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
Exploring grade 3 teachers’ resistance to ‘take up’progressive mathematics teaching roles
- Graven, Mellony, Westaway, Lise
- Authors: Graven, Mellony , Westaway, Lise
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69700 , vital:29568 , https://DOI: 10.1007/s13394-018-0237-7
- Description: This article addresses the question: Why teachers of mathematics have yet to ‘take up’ progressive roles? Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers’ identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers’ beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to ‘take-up’ progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching mathematics.
- Full Text:
- Date Issued: 2018
- Authors: Graven, Mellony , Westaway, Lise
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69700 , vital:29568 , https://DOI: 10.1007/s13394-018-0237-7
- Description: This article addresses the question: Why teachers of mathematics have yet to ‘take up’ progressive roles? Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers’ identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers’ beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to ‘take-up’ progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching mathematics.
- Full Text:
- Date Issued: 2018
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
Learning affordances and participation enablers within a primary mathematics in-service community of practice:
- Graven, Mellony, Pausigere, Peter
- Authors: Graven, Mellony , Pausigere, Peter
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/144622 , vital:38363 , https://sajce.co.za/index.php/sajce/article/view/551
- Description: This article investigates the participation enablers and learning affordances identified by teachers through participation within an in-service community of practice (CoP) of primary teachers called the Numeracy Inquiry Community of Leader Educators (NICLE) in the Eastern Cape. The article draws on three qualitative sources of data: the annual teacher questionnaires of 42 participating teachers, interview data from 8 of the 42 sampled teachers and reflective journal entries of these 8 teachers over the first 2 years of NICLE. All three data sets point to teachers foregrounding the affordances and enablers of NICLE participation across the fundamental elements of a CoP, namely domain, community and practice. We illuminate the way in which teachers' identification of learning affordances relates to these three structural features of a CoP. In concluding, we argue that explicit consideration of these structural elements, and their interrelationship in the design of in-service programmes, could enable clearer articulation of programme aspects and support reflection on the coherence between teacher feedback on these as programmes evolve.
- Full Text:
- Date Issued: 2017
- Authors: Graven, Mellony , Pausigere, Peter
- Date: 2017
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/144622 , vital:38363 , https://sajce.co.za/index.php/sajce/article/view/551
- Description: This article investigates the participation enablers and learning affordances identified by teachers through participation within an in-service community of practice (CoP) of primary teachers called the Numeracy Inquiry Community of Leader Educators (NICLE) in the Eastern Cape. The article draws on three qualitative sources of data: the annual teacher questionnaires of 42 participating teachers, interview data from 8 of the 42 sampled teachers and reflective journal entries of these 8 teachers over the first 2 years of NICLE. All three data sets point to teachers foregrounding the affordances and enablers of NICLE participation across the fundamental elements of a CoP, namely domain, community and practice. We illuminate the way in which teachers' identification of learning affordances relates to these three structural features of a CoP. In concluding, we argue that explicit consideration of these structural elements, and their interrelationship in the design of in-service programmes, could enable clearer articulation of programme aspects and support reflection on the coherence between teacher feedback on these as programmes evolve.
- 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
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
Exploratory mathematics talk in a second language: a sociolinguistic perspective:
- Graven, Mellony, Robertson, Sally-Ann
- Authors: Graven, Mellony , Robertson, Sally-Ann
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69907 , vital:29594 , https://doi.org/10.1007/s11858-018-0952-2
- Description: This paper illuminates challenges confronting teachers and students at the literacy/numeracy interface in contexts where students have not developed sufficient English language proficiency to be learning mathematics through English but, due to socio-politically and economically driven perceptions are being taught in English. We analyse transcript data of classroom talk in a South African grade 4 mathematics lesson on fractions. Together with interview data, the lesson data highlight some of the consequences students’ diminished access to their home language appear to have on their access to mathematical meaning-making.
- Full Text:
- Date Issued: 2009
- Authors: Graven, Mellony , Robertson, Sally-Ann
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69907 , vital:29594 , https://doi.org/10.1007/s11858-018-0952-2
- Description: This paper illuminates challenges confronting teachers and students at the literacy/numeracy interface in contexts where students have not developed sufficient English language proficiency to be learning mathematics through English but, due to socio-politically and economically driven perceptions are being taught in English. We analyse transcript data of classroom talk in a South African grade 4 mathematics lesson on fractions. Together with interview data, the lesson data highlight some of the consequences students’ diminished access to their home language appear to have on their access to mathematical meaning-making.
- Full Text:
- Date Issued: 2009
Using a transdisciplinary framework to examine mathematics classroom talk taking place in and through a second language
- Graven, Mellony, Robertson, Sally-Ann
- Authors: Graven, Mellony , Robertson, Sally-Ann
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69838 , vital:29586 , https://DOI: 10.1007/s11858-018-0952-2
- Description: This paper proposes a transdisciplinary framework to allow for a multifocal exploration of classroom talk practices. It draws on data from a broader study of talk in South African Grade 4 mathematics classrooms where the language of teaching and learning (English) was the home language for neither the teachers nor their students. Lesson transcript data from one teacher’s lessons on fractions are used to demonstrate how working with three strands of conceptual insight from the disciplines of psychology, sociology and linguistics conduces to a potentially richer understanding of a teacher’s use of classroom talk in mediating her students’ mathematical understanding. By drawing on elements of Vygotsky’s sociocultural psychology, we make visible in the lesson data the ways in which this teacher used the ‘everyday’ in trying to navigate her students’ towards more ‘scientific’ conceptualizations of unit fractions. By then taking up aspects of Bernstein’s sociological work, we articulate, and make visible, how societal circumstances impinge on students’ access to exploratory mathematical discourse needed for epistemological access to abstract and generalized mathematical concepts. Finally, through Halliday’s work on the power of particular linguistic registers for meaning-making, we highlight challenges in learning mathematics in and through a second language and reveal the constraints placed on students’ opportunity to maximally exploit the distinct forms of meaning contained within the mathematics register.
- Full Text:
- Date Issued: 2009
- Authors: Graven, Mellony , Robertson, Sally-Ann
- Date: 2009
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/69838 , vital:29586 , https://DOI: 10.1007/s11858-018-0952-2
- Description: This paper proposes a transdisciplinary framework to allow for a multifocal exploration of classroom talk practices. It draws on data from a broader study of talk in South African Grade 4 mathematics classrooms where the language of teaching and learning (English) was the home language for neither the teachers nor their students. Lesson transcript data from one teacher’s lessons on fractions are used to demonstrate how working with three strands of conceptual insight from the disciplines of psychology, sociology and linguistics conduces to a potentially richer understanding of a teacher’s use of classroom talk in mediating her students’ mathematical understanding. By drawing on elements of Vygotsky’s sociocultural psychology, we make visible in the lesson data the ways in which this teacher used the ‘everyday’ in trying to navigate her students’ towards more ‘scientific’ conceptualizations of unit fractions. By then taking up aspects of Bernstein’s sociological work, we articulate, and make visible, how societal circumstances impinge on students’ access to exploratory mathematical discourse needed for epistemological access to abstract and generalized mathematical concepts. Finally, through Halliday’s work on the power of particular linguistic registers for meaning-making, we highlight challenges in learning mathematics in and through a second language and reveal the constraints placed on students’ opportunity to maximally exploit the distinct forms of meaning contained within the mathematics register.
- Full Text:
- Date Issued: 2009
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