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
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- 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
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Examining the nature of the relationship between learners' conceptual understanding and their mathematical dispositions in the context of multiplication
- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
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- Authors: Ndongeni, Siviwe Lungelwa
- Date: 2014
- Subjects: Multiplication -- Study and teaching (Elementary) -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa , Problem solving in children , Multiplication -- Ability testing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1987 , http://hdl.handle.net/10962/d1013217
- Description: The focus of this study is to explore three key aspects of learners’ multiplicative proficiency: the nature of learners’ conceptual understanding of multiplication, the nature of learners’ numeracy dispositions (in the context of learning multiplication), and the relationship between conceptual understanding and productive dispositions in the context of multiplication. The study used a qualitative case study approach to gather rich data in relation to these. In the study a purposively selected sample of six Grade 4 learners was used from the same school: two high, two average, and two low performers. Kilpatrick, Swafford, and Findell (2001) define conceptual understanding as a functional grasp of mathematical ideas and its significant indicator is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. They then refer to productive disposition as the ‘tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (p.131). Individual interviews were conducted using Wright, et al.’s (2006) instrument for exploring the nature of students’ conceptual understanding of multiplication. Wright, et al. (2006) argue that the topics of multiplication and division build on the students’ knowledge of addition and subtraction, and also multiplication and division provide foundational knowledge for topics such as fractions, ratios, proportion and percentage, all of which are core and essential areas of mathematical learning typically addressed in the primary or elementary grades. Researchers agree that learners have to be exposed to various strategies so that they are able to see that there is a difference between additive reasoning and multiplicative reasoning. In order to classify learners’ conceptual understanding of multiplication an analysis of the data was done and learners were allocated levels according to the Wright, et al. (2006) levels of achievement. For the classification of learner dispositions, the data was analysed in terms of the elements of productive disposition as defined by Kilpatrick, et al. (2001) and Carr and Claxton (2002). The key findings of the study indicate that for conceptual understanding most of the learners depended on using concrete materials in solving multiplication and they also used basic strategies and methods. The findings for productive dispositions were that most of the learners saw themselves as competent in doing multiplication but the aspect of sense making and steady effort was less developed. The findings for the relationship between conceptual understanding and productive disposition were that both strands have a mutual relationship in which one helped the other to develop.
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Investigating how problem solving skills can be developed using a collaborative learning environment
- Authors: Sonne, Anita
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Social learning , Active learning , Problem solving in children , Educational equalization -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1977 , http://hdl.handle.net/10962/d1013017
- Description: This thesis examines whether problem solving strategies develop and improve through working in a collaborative environment and, if so, how. The study explored the way peer-topeer discussions which are focussed on finding solutions to mathematical problems might shape learners' attitudes and participation in mathematical problem solving. I use the Vygotskian (1978) socio-cultural perspective where the process of learning takes place within the Zone of Proximal Development (ZPD). Polya's problem solving heuristics (Polya, 1973) and Kilpatrick's "Instructional Triangle" (Kilpatrick, Swafford & Findell, 2001) provided the analytical framework for the study. Seven grade 7 learners from a Ex-Model C school, volunteered to participate in the study. The data gathering process involved an initial problem solving assessment, a written questionnaire, observations and video recordings of the seven learners during a series of after school problem solving sessions and post intervention learner interviews. The study showed that group discussion can have a positive impact on learners' problem solving in several respects: My key findings point to: Mathematical communication does play a role in development of problem solving strategies. A more knowledgeable other, with regards to Vygotsky's (1978) ZPD and Kilpatrick et al's (2001) instructional triangle is a critical factor in the development of problem solving strategies. All five strands of Kilpatrick et al., (2001), strands for mathematical proficiency are required for correct solutions to be calculated. At times Polya's (1973) steps for problem solving move at a rapid pace and are difficult to notice. These steps develop at different speeds for different people.
- Full Text:
Investigating how problem solving skills can be developed using a collaborative learning environment
- Authors: Sonne, Anita
- Date: 2014
- Subjects: Mathematics -- Study and teaching (Elementary) -- South Africa , Social learning , Active learning , Problem solving in children , Educational equalization -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1977 , http://hdl.handle.net/10962/d1013017
- Description: This thesis examines whether problem solving strategies develop and improve through working in a collaborative environment and, if so, how. The study explored the way peer-topeer discussions which are focussed on finding solutions to mathematical problems might shape learners' attitudes and participation in mathematical problem solving. I use the Vygotskian (1978) socio-cultural perspective where the process of learning takes place within the Zone of Proximal Development (ZPD). Polya's problem solving heuristics (Polya, 1973) and Kilpatrick's "Instructional Triangle" (Kilpatrick, Swafford & Findell, 2001) provided the analytical framework for the study. Seven grade 7 learners from a Ex-Model C school, volunteered to participate in the study. The data gathering process involved an initial problem solving assessment, a written questionnaire, observations and video recordings of the seven learners during a series of after school problem solving sessions and post intervention learner interviews. The study showed that group discussion can have a positive impact on learners' problem solving in several respects: My key findings point to: Mathematical communication does play a role in development of problem solving strategies. A more knowledgeable other, with regards to Vygotsky's (1978) ZPD and Kilpatrick et al's (2001) instructional triangle is a critical factor in the development of problem solving strategies. All five strands of Kilpatrick et al., (2001), strands for mathematical proficiency are required for correct solutions to be calculated. At times Polya's (1973) steps for problem solving move at a rapid pace and are difficult to notice. These steps develop at different speeds for different people.
- Full Text:
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