘insiding’ and ‘outcropping’. Interpreting qualitative data from the empirical field indicates that teachers participating in NICLE mostly took-up into their maths classrooms key numeracy-domain concepts, resources and issues presented by primary maths experts which are informed by research and theory that link to practices. Teachers collaboratively and actively engaged in a range of activities that relate to classroom practices. Teacher learning was also enabled when teachers engaged in maths overlapping communities of practice, shared classroom experiences in friendly ways with fellow NICLE teachers and engaged with NICLE presenters who mutually respected and regarded them as professionals. Such affordances were said to enable teachers to engage learners in maths classes and improve their understanding of specific primary maths concepts. On the other hand teachers felt challenged by the travelling distance, limited time and also raised the tension of how to scale-up maths professional development initiatives to include schools from their community. The study makes a theoretical contribution by illustrating how Bernstein’s pedagogic identity model and its elaboration by Tyler (1999) provides analytical tools to interrogate macro educational changes and connect these to the micro processes and teacher identities.
- Full Text:
An investigation into the nature of grade 4 learners’ evolving mathematics learning dispositions: a case study of 3 learners participating in an after school mathematics club
- Authors: Hewana, Diliza Ronald
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- Case studies , Mathematics -- Study and teaching (Elementary) -- Psychological aspects , After-school programs -- South Africa -- Grahamstown , Students -- Attitudes -- Case studies , Education, Elementary -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1983 , http://hdl.handle.net/10962/d1013140
- Description: Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off.
- Full Text:
- Authors: Hewana, Diliza Ronald
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- Case studies , Mathematics -- Study and teaching (Elementary) -- Psychological aspects , After-school programs -- South Africa -- Grahamstown , Students -- Attitudes -- Case studies , Education, Elementary -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1983 , http://hdl.handle.net/10962/d1013140
- Description: Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off.
- Full Text:
An investigation of a mathematics recovery programme for multiplicative reasoning to a group of learners in the South African context : a case study approach
- Authors: Mofu, Zanele Abegail
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa -- Case studies , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Learning -- Research -- South Africa , Mathematics -- Study and teaching -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1991 , http://hdl.handle.net/10962/d1013333
- Description: This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.
- Full Text:
- Authors: Mofu, Zanele Abegail
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa -- Case studies , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Learning -- Research -- South Africa , Mathematics -- Study and teaching -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1991 , http://hdl.handle.net/10962/d1013333
- Description: This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.
- Full Text:
Examining the nature of the relationship between learners' conceptual understanding and their mathematical dispositions in the context of multiplication
- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
- Full Text:
- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
- Full Text:
Investigating how problem solving skills can be developed using a collaborative learning environment
- Authors: Sonne, Anita
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Social learning , Active learning , Problem solving in children , Educational equalization -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1977 , http://hdl.handle.net/10962/d1013017
- Description: This thesis examines whether problem solving strategies develop and improve through working in a collaborative environment and, if so, how. The study explored the way peer-topeer discussions which are focussed on finding solutions to mathematical problems might shape learners' attitudes and participation in mathematical problem solving. I use the Vygotskian (1978) socio-cultural perspective where the process of learning takes place within the Zone of Proximal Development (ZPD). Polya's problem solving heuristics (Polya, 1973) and Kilpatrick's "Instructional Triangle" (Kilpatrick, Swafford & Findell, 2001) provided the analytical framework for the study. Seven grade 7 learners from a Ex-Model C school, volunteered to participate in the study. The data gathering process involved an initial problem solving assessment, a written questionnaire, observations and video recordings of the seven learners during a series of after school problem solving sessions and post intervention learner interviews. The study showed that group discussion can have a positive impact on learners' problem solving in several respects: My key findings point to: Mathematical communication does play a role in development of problem solving strategies. A more knowledgeable other, with regards to Vygotsky's (1978) ZPD and Kilpatrick et al's (2001) instructional triangle is a critical factor in the development of problem solving strategies. All five strands of Kilpatrick et al., (2001), strands for mathematical proficiency are required for correct solutions to be calculated. At times Polya's (1973) steps for problem solving move at a rapid pace and are difficult to notice. These steps develop at different speeds for different people.
- Full Text:
Investigating how problem solving skills can be developed using a collaborative learning environment
- Authors: Sonne, Anita
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Social learning , Active learning , Problem solving in children , Educational equalization -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1977 , http://hdl.handle.net/10962/d1013017
- Description: This thesis examines whether problem solving strategies develop and improve through working in a collaborative environment and, if so, how. The study explored the way peer-topeer discussions which are focussed on finding solutions to mathematical problems might shape learners' attitudes and participation in mathematical problem solving. I use the Vygotskian (1978) socio-cultural perspective where the process of learning takes place within the Zone of Proximal Development (ZPD). Polya's problem solving heuristics (Polya, 1973) and Kilpatrick's "Instructional Triangle" (Kilpatrick, Swafford & Findell, 2001) provided the analytical framework for the study. Seven grade 7 learners from a Ex-Model C school, volunteered to participate in the study. The data gathering process involved an initial problem solving assessment, a written questionnaire, observations and video recordings of the seven learners during a series of after school problem solving sessions and post intervention learner interviews. The study showed that group discussion can have a positive impact on learners' problem solving in several respects: My key findings point to: Mathematical communication does play a role in development of problem solving strategies. A more knowledgeable other, with regards to Vygotsky's (1978) ZPD and Kilpatrick et al's (2001) instructional triangle is a critical factor in the development of problem solving strategies. All five strands of Kilpatrick et al., (2001), strands for mathematical proficiency are required for correct solutions to be calculated. At times Polya's (1973) steps for problem solving move at a rapid pace and are difficult to notice. These steps develop at different speeds for different people.
- Full Text: