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.
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Exploratory mathematics talk in a second language: a sociolinguistic perspective:
- 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.
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Using a transdisciplinary framework to examine mathematics classroom talk taking place in and through a second language
- 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.
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