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
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
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.
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- Date Issued: 2012
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