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:
- 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.
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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:
- 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.
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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:
- 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.
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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:
- 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.
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