How selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in a screencast intervention
- Authors: Wienekus, George Renier
- Date: 2021-04
- Subjects: Algebra -- Study and teaching -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Algebra -- Ability testing , Algebra -- Computer-assisted instruction
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/176833 , vital:42763
- Description: This research project is an interventionist case study, oriented in the interpretive paradigm, which aims to investigate how selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in screencast interventions. The aim of my screencast intervention programme, which lies at the heart of this study, is to develop practices, inter alia, of how such devices and software may be “used to develop conceptual rather than procedural or decorative knowledge” (Larkin & Calder, 2015:1) in solving linear equations. The planned intervention was delivered in the form of a series of screencasts: these take the form of audio-video lessons with an emphasis on the visual impact, and were recorded using an application called Explain Everything. The screencast interventions were delivered via Google Classroom and included animations supported by such conceptual explanations of early algebra as are relevant to Grade 7 students, and in line with the South African Curriculum and Assessment Policy Statements - Department of Education, 2011. The fundamental components of an early algebraic equation that would be relevant to a Grade 7 student were considered and used to develop an analytic framework. This was based on a taxonomy designed according to four identified “clusters” in order to analyse the workings of the purposefully selected Grade 7 participants who were video recorded and questioned in a talk-aloud interview while they completed a post-intervention pencil-and-paper test. What emerges from this research project is that there is a significant need for specific and concentrated technology-based techniques, such as the interventions undertaken here, and that exploration and development in the field could benefit the delivery of a pedagogy for algebra. The pedagogical methods implemented and studied in the form of screencasts proved to be successful and were well received by the learners particularly in relation to the conceptualisation of “symbol sense” and transformation in early algebra. The structure and design of the screencast interventions were important in supporting the acquisition of these concepts and were demonstrated to be worthwhile tools for an epistemological application in a classroom or teaching context. , Thesis (MEd) -- Rhodes University, Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Wienekus, George Renier
- Date: 2021-04
- Subjects: Algebra -- Study and teaching -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Algebra -- Ability testing , Algebra -- Computer-assisted instruction
- Language: English
- Type: thesis , text , Masters , MEd
- Identifier: http://hdl.handle.net/10962/176833 , vital:42763
- Description: This research project is an interventionist case study, oriented in the interpretive paradigm, which aims to investigate how selected Grade 7 participants develop conceptual understanding in solving algebraic problems as a result of participating in screencast interventions. The aim of my screencast intervention programme, which lies at the heart of this study, is to develop practices, inter alia, of how such devices and software may be “used to develop conceptual rather than procedural or decorative knowledge” (Larkin & Calder, 2015:1) in solving linear equations. The planned intervention was delivered in the form of a series of screencasts: these take the form of audio-video lessons with an emphasis on the visual impact, and were recorded using an application called Explain Everything. The screencast interventions were delivered via Google Classroom and included animations supported by such conceptual explanations of early algebra as are relevant to Grade 7 students, and in line with the South African Curriculum and Assessment Policy Statements - Department of Education, 2011. The fundamental components of an early algebraic equation that would be relevant to a Grade 7 student were considered and used to develop an analytic framework. This was based on a taxonomy designed according to four identified “clusters” in order to analyse the workings of the purposefully selected Grade 7 participants who were video recorded and questioned in a talk-aloud interview while they completed a post-intervention pencil-and-paper test. What emerges from this research project is that there is a significant need for specific and concentrated technology-based techniques, such as the interventions undertaken here, and that exploration and development in the field could benefit the delivery of a pedagogy for algebra. The pedagogical methods implemented and studied in the form of screencasts proved to be successful and were well received by the learners particularly in relation to the conceptualisation of “symbol sense” and transformation in early algebra. The structure and design of the screencast interventions were important in supporting the acquisition of these concepts and were demonstrated to be worthwhile tools for an epistemological application in a classroom or teaching context. , Thesis (MEd) -- Rhodes University, Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-04
BEd foundation phase fourth year student teachers’ self-efficacy beliefs towards teaching mathematics and the self-reported factors that influence these self-efficacy beliefs
- Authors: Harrison, Chloe
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Educational evaluation -- South Africa , Student teachers -- Training of -- South Africa , Student teachers -- Rating of -- South Africa , Social cognitive theory , Self-efficacy
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/147004 , vital:38584
- Description: The underperformance of mathematics teaching and learning is a pressing concern in South Africa. Many foundation phase in-service teachers show inadequate mathematics content knowledge which creates barriers to their learners acquiring adequate mathematics skills. Teacher training programmes offer a key opportunity to improve the instructional practices of teachers at foundation phase level. In order to improve the teaching skills of in-service teachers, one focus must be on teacher training programmes. Unfortunately, there are many foundation phase student teachers who are leaving the profession within the first few years of teaching reportedly due to low levels of motivation. This research investigates the self-efficacy beliefs of pre-service student teachers. It also focuses on foundation phase student teachers as they experience significant challenges to their self-efficacy beliefs in mathematics and mathematics teaching. Self-efficacy is the key theory of the study. It stems from Bandura’s social cognitive theory and is an individual’s judgments about their capabilities, skills and perceived performance. This qualitative research adopts an interpretivist approach which seeks to identify Bed foundation phase fourth year student teachers’ self-efficacy beliefs towards teaching mathematics and the self-reported factors influencing such beliefs. This research found that BEd foundation phase fourth year student teachers have low self-efficacy beliefs towards teaching mathematics. The purpose of this research is to raise awareness of the BEd student teachers’ low self-efficacy beliefs towards teaching mathematics. The results from this research will provide a platform for future intervention research, as well as potentially influencing student teacher training programmes.
- Full Text:
- Date Issued: 2020
- Authors: Harrison, Chloe
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Educational evaluation -- South Africa , Student teachers -- Training of -- South Africa , Student teachers -- Rating of -- South Africa , Social cognitive theory , Self-efficacy
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/147004 , vital:38584
- Description: The underperformance of mathematics teaching and learning is a pressing concern in South Africa. Many foundation phase in-service teachers show inadequate mathematics content knowledge which creates barriers to their learners acquiring adequate mathematics skills. Teacher training programmes offer a key opportunity to improve the instructional practices of teachers at foundation phase level. In order to improve the teaching skills of in-service teachers, one focus must be on teacher training programmes. Unfortunately, there are many foundation phase student teachers who are leaving the profession within the first few years of teaching reportedly due to low levels of motivation. This research investigates the self-efficacy beliefs of pre-service student teachers. It also focuses on foundation phase student teachers as they experience significant challenges to their self-efficacy beliefs in mathematics and mathematics teaching. Self-efficacy is the key theory of the study. It stems from Bandura’s social cognitive theory and is an individual’s judgments about their capabilities, skills and perceived performance. This qualitative research adopts an interpretivist approach which seeks to identify Bed foundation phase fourth year student teachers’ self-efficacy beliefs towards teaching mathematics and the self-reported factors influencing such beliefs. This research found that BEd foundation phase fourth year student teachers have low self-efficacy beliefs towards teaching mathematics. The purpose of this research is to raise awareness of the BEd student teachers’ low self-efficacy beliefs towards teaching mathematics. The results from this research will provide a platform for future intervention research, as well as potentially influencing student teacher training programmes.
- Full Text:
- Date Issued: 2020
IsiXhosa as the language of teaching and learning mathematics in Grade Six: investigating the mother tongue based bilingual education mathematics pilot in the Eastern Cape Province, South Africa
- Authors: Mbude, Naledi Ntombizanele
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Education, Bilingual -- South Africa , Native language and education -- South Africa , Language policy -- South Africa
- Language: English
- Type: text , Thesis , Doctoral , PHD
- Identifier: http://hdl.handle.net/10962/143262 , vital:38215
- Description: This study is an investigation on lessons learnt when the language of learners is maintained for teaching and learning mathematics beyond Grade 3 for another 3 years. It is undertaken in Cofimvaba, a rural village of the Eastern Cape in South Africa. We investigate lessons that can be learnt from the Mother Tongue based- Bilingual Education (MTbBE) strategy, that can be replicated. South Africa post-1994 has a Language-in-Education Policy (1997) that provides for the use of all official languages as Languages of Teaching and Learning (LoLT), this has remained on paper as the schooling system focusses on an early –exit model of three years of the Mother Tongue Education (MTE) for the Foundation Phase (FP) then exit to English instruction in Grade 4; this applies to African language learners only. English and Afrikaans speakers have mother tongue education from cradle to university; a benefit they have enjoyed pre- and post-apartheid. Various studies have been conducted to understand the relationship between language and mathematics learning as it is crucial to design mathematics instruction for students who are English Learners (ELs) and/or bilingual. However, in South Africa, there had not been a direct exploration of the achievement of learners in mathematics when their mother tongue is used and sustained throughout the first six years of learning mathematics, while English is a supportive resource. This is the focus of this study. The study lends itself to the adoption of a mixed methods design (QUALT+QUANT), while also employing documents, observation and test scores of learners to obtain data. Content analysis and thematic analysis approaches were used in analyzing the qualitative-type data while a statistical approach was used in the analysis of quantitative data. The main aim of the study was to establish whether in the Cofimvaba pilot, there is any evidence to make a case for extending Mother Tongue Based-bilingual Education (MTBBE) beyond Grade 3 for black African children. Another aim, was to highlight and document the effort that was the first of its kind in South Africa, undertaken in a small rural area to develop isiXhosa as language of Mathematics and Science. The most salient of this effort was the fact that it was underpinned by deliberate theoretical and empirical foundations central to language policy and planning. The finding of this study is that the use of isiXhosa for MTbBE was effective for boosting mathematical and science skills in the mother tongue and English in Grade 6 as demonstrated in Chapter 7 and 8. Lastly, this study demonstrates the power of political will and how a decision backed by financial investment can transform the wider system despite the challenges of transformation. For the first time in the history of education; a poor department has stuck to its guns; unwearied by the negativity surrounding the development of African languages. It committed to the cause of improving the academic achievement of the poorest of the poor. Historically, in implementing a Mathematics Curriculum, the Department of Education (both officials and teachers) has never efficiently implemented the LiEP (1997) in the manner spelt out in its policy documents viz, multilingualism as the norm. The focus has been on a perspective of learners who are learning and must English, then mathematics and ways to get them to know English at all costs. This view creates inequities in the classroom because it places emphasis on what learners don’t know or can’t do. In contrast, this study proposes a sociocultural perspective that shifts away from deficiency models of bilingual learners and instead focuses on describing the resources bilingual students use to communicate mathematically (Moskovich, 1988). Without this shift we will have a limited view of these learners and will design instruction that neglects the competencies they bring to mathematics classrooms. If, instead, we learn to recognize the mathematical ideas these students express in spite of their accents, code-switching, or missing vocabulary, then instruction can build on students’ competencies and resources (Moskovich, 1998). This study recommends a plethora of strategies that must be taken by the Department of Education to widen epistemological access to mathematics for African language learners using MTbBE as a viable strategy.
- Full Text:
- Date Issued: 2020
- Authors: Mbude, Naledi Ntombizanele
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Education, Bilingual -- South Africa , Native language and education -- South Africa , Language policy -- South Africa
- Language: English
- Type: text , Thesis , Doctoral , PHD
- Identifier: http://hdl.handle.net/10962/143262 , vital:38215
- Description: This study is an investigation on lessons learnt when the language of learners is maintained for teaching and learning mathematics beyond Grade 3 for another 3 years. It is undertaken in Cofimvaba, a rural village of the Eastern Cape in South Africa. We investigate lessons that can be learnt from the Mother Tongue based- Bilingual Education (MTbBE) strategy, that can be replicated. South Africa post-1994 has a Language-in-Education Policy (1997) that provides for the use of all official languages as Languages of Teaching and Learning (LoLT), this has remained on paper as the schooling system focusses on an early –exit model of three years of the Mother Tongue Education (MTE) for the Foundation Phase (FP) then exit to English instruction in Grade 4; this applies to African language learners only. English and Afrikaans speakers have mother tongue education from cradle to university; a benefit they have enjoyed pre- and post-apartheid. Various studies have been conducted to understand the relationship between language and mathematics learning as it is crucial to design mathematics instruction for students who are English Learners (ELs) and/or bilingual. However, in South Africa, there had not been a direct exploration of the achievement of learners in mathematics when their mother tongue is used and sustained throughout the first six years of learning mathematics, while English is a supportive resource. This is the focus of this study. The study lends itself to the adoption of a mixed methods design (QUALT+QUANT), while also employing documents, observation and test scores of learners to obtain data. Content analysis and thematic analysis approaches were used in analyzing the qualitative-type data while a statistical approach was used in the analysis of quantitative data. The main aim of the study was to establish whether in the Cofimvaba pilot, there is any evidence to make a case for extending Mother Tongue Based-bilingual Education (MTBBE) beyond Grade 3 for black African children. Another aim, was to highlight and document the effort that was the first of its kind in South Africa, undertaken in a small rural area to develop isiXhosa as language of Mathematics and Science. The most salient of this effort was the fact that it was underpinned by deliberate theoretical and empirical foundations central to language policy and planning. The finding of this study is that the use of isiXhosa for MTbBE was effective for boosting mathematical and science skills in the mother tongue and English in Grade 6 as demonstrated in Chapter 7 and 8. Lastly, this study demonstrates the power of political will and how a decision backed by financial investment can transform the wider system despite the challenges of transformation. For the first time in the history of education; a poor department has stuck to its guns; unwearied by the negativity surrounding the development of African languages. It committed to the cause of improving the academic achievement of the poorest of the poor. Historically, in implementing a Mathematics Curriculum, the Department of Education (both officials and teachers) has never efficiently implemented the LiEP (1997) in the manner spelt out in its policy documents viz, multilingualism as the norm. The focus has been on a perspective of learners who are learning and must English, then mathematics and ways to get them to know English at all costs. This view creates inequities in the classroom because it places emphasis on what learners don’t know or can’t do. In contrast, this study proposes a sociocultural perspective that shifts away from deficiency models of bilingual learners and instead focuses on describing the resources bilingual students use to communicate mathematically (Moskovich, 1988). Without this shift we will have a limited view of these learners and will design instruction that neglects the competencies they bring to mathematics classrooms. If, instead, we learn to recognize the mathematical ideas these students express in spite of their accents, code-switching, or missing vocabulary, then instruction can build on students’ competencies and resources (Moskovich, 1998). This study recommends a plethora of strategies that must be taken by the Department of Education to widen epistemological access to mathematics for African language learners using MTbBE as a viable strategy.
- Full Text:
- Date Issued: 2020
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:
- Date Issued: 2019
- 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:
- Date Issued: 2019
An investigation into the mathematics knowledge for teaching required to develop grade 2 learners’ number sense through counting
- Authors: Chikiwa, Samukeliso
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Number concept in children -- South Africa , Number concept -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6042 , vital:21019
- Description: Poor learner performance in mathematics has a long-standing record in South Africa. More than two decades after attainment of democracy South Africa is still seeking ways of addressing this crisis. Research around poor mathematics points to a number of factors, however, the dominant being that South African teachers lack both mathematics content and the pedagogical knowledge to teach it effectively. Ball, Thames and Phelps (2008) refer to the knowledge to teach mathematics effectively as Mathematics Knowledge for Teaching [MKfT]. MKfT combines the knowledge of both the content with the pedagogical skills. Mathematics teachers in South Africa are said to lack MKfT to teach mathematics in ways that enhance conceptual understanding and the effect of this deficiency is felt as far back in the education system as Foundation Phase. Research suggests Foundation Phase teachers do not develop the learners’ number sense well enough to equip them with essential mathematical strategies and proficiency that would help them learn mathematics with ease and understanding. This deficit expands as learners move up the grades. My qualitative research, case study approach was employed to investigate MKfT enacted in the teaching of an expert Foundation Phase teacher, which she used while developing number sense in her Grade Two learners. A key aim is to inform fellow Foundation Phase teachers and Foundation Phase teacher educators, both in-service and in-training, of the key aspects of MKfT required in developing number sense. The study found that Foundation Phase teaching requires employment of all the domains of the MKfT to develop number sense to Grade 2 learners. These domains are complexly interconnected and interdependent and the research shows that while one needs the full set to be able to teach effectively, the expertise becomes visible in the seamless and somewhat automated interweaving of these domains. Furthermore, the research will illuminate how such seamless and automated interweaving can render the individual domains difficult to discern.
- Full Text:
- Date Issued: 2017
- Authors: Chikiwa, Samukeliso
- Date: 2017
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Mathematics teachers -- Training of -- South Africa , Number concept in children -- South Africa , Number concept -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6042 , vital:21019
- Description: Poor learner performance in mathematics has a long-standing record in South Africa. More than two decades after attainment of democracy South Africa is still seeking ways of addressing this crisis. Research around poor mathematics points to a number of factors, however, the dominant being that South African teachers lack both mathematics content and the pedagogical knowledge to teach it effectively. Ball, Thames and Phelps (2008) refer to the knowledge to teach mathematics effectively as Mathematics Knowledge for Teaching [MKfT]. MKfT combines the knowledge of both the content with the pedagogical skills. Mathematics teachers in South Africa are said to lack MKfT to teach mathematics in ways that enhance conceptual understanding and the effect of this deficiency is felt as far back in the education system as Foundation Phase. Research suggests Foundation Phase teachers do not develop the learners’ number sense well enough to equip them with essential mathematical strategies and proficiency that would help them learn mathematics with ease and understanding. This deficit expands as learners move up the grades. My qualitative research, case study approach was employed to investigate MKfT enacted in the teaching of an expert Foundation Phase teacher, which she used while developing number sense in her Grade Two learners. A key aim is to inform fellow Foundation Phase teachers and Foundation Phase teacher educators, both in-service and in-training, of the key aspects of MKfT required in developing number sense. The study found that Foundation Phase teaching requires employment of all the domains of the MKfT to develop number sense to Grade 2 learners. These domains are complexly interconnected and interdependent and the research shows that while one needs the full set to be able to teach effectively, the expertise becomes visible in the seamless and somewhat automated interweaving of these domains. Furthermore, the research will illuminate how such seamless and automated interweaving can render the individual domains difficult to discern.
- Full Text:
- Date Issued: 2017
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
A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
Examining the nature of the relationship between learners' conceptual understanding and their mathematical dispositions in the context of multiplication
- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
- Full Text:
- Date Issued: 2014
- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
- Full Text:
- Date Issued: 2014
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:
- Date Issued: 2014
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:
- Date Issued: 2014
Using language as a resource: strategies to teach mathematics in multilingual classes
- Authors: Whale, Susan Gaye
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Code switching (Linguistics) -- South Africa , Education, Bilingual -- South Africa -- Eastern Cape , Language and education -- South Africa -- Eastern Cape , Blacks -- Education -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9469 , http://hdl.handle.net/10948/1669 , Mathematics -- Study and teaching (Elementary) -- South Africa , Code switching (Linguistics) -- South Africa , Education, Bilingual -- South Africa -- Eastern Cape , Language and education -- South Africa -- Eastern Cape , Blacks -- Education -- South Africa -- Eastern Cape
- Description: South Africa is a complex multilingual country. In the majority of schools in the Eastern Cape, a province in South Africa, the teachers and learners share the same home language, isiXhosa, but teach and learn mathematics in English. The purpose of this study was to encourage teachers to use the home language as a resource to teach mathematics in multilingual classes. The study follows a mixed method design, using both qualitative and quantitative data. Qualitative data were collected from a survey and poetry, which teachers crafted, in which they highlighted their perceptions about language in their lives. They also reflected on their practices and submitted pieces of contemplative writing. Quantitative data were collected from participating teachers who administered a pre-test to their learners as well as a post- test approximately nine months later after conducting an intervention. The results showed that where strategies, such as the implementation of exploratory talk and code switching which used language as a resource, had been introduced mathematical reasoning improved and classroom climate became more positive. The learners’ lack of confidence in being able to express their reasoning in English was prevalent throughout the reflective writing. By enabling learners to use isiXhosa in discussions the teachers felt that the learners gained in both confidence and mathematical understanding. This study has demonstrated that using the learners’ and teachers’ home language unlocks doors to communication and spotlights mathematical reasoning, but there is still an urgency to encourage learners to become fluent in Mathematical English. It is important to note that a positive classroom climate is essential for learners to build confidence and to encourage them to attempt to formulate sentences in English - to start on the journey from informal to formal usage of language as advocated by Setati and Adler (2001:250). My main conclusion is that an intervention that develops exploratory talk by using language as a resource can improve learners’ mathematical reasoning. I wish to emphasise that I am not advocating teaching mathematics in isiXhosa only, but the research has shown the advantages of using the home language as a resource together with English in Eastern Cape multilingual mathematics classes. Learners need to be able to express themselves in English, written and spoken, in order to achieve mathematically. This study therefore shows that teachers can gauge their learners’ improvement in mathematical reasoning after an intervention that develops exploratory talk in class by using the home language as a resource.
- Full Text:
- Date Issued: 2012
- Authors: Whale, Susan Gaye
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Code switching (Linguistics) -- South Africa , Education, Bilingual -- South Africa -- Eastern Cape , Language and education -- South Africa -- Eastern Cape , Blacks -- Education -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9469 , http://hdl.handle.net/10948/1669 , Mathematics -- Study and teaching (Elementary) -- South Africa , Code switching (Linguistics) -- South Africa , Education, Bilingual -- South Africa -- Eastern Cape , Language and education -- South Africa -- Eastern Cape , Blacks -- Education -- South Africa -- Eastern Cape
- Description: South Africa is a complex multilingual country. In the majority of schools in the Eastern Cape, a province in South Africa, the teachers and learners share the same home language, isiXhosa, but teach and learn mathematics in English. The purpose of this study was to encourage teachers to use the home language as a resource to teach mathematics in multilingual classes. The study follows a mixed method design, using both qualitative and quantitative data. Qualitative data were collected from a survey and poetry, which teachers crafted, in which they highlighted their perceptions about language in their lives. They also reflected on their practices and submitted pieces of contemplative writing. Quantitative data were collected from participating teachers who administered a pre-test to their learners as well as a post- test approximately nine months later after conducting an intervention. The results showed that where strategies, such as the implementation of exploratory talk and code switching which used language as a resource, had been introduced mathematical reasoning improved and classroom climate became more positive. The learners’ lack of confidence in being able to express their reasoning in English was prevalent throughout the reflective writing. By enabling learners to use isiXhosa in discussions the teachers felt that the learners gained in both confidence and mathematical understanding. This study has demonstrated that using the learners’ and teachers’ home language unlocks doors to communication and spotlights mathematical reasoning, but there is still an urgency to encourage learners to become fluent in Mathematical English. It is important to note that a positive classroom climate is essential for learners to build confidence and to encourage them to attempt to formulate sentences in English - to start on the journey from informal to formal usage of language as advocated by Setati and Adler (2001:250). My main conclusion is that an intervention that develops exploratory talk by using language as a resource can improve learners’ mathematical reasoning. I wish to emphasise that I am not advocating teaching mathematics in isiXhosa only, but the research has shown the advantages of using the home language as a resource together with English in Eastern Cape multilingual mathematics classes. Learners need to be able to express themselves in English, written and spoken, in order to achieve mathematically. This study therefore shows that teachers can gauge their learners’ improvement in mathematical reasoning after an intervention that develops exploratory talk in class by using the home language as a resource.
- Full Text:
- Date Issued: 2012
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