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
The Quakers in South Africa a social witness
- Authors: Tonsing, Betty Kathryn
- Date: 1994
- Subjects: Society of Friends Quakers -- History Quakers -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2564 , http://hdl.handle.net/10962/d1002417
- Description: The Religious Society of Friends, or Quakers, began their witness in the 1600s during a time of religious debate when competing doctrines reflected the political, social and intellectual turmoil of seventeenth-century England. George Fox (1624-1691), the founder, preached that people are guided by God's inner light which is present in the hearts and conscience of all people and reflects God's 'divine' will. The Quakers form a small religious membership not larger than 200,000 people sect, its world-wide. Yet, historically, the group's impact on social issues has always outweighed its numerical strength. The earliest Quakers to reside more permanently in South Africa were British settlers, several of whom became outspoken civic leaders. Quaker humanitarian gestures led to the opening of a multi-racial school for poor children in Cape Town (1840) and investigations into the treatment of Afrikaner women and children in concentration camps during the Anglo-Boer War (1899-1902). Early Quakers are also credited with initiating the Joint Council Movement of Europeans and Africans (1920s), forerunner to the South African Institute of Race Relations. This study traces the Quaker presence in South Africa from its earliest history to the present, with particular emphasis on the twentieth century. Specifically, the examination of the Quaker presence addresses the group's reaction to South African society and politics in reference to segregationist and apartheid legislation. The study includes a comparative analysis of the response among South African Quakers to these issues with Quaker response in England and the United states. The purpose of this analysis is to attempt an assessment of the extent to which South African Quaker practices were consistent with the philosophies of their world-wide religious fellowship. Relevant to the Quaker belief in peace and justice for all, with no discrimination, specific issues that involved South African Quakers and for which sufficient primary sources were available are closely examined. Of particular interest is the opening of a Quaker boarding school during the early 1930s, the Quaker response to the Defiance Campaign in 1952, and South African Quaker response to the call for international sanctions and boycotts against South Africa. More recent Quaker activities, including mediation between the African National Congress and the government, provide significant data. South African Quakers have defined themselves as members of a religious body whose belief of pacifism and commitment to non-violence dictates to a certain extent their obedience to a higher authority -- which some call their conscience and others call God -- if a civil law is deemed immoral and unjust . Thus, the study seeks to define the individual and corporate Quaker witness in South Africa in relation to the Society's principles.
- Full Text:
- Date Issued: 1994
- Authors: Tonsing, Betty Kathryn
- Date: 1994
- Subjects: Society of Friends Quakers -- History Quakers -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2564 , http://hdl.handle.net/10962/d1002417
- Description: The Religious Society of Friends, or Quakers, began their witness in the 1600s during a time of religious debate when competing doctrines reflected the political, social and intellectual turmoil of seventeenth-century England. George Fox (1624-1691), the founder, preached that people are guided by God's inner light which is present in the hearts and conscience of all people and reflects God's 'divine' will. The Quakers form a small religious membership not larger than 200,000 people sect, its world-wide. Yet, historically, the group's impact on social issues has always outweighed its numerical strength. The earliest Quakers to reside more permanently in South Africa were British settlers, several of whom became outspoken civic leaders. Quaker humanitarian gestures led to the opening of a multi-racial school for poor children in Cape Town (1840) and investigations into the treatment of Afrikaner women and children in concentration camps during the Anglo-Boer War (1899-1902). Early Quakers are also credited with initiating the Joint Council Movement of Europeans and Africans (1920s), forerunner to the South African Institute of Race Relations. This study traces the Quaker presence in South Africa from its earliest history to the present, with particular emphasis on the twentieth century. Specifically, the examination of the Quaker presence addresses the group's reaction to South African society and politics in reference to segregationist and apartheid legislation. The study includes a comparative analysis of the response among South African Quakers to these issues with Quaker response in England and the United states. The purpose of this analysis is to attempt an assessment of the extent to which South African Quaker practices were consistent with the philosophies of their world-wide religious fellowship. Relevant to the Quaker belief in peace and justice for all, with no discrimination, specific issues that involved South African Quakers and for which sufficient primary sources were available are closely examined. Of particular interest is the opening of a Quaker boarding school during the early 1930s, the Quaker response to the Defiance Campaign in 1952, and South African Quaker response to the call for international sanctions and boycotts against South Africa. More recent Quaker activities, including mediation between the African National Congress and the government, provide significant data. South African Quakers have defined themselves as members of a religious body whose belief of pacifism and commitment to non-violence dictates to a certain extent their obedience to a higher authority -- which some call their conscience and others call God -- if a civil law is deemed immoral and unjust . Thus, the study seeks to define the individual and corporate Quaker witness in South Africa in relation to the Society's principles.
- Full Text:
- Date Issued: 1994
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