A mathematics teacher's response to a dilemma: 'I'm supposed to teach them in English but they don't understand'
- Robertson, Sally-Ann, Graven, Mellony
- Authors: Robertson, Sally-Ann , Graven, Mellony
- Date: 2020
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/148889 , vital:38783 , https://doi.org/10.4102/sajce.v10i1.800
- Description: English is the dominant language in South African schools although it is the home language for less than 10% of the population. Many schools have yet to embrace the Language in Education Policy’s advocacy of additive bilingualism. This has led to a majority of the country’s children learning and being assessed through a language in which they lack proficiency. This article draws on second language teaching and learning theory to make a case for more systematic support for learners’ second language development and for legitimation of use of home language in mathematics classrooms where a different language is the official medium. The article shares empirical data from a South African Grade 4 mathematics teacher’s classroom to illuminate arguments in favour of additive bilingualism.
- Full Text:
- Date Issued: 2020
- Authors: Robertson, Sally-Ann , Graven, Mellony
- Date: 2020
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/148889 , vital:38783 , https://doi.org/10.4102/sajce.v10i1.800
- Description: English is the dominant language in South African schools although it is the home language for less than 10% of the population. Many schools have yet to embrace the Language in Education Policy’s advocacy of additive bilingualism. This has led to a majority of the country’s children learning and being assessed through a language in which they lack proficiency. This article draws on second language teaching and learning theory to make a case for more systematic support for learners’ second language development and for legitimation of use of home language in mathematics classrooms where a different language is the official medium. The article shares empirical data from a South African Grade 4 mathematics teacher’s classroom to illuminate arguments in favour of additive bilingualism.
- Full Text:
- Date Issued: 2020
Examining the nature of learning within an afterschool mathematics club : a case study of four learners
- Pohamba, Penehafo K, Graven, Mellony, Stott, Deborah A, Ashipala, Daniel O
- Authors: Pohamba, Penehafo K , Graven, Mellony , Stott, Deborah A , Ashipala, Daniel O
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/70121 , vital:29623 , http://dx.doi.org/10.5430/irhe.v2n1p21
- Description: This study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. This study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. This study was interpretive in nature drawing on qualitative methods with some elements of quantification in relation to learners’ progression. The club consists of 10 learners of mixed ability (5 girls and 5 boys) at a township school in Graham’s town, South Africa. Learners in this case study were selected through purposive sampling. As part of the data collection strategies, the learners were interviewed twice in terms of their numeracy proficiency. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. This study also recommended Wright et al.’s (2006) LFIN framework to be used in assessing learners’ progress in mathematics, as it could inform the refinement of instructional design within the school curriculum and teachers’ education in the Namibian context.
- Full Text:
- Date Issued: 2017
- Authors: Pohamba, Penehafo K , Graven, Mellony , Stott, Deborah A , Ashipala, Daniel O
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/70121 , vital:29623 , http://dx.doi.org/10.5430/irhe.v2n1p21
- Description: This study examined the nature of learning within an afterschool mathematics club established by the South African Numeracy Chair project. This study sought to establish what sort of progress in mathematical learning occurred in a grade 3 afterschool maths club, using assessment instruments associated with the Learning Framework in Number. The study also sought to understand the nature and effects of mentor mediation in the maths club, using Vygotsky’s notion of the Zone of Proximal Development (ZPD) together with the notion and practice of scaffolding. This study was interpretive in nature drawing on qualitative methods with some elements of quantification in relation to learners’ progression. The club consists of 10 learners of mixed ability (5 girls and 5 boys) at a township school in Graham’s town, South Africa. Learners in this case study were selected through purposive sampling. As part of the data collection strategies, the learners were interviewed twice in terms of their numeracy proficiency. The assessment interview results revealed that, in terms of proficiency in early arithmetical learning, all four learners showed progress after spending four months in an afterschool maths club. This study also recommended Wright et al.’s (2006) LFIN framework to be used in assessing learners’ progress in mathematics, as it could inform the refinement of instructional design within the school curriculum and teachers’ education in the Namibian context.
- Full Text:
- Date Issued: 2017
Resisting the desire for the unambiguous: productive gaps in researcher, teacher and student interpretations of a number story task
- Authors: Graven, Mellony , Coles, Alf
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69673 , vital:29564 , https://DOI: 10.1007/s11858-017-0863-7
- Description: This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of that recasting. This question is situated within a two-pronged task design challenge as to emerging gaps between the task designer’s intentions and teacher’s actions and secondly between the teachers’ intentions and students’ actions. Through analysing two teachers and their respective Grade R students’ interpretations of a worksheet task, provided to teachers in the project, we illuminate the way explicit constraints, in the form of task specifications, can be both enabling and constraining of learning. In so doing we recast this ‘double gap’ as enabling productive learning spaces for teacher educators, teachers and students.
- Full Text:
- Date Issued: 2017
- Authors: Graven, Mellony , Coles, Alf
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69673 , vital:29564 , https://DOI: 10.1007/s11858-017-0863-7
- Description: This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of that recasting. This question is situated within a two-pronged task design challenge as to emerging gaps between the task designer’s intentions and teacher’s actions and secondly between the teachers’ intentions and students’ actions. Through analysing two teachers and their respective Grade R students’ interpretations of a worksheet task, provided to teachers in the project, we illuminate the way explicit constraints, in the form of task specifications, can be both enabling and constraining of learning. In so doing we recast this ‘double gap’ as enabling productive learning spaces for teacher educators, teachers and students.
- Full Text:
- Date Issued: 2017
Learning metaphors and learning stories (stelos) of teachers participating in an in-service numeracy community of practice
- Pausigere, Peter, Graven, Mellony
- Authors: Pausigere, Peter , Graven, Mellony
- Date: 2013
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482430 , vital:78650 , https://doi.org/10.1080/16823206.2013.847027
- Description: This paper uses metaphors to describe how nine selected teachers are learning and developing maths identities through their participation in a primary maths focused in-service education teacher community, called the Numeracy Inquiry Community of Leader Educators (NICLE). The metaphors emerge from data obtained in interactive interviews about their learning and participation in the NICLE, focusing on their evolving mathematical identities. The focus on metaphorical terms is informed by the sociocultural-participationist theoretical perspective. The learning stories of these educators point to the emergence of two metaphors, namely activation and reinvigoration, in relation to their mathematics learning experiences and participation in the primary maths teacher in-service programme. Teachers with a history of mathematical competence reinvigorated their mathematical identities through participation in the NICLE with some of the teachers’ identities outcropping into a wider range of mathematical and maths education practices. The identities of teachers with weak mathematical histories (stunted by negative school mathematical experiences) become remediated, and new mathematical identities are activated through participation in the NICLE Communities of Practice. We conclude the paper by discussing the potentials and limitations of the Communities of Practice teacher in-service model for primary maths teachers and teacher education.
- Full Text:
- Date Issued: 2013
- Authors: Pausigere, Peter , Graven, Mellony
- Date: 2013
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482430 , vital:78650 , https://doi.org/10.1080/16823206.2013.847027
- Description: This paper uses metaphors to describe how nine selected teachers are learning and developing maths identities through their participation in a primary maths focused in-service education teacher community, called the Numeracy Inquiry Community of Leader Educators (NICLE). The metaphors emerge from data obtained in interactive interviews about their learning and participation in the NICLE, focusing on their evolving mathematical identities. The focus on metaphorical terms is informed by the sociocultural-participationist theoretical perspective. The learning stories of these educators point to the emergence of two metaphors, namely activation and reinvigoration, in relation to their mathematics learning experiences and participation in the primary maths teacher in-service programme. Teachers with a history of mathematical competence reinvigorated their mathematical identities through participation in the NICLE with some of the teachers’ identities outcropping into a wider range of mathematical and maths education practices. The identities of teachers with weak mathematical histories (stunted by negative school mathematical experiences) become remediated, and new mathematical identities are activated through participation in the NICLE Communities of Practice. We conclude the paper by discussing the potentials and limitations of the Communities of Practice teacher in-service model for primary maths teachers and teacher education.
- Full Text:
- Date Issued: 2013
Conceptualising the more knowledgeable other within a multi-directional ZPD:
- Authors: Graven, Mellony
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69519 , vital:29545 , https://doi.org/10.1007/s10649-017-9768-1
- Description: From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see how such learning with others occurs, what is the role of the (more knowledgeable) other, and if at all this role alternates between the participants. In this paper, we looked at a 5-year-old’s (Lila) interaction with her mother (Mellony) and a television remote control as Lila attempted to count in threes using the three by three physical layout of the numbered buttons 1–9 on the remote control. We specifically looked at the emergence of the Zone of Proximal Development (ZPD) as Lila’s attention was caught by the properties of the remote control and by her mother’s questions. We also pay attention to how the role of the more knowledgeable other alternates among the participants. Our findings suggest that Lila, at times, used resources provided by the physical properties of the remote control and sometimes, used resources provided by Mellony to think about the task of counting in threes. In Lila’s interaction, we interpreted a multi-directional ZPD as the role of the more knowledgeable other alternated between Mellony, Lila and the remote control.
- Full Text:
- Date Issued: 2009
- Authors: Graven, Mellony
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69519 , vital:29545 , https://doi.org/10.1007/s10649-017-9768-1
- Description: From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see how such learning with others occurs, what is the role of the (more knowledgeable) other, and if at all this role alternates between the participants. In this paper, we looked at a 5-year-old’s (Lila) interaction with her mother (Mellony) and a television remote control as Lila attempted to count in threes using the three by three physical layout of the numbered buttons 1–9 on the remote control. We specifically looked at the emergence of the Zone of Proximal Development (ZPD) as Lila’s attention was caught by the properties of the remote control and by her mother’s questions. We also pay attention to how the role of the more knowledgeable other alternates among the participants. Our findings suggest that Lila, at times, used resources provided by the physical properties of the remote control and sometimes, used resources provided by Mellony to think about the task of counting in threes. In Lila’s interaction, we interpreted a multi-directional ZPD as the role of the more knowledgeable other alternated between Mellony, Lila and the remote control.
- Full Text:
- Date Issued: 2009
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