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:
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:
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:
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.
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- 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.
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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.
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- 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.
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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.
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The importance's of the physical analogue clock in mediating learning of analogue clock time in Grade 4 learners
- Authors: Metelerkamp, Roger Gregory
- Date: 2014
- Subjects: Clocks and watches , Mathematics -- Study and teaching (Elementary) , Time measurements -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1986 , http://hdl.handle.net/10962/d1013169
- Description: My research topic concerns how learners use the analogue clock (as a human tool) to make meaning of clock time. This study is informed by a Vygotskian socio-cultural framework to learning and development based on the concept that human activities take place in cultural contexts and is mediated by tools. In this qualitative study I report on the learners meaning making of analogue clock time using the physical clock. This study was carried out at a South African primary school through an intervention programme after school. The research employed a case study method. It involved a purposeful sample of 4 learners (n=38) from the grade four class group based on their response to a baseline assessment task. The selected sample of learners included learners across the ability spectrum to gain rich insight into how learners make meaning of analogue clock time. Data collection and analysis was done through an interpretive approach. The video-taped interviews and intervention programme was my main instrument of data collection. Other research instruments included document analysis of responses to baseline assessment tasks. These research tools yielded the data collected and also allowed for triangulation. My research topic explored how the learners make meaning of analogue clock time. In particular the two-way movement of how the learners use the physical tool namely the analogue clock to develop meaning and how the clock mediates clock knowledge in return. The findings of the study suggest that learners’ find it difficult to conceptualise analogue clock symbols and signs, in particular, in Afrikaans the half hour concept, in relation to the two hands. The physical analogue clock is also important to support and extend clock knowledge in solving time-related problems. This shows the power of the analogue clock to mediate meaning making of clock time in young learners. Because of its potential to improve teaching and learning analogue clock time in primary school it is therefore recommended that the analogue clock time be further researched in South Africa.
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- Authors: Metelerkamp, Roger Gregory
- Date: 2014
- Subjects: Clocks and watches , Mathematics -- Study and teaching (Elementary) , Time measurements -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1986 , http://hdl.handle.net/10962/d1013169
- Description: My research topic concerns how learners use the analogue clock (as a human tool) to make meaning of clock time. This study is informed by a Vygotskian socio-cultural framework to learning and development based on the concept that human activities take place in cultural contexts and is mediated by tools. In this qualitative study I report on the learners meaning making of analogue clock time using the physical clock. This study was carried out at a South African primary school through an intervention programme after school. The research employed a case study method. It involved a purposeful sample of 4 learners (n=38) from the grade four class group based on their response to a baseline assessment task. The selected sample of learners included learners across the ability spectrum to gain rich insight into how learners make meaning of analogue clock time. Data collection and analysis was done through an interpretive approach. The video-taped interviews and intervention programme was my main instrument of data collection. Other research instruments included document analysis of responses to baseline assessment tasks. These research tools yielded the data collected and also allowed for triangulation. My research topic explored how the learners make meaning of analogue clock time. In particular the two-way movement of how the learners use the physical tool namely the analogue clock to develop meaning and how the clock mediates clock knowledge in return. The findings of the study suggest that learners’ find it difficult to conceptualise analogue clock symbols and signs, in particular, in Afrikaans the half hour concept, in relation to the two hands. The physical analogue clock is also important to support and extend clock knowledge in solving time-related problems. This shows the power of the analogue clock to mediate meaning making of clock time in young learners. Because of its potential to improve teaching and learning analogue clock time in primary school it is therefore recommended that the analogue clock time be further researched in South Africa.
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Examining the nature of learning within an afterschool mathematics club : a case study of four learners
- Authors: Kaulinge, Penehafo Olivia
- Date: 2013
- Subjects: Stott, Debbie Mathematics -- Study and teaching (Elementary) -- South Africa After-school programs -- Research -- South Africa Learning -- Research -- South Africa Education, Elementary -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1401 , http://hdl.handle.net/10962/d1001835
- Description: This study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. The study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. The study made use of a variety of data collection techniques, including one-to-one assessment interviews, task-based interviews and observations. In line with the case study approach adopted, four learners were selected for interviews. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. Even though they were found to have advanced in their Strategies for Early Arithmetic Learning (SEAL), some of them were observed still using their fingers to support their counting. Such strategies were likely to mirror the teaching approaches used in their usual school mathematical lessons. The overall findings in terms of learners’ proficiency and progress give rise to concerns about current number teaching practices in their school, which emphasize the standard written algorithm in the lower primary grades. The study also made use of Vygotsky’s notion of the ZPD to analyse the nature of mentor-peer mediation. Witnessing the learners’ use of trial and error strategies during the task-based interview allowed both mentors to support learners through understanding their thinking, prompting them and encouraging them to reflect on their answers and develop more effective strategies. Learners progressed through the ZPD at different paces and in different ways, with ‘aha’ moments happening at different points for individual learners. Their progression in the ZPD seemed to depend on interaction among all participants, which varied according to what was contributed and what requested by each participant. The findings revealed that although there was evidence of learners achieving success at the tasks in task based interviews there were also there were also some learners who experienced difficulties. Additionally, in order to argue that learning was fully realised within the ZPD would have required follow up task based interviews to assess the extent to which learners were able to complete the tasks independently without the scaffolding of mentors. This was not possible within the scope of this research but would be useful in future research.
- Full Text:
- Authors: Kaulinge, Penehafo Olivia
- Date: 2013
- Subjects: Stott, Debbie Mathematics -- Study and teaching (Elementary) -- South Africa After-school programs -- Research -- South Africa Learning -- Research -- South Africa Education, Elementary -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1401 , http://hdl.handle.net/10962/d1001835
- Description: This study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. The study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. The study made use of a variety of data collection techniques, including one-to-one assessment interviews, task-based interviews and observations. In line with the case study approach adopted, four learners were selected for interviews. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. Even though they were found to have advanced in their Strategies for Early Arithmetic Learning (SEAL), some of them were observed still using their fingers to support their counting. Such strategies were likely to mirror the teaching approaches used in their usual school mathematical lessons. The overall findings in terms of learners’ proficiency and progress give rise to concerns about current number teaching practices in their school, which emphasize the standard written algorithm in the lower primary grades. The study also made use of Vygotsky’s notion of the ZPD to analyse the nature of mentor-peer mediation. Witnessing the learners’ use of trial and error strategies during the task-based interview allowed both mentors to support learners through understanding their thinking, prompting them and encouraging them to reflect on their answers and develop more effective strategies. Learners progressed through the ZPD at different paces and in different ways, with ‘aha’ moments happening at different points for individual learners. Their progression in the ZPD seemed to depend on interaction among all participants, which varied according to what was contributed and what requested by each participant. The findings revealed that although there was evidence of learners achieving success at the tasks in task based interviews there were also there were also some learners who experienced difficulties. Additionally, in order to argue that learning was fully realised within the ZPD would have required follow up task based interviews to assess the extent to which learners were able to complete the tasks independently without the scaffolding of mentors. This was not possible within the scope of this research but would be useful in future research.
- Full Text:
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