An investigation into the nature of grade 4 learners’ evolving mathematics learning dispositions: a case study of 3 learners participating in an after school mathematics club
- Authors: Hewana, Diliza Ronald
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- Case studies , Mathematics -- Study and teaching (Elementary) -- Psychological aspects , After-school programs -- South Africa -- Grahamstown , Students -- Attitudes -- Case studies , Education, Elementary -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1983 , http://hdl.handle.net/10962/d1013140
- Description: Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off.
- Full Text:
- Date Issued: 2014
- Authors: Hewana, Diliza Ronald
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- Case studies , Mathematics -- Study and teaching (Elementary) -- Psychological aspects , After-school programs -- South Africa -- Grahamstown , Students -- Attitudes -- Case studies , Education, Elementary -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1983 , http://hdl.handle.net/10962/d1013140
- Description: Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off.
- Full Text:
- Date Issued: 2014
An investigation of a mathematics recovery programme for multiplicative reasoning to a group of learners in the South African context : a case study approach
- Authors: Mofu, Zanele Abegail
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa -- Case studies , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Learning -- Research -- South Africa , Mathematics -- Study and teaching -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1991 , http://hdl.handle.net/10962/d1013333
- Description: This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.
- Full Text:
- Date Issued: 2014
- Authors: Mofu, Zanele Abegail
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa -- Case studies , Mathematics -- Study and teaching (Elementary) -- South Africa -- Case studies , Learning -- Research -- South Africa , Mathematics -- Study and teaching -- Evaluation
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1991 , http://hdl.handle.net/10962/d1013333
- Description: This thesis describes an intervention using the Mathematics Recovery programme in a South African context with a small sample of Grade 4 learners. The study uses a qualitative case study approach. The data collection included video recorded one-to-one oral interviews with the learners. I used the Learning Framework in Number (LFIN) developed by Wright, Martland, Stafford and Stanger (2006) to profile the learners using pre and post intervention interview data and to determine their levels of multiplicative reasoning. The analysis showed the positive impact of the Mathematics Recovery programme on the improvement of multiplicative reasoning. The study contributes to the use of Mathematics Recovery programmes in South Africa from both a teacher and teacher educator perspective.
- 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
The importance's of the physical analogue clock in mediating learning of analogue clock time in Grade 4 learners
- Authors: Metelerkamp, Roger Gregory
- Date: 2014
- Subjects: Clocks and watches , Mathematics -- Study and teaching (Elementary) , Time measurements -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1986 , http://hdl.handle.net/10962/d1013169
- Description: My research topic concerns how learners use the analogue clock (as a human tool) to make meaning of clock time. This study is informed by a Vygotskian socio-cultural framework to learning and development based on the concept that human activities take place in cultural contexts and is mediated by tools. In this qualitative study I report on the learners meaning making of analogue clock time using the physical clock. This study was carried out at a South African primary school through an intervention programme after school. The research employed a case study method. It involved a purposeful sample of 4 learners (n=38) from the grade four class group based on their response to a baseline assessment task. The selected sample of learners included learners across the ability spectrum to gain rich insight into how learners make meaning of analogue clock time. Data collection and analysis was done through an interpretive approach. The video-taped interviews and intervention programme was my main instrument of data collection. Other research instruments included document analysis of responses to baseline assessment tasks. These research tools yielded the data collected and also allowed for triangulation. My research topic explored how the learners make meaning of analogue clock time. In particular the two-way movement of how the learners use the physical tool namely the analogue clock to develop meaning and how the clock mediates clock knowledge in return. The findings of the study suggest that learners’ find it difficult to conceptualise analogue clock symbols and signs, in particular, in Afrikaans the half hour concept, in relation to the two hands. The physical analogue clock is also important to support and extend clock knowledge in solving time-related problems. This shows the power of the analogue clock to mediate meaning making of clock time in young learners. Because of its potential to improve teaching and learning analogue clock time in primary school it is therefore recommended that the analogue clock time be further researched in South Africa.
- Full Text:
- Date Issued: 2014
- Authors: Metelerkamp, Roger Gregory
- Date: 2014
- Subjects: Clocks and watches , Mathematics -- Study and teaching (Elementary) , Time measurements -- Study and teaching (Elementary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1986 , http://hdl.handle.net/10962/d1013169
- Description: My research topic concerns how learners use the analogue clock (as a human tool) to make meaning of clock time. This study is informed by a Vygotskian socio-cultural framework to learning and development based on the concept that human activities take place in cultural contexts and is mediated by tools. In this qualitative study I report on the learners meaning making of analogue clock time using the physical clock. This study was carried out at a South African primary school through an intervention programme after school. The research employed a case study method. It involved a purposeful sample of 4 learners (n=38) from the grade four class group based on their response to a baseline assessment task. The selected sample of learners included learners across the ability spectrum to gain rich insight into how learners make meaning of analogue clock time. Data collection and analysis was done through an interpretive approach. The video-taped interviews and intervention programme was my main instrument of data collection. Other research instruments included document analysis of responses to baseline assessment tasks. These research tools yielded the data collected and also allowed for triangulation. My research topic explored how the learners make meaning of analogue clock time. In particular the two-way movement of how the learners use the physical tool namely the analogue clock to develop meaning and how the clock mediates clock knowledge in return. The findings of the study suggest that learners’ find it difficult to conceptualise analogue clock symbols and signs, in particular, in Afrikaans the half hour concept, in relation to the two hands. The physical analogue clock is also important to support and extend clock knowledge in solving time-related problems. This shows the power of the analogue clock to mediate meaning making of clock time in young learners. Because of its potential to improve teaching and learning analogue clock time in primary school it is therefore recommended that the analogue clock time be further researched in South Africa.
- Full Text:
- Date Issued: 2014
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