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:
- Date Issued: 2015
- 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:
- Date Issued: 2015
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:
- Date Issued: 2015
- 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:
- Date Issued: 2015
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