Pre-schoolers’ symbolic learning of mathematics : a description of 4-5 year-olds’ mathematical concept knowledge
- Authors: Reyneke, Ingrid
- Date: 2018
- Subjects: Mathematics - Study and teaching (Early childhood) , Early childhood education , Mathematical notation
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/286158 , uj:30959
- Description: M.Ed. (Education) , Abstract: When children start their engagement with symbolic learning, they lay the foundations for future learning. Engaging with the world though mathematical symbols and concomitant linguistic symbols is no mean feat. Learning to ‘make their world mathematical’ is a human activity that is guided by instruction and clear communication. This is the central premise of the study – that children have not only innate number sense, but that they are also innately responsive to their environment. I thus set out to find out how a group of pre-schoolers expressed their learning of the mathematical world. This early manifestation of getting to know the world mathematically is too often underestimated in studies of learning in the early years, specifically when children are being prepared for formal education. Added to that, education curriculum development is currently the focal point in early childhood development in South Africa. In the study, I posit that the curriculum still lacks focused and direct practical assessments that are needed to optimise the programme, specifically in the development of early number concepts. I argue that young children in the pre-Grade R classes should have access to a variety of mathematical concept development activities, in an environment that allows for learning through play. This optimal learning environment is often not available for many children in South Africa. I thus approached the study with a central research question: How do children in the pre-Grade R classroom respond to a set of tasks that aims to elicit descriptions of their mathematical concept knowledge? I wanted to investigate if there is a relationship between children’s number concepts, specifically their recognition of mathematical symbols (such as digits/numerals), and their counting competence. I wondered how children respond to object classification and pattern identification tasks and what role language plays in children’s basic number concept development. To this end, customised lab tasks were developed for a sample of young children. This was done to gain insight into some of the...
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- Authors: Reyneke, Ingrid
- Date: 2018
- Subjects: Mathematics - Study and teaching (Early childhood) , Early childhood education , Mathematical notation
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/286158 , uj:30959
- Description: M.Ed. (Education) , Abstract: When children start their engagement with symbolic learning, they lay the foundations for future learning. Engaging with the world though mathematical symbols and concomitant linguistic symbols is no mean feat. Learning to ‘make their world mathematical’ is a human activity that is guided by instruction and clear communication. This is the central premise of the study – that children have not only innate number sense, but that they are also innately responsive to their environment. I thus set out to find out how a group of pre-schoolers expressed their learning of the mathematical world. This early manifestation of getting to know the world mathematically is too often underestimated in studies of learning in the early years, specifically when children are being prepared for formal education. Added to that, education curriculum development is currently the focal point in early childhood development in South Africa. In the study, I posit that the curriculum still lacks focused and direct practical assessments that are needed to optimise the programme, specifically in the development of early number concepts. I argue that young children in the pre-Grade R classes should have access to a variety of mathematical concept development activities, in an environment that allows for learning through play. This optimal learning environment is often not available for many children in South Africa. I thus approached the study with a central research question: How do children in the pre-Grade R classroom respond to a set of tasks that aims to elicit descriptions of their mathematical concept knowledge? I wanted to investigate if there is a relationship between children’s number concepts, specifically their recognition of mathematical symbols (such as digits/numerals), and their counting competence. I wondered how children respond to object classification and pattern identification tasks and what role language plays in children’s basic number concept development. To this end, customised lab tasks were developed for a sample of young children. This was done to gain insight into some of the...
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Early grade teachers and children’s difficulties with mathematics learning
- Authors: Simelane, Winnie Fikile
- Date: 2018
- Subjects: Elementary school teachers , Mathematics - Study and teaching (Early childhood)
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/286238 , uj:30969
- Description: M.Ed. (Childhood Education) , Abstract: The study aimed to explore ways in which early grade teachers identify children’s learning difficulties in mathematics, including how teachers utilised a model of conceptual development of number to interpret children’s performance. The research also aimed to establish how teachers could use a diagnostic tool, such as the MARKO-D test, to diagnose children’s numerical concept development and arithmetical competence. I was motivated to conduct this study not only because of my professional interest, but also because of the common knowledge that primary school mathematics education fails the majority of young learners in South African schools (Spaull & Kotze, 2015). According to Le Corre and Carey (2007) and Chinn (2015) learners develop learning deficits early on in their schooling career and this can create a backlog if not addressed. This backlog may later be the root of underperformance. I utilised a qualitative research design, observing teachers in their classroom, interviewing them and also scrutinising some of their lesson plans. I analysed the data inductively, coding relevant parts of the content and then coding and clustering the different codes to form categories. From these I identified themes across the categories from the different data sets, which I considered the main findings: The teachers and the Grade R practitioners struggled to apply knowledge of children’s mathematical cognition, specifically number concept development in the classroom. They did not adapt their teaching or identify mathematics learning difficulties to any depth. They were set on following the policy as per the curriculum and did not feel free to use their knowledge about ‘conceptual’ teaching of mathematics. The issue of assessment was another challenge; they did not have an accurate diagnostic tool to assess and diagnose adequately, although the MARKO-D tool was at their disposal. It was also evident that both the Grade R practitioners and the grade one teachers found it difficult to identify mathematics learning challenges in early grades learners. I drew the conclusion that they did not yet understand what type of difficulties could arise because they did not yet fully grasp what numerical cognition is. I argue, ultimately, that there is a need for early grade teachers to utilise a model of conceptual development of number to interpret children’s test results and to design an...
- Full Text:
- Authors: Simelane, Winnie Fikile
- Date: 2018
- Subjects: Elementary school teachers , Mathematics - Study and teaching (Early childhood)
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/286238 , uj:30969
- Description: M.Ed. (Childhood Education) , Abstract: The study aimed to explore ways in which early grade teachers identify children’s learning difficulties in mathematics, including how teachers utilised a model of conceptual development of number to interpret children’s performance. The research also aimed to establish how teachers could use a diagnostic tool, such as the MARKO-D test, to diagnose children’s numerical concept development and arithmetical competence. I was motivated to conduct this study not only because of my professional interest, but also because of the common knowledge that primary school mathematics education fails the majority of young learners in South African schools (Spaull & Kotze, 2015). According to Le Corre and Carey (2007) and Chinn (2015) learners develop learning deficits early on in their schooling career and this can create a backlog if not addressed. This backlog may later be the root of underperformance. I utilised a qualitative research design, observing teachers in their classroom, interviewing them and also scrutinising some of their lesson plans. I analysed the data inductively, coding relevant parts of the content and then coding and clustering the different codes to form categories. From these I identified themes across the categories from the different data sets, which I considered the main findings: The teachers and the Grade R practitioners struggled to apply knowledge of children’s mathematical cognition, specifically number concept development in the classroom. They did not adapt their teaching or identify mathematics learning difficulties to any depth. They were set on following the policy as per the curriculum and did not feel free to use their knowledge about ‘conceptual’ teaching of mathematics. The issue of assessment was another challenge; they did not have an accurate diagnostic tool to assess and diagnose adequately, although the MARKO-D tool was at their disposal. It was also evident that both the Grade R practitioners and the grade one teachers found it difficult to identify mathematics learning challenges in early grades learners. I drew the conclusion that they did not yet understand what type of difficulties could arise because they did not yet fully grasp what numerical cognition is. I argue, ultimately, that there is a need for early grade teachers to utilise a model of conceptual development of number to interpret children’s test results and to design an...
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