Investigating the Transparency of Language for Place Value Understanding Comparing Indigenous Southern African Languages and European-based Languages
- Larkin, Kevin, Vale, Pamela, Ladel, Silke, Westaway, Lise, Graven, Mellony, Kortenkamp, Ulrich
- Authors: Larkin, Kevin , Vale, Pamela , Ladel, Silke , Westaway, Lise , Graven, Mellony , Kortenkamp, Ulrich
- Date: 2025
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482410 , vital:78648 , https://doi.org/10.1080/18117295.2024.2438452
- Description: In this article we investigate the transparency of language in learning place value in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo or Emakhuwa) or a European-based language (Afrikaans, English, German or Portuguese). Since language is a key mediator in developing place value understanding, it is important to investigate the ways in which the transparency of various languages may impact place value learning. A review of pertinent literature and an analysis of literal translations of number words (to thousands) of our eight languages lead us to the conclusion that Southern African indigenous languages are more accessible in their meaning, in relation to place value, than the four European-based languages spoken in Southern Africa, which we analysed. We identified two key advantages in the indigenous languages: (i) there was transparency of the ‘places’ in how numbers are named; and (ii) there was logical alignment between the spoken and symbolic representation of numbers. Despite this, many Southern African learners learn mathematics in English, Afrikaans or Portuguese even though this is not their home language (L1). This means that many learners are denied access to the transparency of the place value concepts that exist in their L1 and must manage learning place value, not only in a yet to be learned ‘foreign’ language, but also in one where they must learn to decode the idiosyncratic ‘irregularities’ of the way those languages name numbers. We conclude this article by discussing the implications of these findings for the teaching of place value in Southern African classrooms, in which indigenous learners are often learning in a European-based language that is not their L1.
- Full Text:
- Date Issued: 2025
- Authors: Larkin, Kevin , Vale, Pamela , Ladel, Silke , Westaway, Lise , Graven, Mellony , Kortenkamp, Ulrich
- Date: 2025
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482410 , vital:78648 , https://doi.org/10.1080/18117295.2024.2438452
- Description: In this article we investigate the transparency of language in learning place value in either a Southern African indigenous language (isiXhosa, Setswana, Oshiwambo or Emakhuwa) or a European-based language (Afrikaans, English, German or Portuguese). Since language is a key mediator in developing place value understanding, it is important to investigate the ways in which the transparency of various languages may impact place value learning. A review of pertinent literature and an analysis of literal translations of number words (to thousands) of our eight languages lead us to the conclusion that Southern African indigenous languages are more accessible in their meaning, in relation to place value, than the four European-based languages spoken in Southern Africa, which we analysed. We identified two key advantages in the indigenous languages: (i) there was transparency of the ‘places’ in how numbers are named; and (ii) there was logical alignment between the spoken and symbolic representation of numbers. Despite this, many Southern African learners learn mathematics in English, Afrikaans or Portuguese even though this is not their home language (L1). This means that many learners are denied access to the transparency of the place value concepts that exist in their L1 and must manage learning place value, not only in a yet to be learned ‘foreign’ language, but also in one where they must learn to decode the idiosyncratic ‘irregularities’ of the way those languages name numbers. We conclude this article by discussing the implications of these findings for the teaching of place value in Southern African classrooms, in which indigenous learners are often learning in a European-based language that is not their L1.
- Full Text:
- Date Issued: 2025
Decolonising Content Narratives in Mathematics and Science Education: The Case of Reinventing Length Measurement
- Visnovska, Jana, Graven, Mellony, Cortina, José L, Vale, Pamela
- Authors: Visnovska, Jana , Graven, Mellony , Cortina, José L , Vale, Pamela
- Date: 2024
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482306 , vital:78638 , https://doi.org/10.1080/18117295.2024.2420469
- Description: AIn South Africa and in many other parts of the world, decolonising the curriculum has become a valued goal, while frameworks that would systematically support the decolonising project through instructional design are not broadly available. In this conceptual paper we bring readers to consider one framework for instructional design, the theory of Realistic Mathematics Education, and discuss how it can aid in decolonising education in primary years. We exemplify our conceptual position through an instructional design for teaching length measurement—a key grounding practice in both early years mathematics and science throughout the world. We propose that the resulting decolonised narratives are not only useful in marginalised contexts of countries with a history of colonisation. Due to their positioning of mathematics as a human endeavour, these narratives are capable of generating meaningful, equitable engagement with mathematics for diverse student groups in a variety of educational settings.
- Full Text:
- Date Issued: 2024
- Authors: Visnovska, Jana , Graven, Mellony , Cortina, José L , Vale, Pamela
- Date: 2024
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482306 , vital:78638 , https://doi.org/10.1080/18117295.2024.2420469
- Description: AIn South Africa and in many other parts of the world, decolonising the curriculum has become a valued goal, while frameworks that would systematically support the decolonising project through instructional design are not broadly available. In this conceptual paper we bring readers to consider one framework for instructional design, the theory of Realistic Mathematics Education, and discuss how it can aid in decolonising education in primary years. We exemplify our conceptual position through an instructional design for teaching length measurement—a key grounding practice in both early years mathematics and science throughout the world. We propose that the resulting decolonised narratives are not only useful in marginalised contexts of countries with a history of colonisation. Due to their positioning of mathematics as a human endeavour, these narratives are capable of generating meaningful, equitable engagement with mathematics for diverse student groups in a variety of educational settings.
- Full Text:
- Date Issued: 2024
A 20-year review of South African Early Grade Mathematics Research Articles
- Morrison, Samantha, Graven, Mellony, Venkat, Hamsa, Vale, Pamela
- Authors: Morrison, Samantha , Graven, Mellony , Venkat, Hamsa , Vale, Pamela
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482278 , vital:78635 , https://doi.org/10.1080/18117295.2023.2226547
- Description: In this article we share the findings emanating from a 20 year (2003–2022) review of South African Early Grade Mathematics (EGM) research articles published in key international and local/regional journals. The review shows a substantial increase in the volume of published EGM articles in the second decade (2013–2022), nationally and internationally. These increases are marked across the key clusters of articles seen in our analysis: Teachers and Teaching, Learners and Learning, Language and Multilingualism, and Assessment. The emergence of the South African Journal of Childhood Education as a phase-specific journal in 2011 has been a particularly important factor within the increasing volume of publication. We note too, that whilst the base of publication across institutions has broadened in the local/regional publication space, international publications are tied primarily to projects linked with established South African Research Chairs.
- Full Text:
- Date Issued: 2023
- Authors: Morrison, Samantha , Graven, Mellony , Venkat, Hamsa , Vale, Pamela
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482278 , vital:78635 , https://doi.org/10.1080/18117295.2023.2226547
- Description: In this article we share the findings emanating from a 20 year (2003–2022) review of South African Early Grade Mathematics (EGM) research articles published in key international and local/regional journals. The review shows a substantial increase in the volume of published EGM articles in the second decade (2013–2022), nationally and internationally. These increases are marked across the key clusters of articles seen in our analysis: Teachers and Teaching, Learners and Learning, Language and Multilingualism, and Assessment. The emergence of the South African Journal of Childhood Education as a phase-specific journal in 2011 has been a particularly important factor within the increasing volume of publication. We note too, that whilst the base of publication across institutions has broadened in the local/regional publication space, international publications are tied primarily to projects linked with established South African Research Chairs.
- Full Text:
- Date Issued: 2023
Early Grade Mathematics Directions of Growth in the Research Field
- Venkat, Hamsa, Graven, Mellony, Morrison, Samantha, Vale, Pamela
- Authors: Venkat, Hamsa , Graven, Mellony , Morrison, Samantha , Vale, Pamela
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482365 , vital:78643 , https://doi.org/10.1080/18117295.2023.2276545
- Description: Early grade mathematics (EGM) has received substantial policy attention in the last decade. In South Africa, the introduction of the ‘CAPS’ curriculum in 2011 was followed by the rollout of the now widely used national workbooks and there have been further policy-linked interventions like the Teaching Mathematics for Understanding model (Department of Basic Education, Citation2019) and the Primary Teacher Education (PrimTEd) initiative. Alongside these policy directions, there has been extensive research activity linked to interventions. These include the large-scale Gauteng Primary Mathematics and Language Strategy (Fleisch et al., Citation2016) and the more recent Bala Wande study (Mpofu et al., Citation2021), the work of longitudinal projects within the two Numeracy Chairs at Wits and Rhodes Universities and the Magic Classroom Collective in South Africa (see chapters in Venkat and Roberts’ (Citation2022) book for overviews of these projects), as well as the series of EGM-focused projects led by Mercy Kazima in Malawi (e.g. Longwe et al.’s (Citation2022) recent paper). Both review papers in this Special Issue (Morrison et al., Citation2023; Graven and Venkat, Citation2023) quantify, detail and disaggregate this growth in research interest from a low base in the previous decade.
- Full Text:
- Date Issued: 2023
- Authors: Venkat, Hamsa , Graven, Mellony , Morrison, Samantha , Vale, Pamela
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482365 , vital:78643 , https://doi.org/10.1080/18117295.2023.2276545
- Description: Early grade mathematics (EGM) has received substantial policy attention in the last decade. In South Africa, the introduction of the ‘CAPS’ curriculum in 2011 was followed by the rollout of the now widely used national workbooks and there have been further policy-linked interventions like the Teaching Mathematics for Understanding model (Department of Basic Education, Citation2019) and the Primary Teacher Education (PrimTEd) initiative. Alongside these policy directions, there has been extensive research activity linked to interventions. These include the large-scale Gauteng Primary Mathematics and Language Strategy (Fleisch et al., Citation2016) and the more recent Bala Wande study (Mpofu et al., Citation2021), the work of longitudinal projects within the two Numeracy Chairs at Wits and Rhodes Universities and the Magic Classroom Collective in South Africa (see chapters in Venkat and Roberts’ (Citation2022) book for overviews of these projects), as well as the series of EGM-focused projects led by Mercy Kazima in Malawi (e.g. Longwe et al.’s (Citation2022) recent paper). Both review papers in this Special Issue (Morrison et al., Citation2023; Graven and Venkat, Citation2023) quantify, detail and disaggregate this growth in research interest from a low base in the previous decade.
- Full Text:
- Date Issued: 2023
Grade R Teacher Expressions of Themselves as Teachers of Early Numeracy Participating in an Intervention Programme
- Long, Roxanne, Graven, Mellony
- Authors: Long, Roxanne , Graven, Mellony
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482388 , vital:78646 , https://doi.org/10.1080/18117295.2023.2224138
- Description: This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools participating monthly over 18 months. Inclusion of Grade R to schooling is relatively new following policy changes in Early Childhood Development. In-service support tends to be subsumed within the Foundation Phase without attention to the specialised nature of Grade R that emphasises learning through play. ENF focused on the development of specialised teacher knowledge to support the development of early number sense through play, particularly with conceptual manipulatives. Data sources include three pre-, during, and post-PD questionnaires. Findings reveal that participation in ENF, and access to multiple research informed numeracy resources, supported teachers in their relationship with numeracy and the teaching thereof. Questionnaire responses indicate greater confidence in themselves as knowledgeable teachers of numeracy and that belonging to the ENF community supported navigation of positive professional identities within the mixed messages of policy. The findings contribute to the community-supported field of Grade R PD research and early numeracy teaching and learning. In concluding we discuss implications of this research for Grade R PD and for policy.
- Full Text:
- Date Issued: 2023
- Authors: Long, Roxanne , Graven, Mellony
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482388 , vital:78646 , https://doi.org/10.1080/18117295.2023.2224138
- Description: This paper explores Grade R teacher expressions of themselves as teachers of numeracy, and as teachers working in the transition phase of schooling, after their participation in a research-informed numeracy-focused professional development (PD) intervention. The Early Number Fun (ENF) programme had 33 teachers from 17 Eastern Cape schools participating monthly over 18 months. Inclusion of Grade R to schooling is relatively new following policy changes in Early Childhood Development. In-service support tends to be subsumed within the Foundation Phase without attention to the specialised nature of Grade R that emphasises learning through play. ENF focused on the development of specialised teacher knowledge to support the development of early number sense through play, particularly with conceptual manipulatives. Data sources include three pre-, during, and post-PD questionnaires. Findings reveal that participation in ENF, and access to multiple research informed numeracy resources, supported teachers in their relationship with numeracy and the teaching thereof. Questionnaire responses indicate greater confidence in themselves as knowledgeable teachers of numeracy and that belonging to the ENF community supported navigation of positive professional identities within the mixed messages of policy. The findings contribute to the community-supported field of Grade R PD research and early numeracy teaching and learning. In concluding we discuss implications of this research for Grade R PD and for policy.
- Full Text:
- Date Issued: 2023
SAARMSTE’s role in building and connecting Early Grade Mathematics research: A review of SAARMSTE Proceedings 2003–2022
- Graven, Mellony, Venkat, Hamsa
- Authors: Graven, Mellony , Venkat, Hamsa
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482481 , vital:78656 , https://doi.org/10.1080/18117295.2023.2223376
- Description: This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education’s (SAARMSTE’s) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE’s role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade.
- Full Text:
- Date Issued: 2023
- Authors: Graven, Mellony , Venkat, Hamsa
- Date: 2023
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482481 , vital:78656 , https://doi.org/10.1080/18117295.2023.2223376
- Description: This paper focuses on the Southern African Association for Research in Mathematics, Science and Technology Education’s (SAARMSTE’s) role as a platform supporting research dissemination and connecting researchers in early grades mathematics (EGM) in the Southern African region. A review of the Long Papers in SAARMSTE over the last 20 years supports the finding of the other review papers in this Special Issue: that there has been substantial growth of attention to EGM since 2013. However, two distinctions are marked when looking at conference papers rather than journal papers. Firstly, there is a particularly large expansion of work in the last 5 years, with a broadening base of participation in this work. Second, looking across all the formats of conference presentations indicates SAARMSTE’s role in supporting and building EGM as a key focus of research attention, and bringing together regional and international groups with interests in this area. Given that conference proceedings usually offer a broader picture of emerging interests than journal papers, we reflect on the range of foci of attention within EGM in the SAARMSTE Proceedings, and trends within this. These trends also help us to point to areas that are likely to be of key interest in the next decade.
- Full Text:
- Date Issued: 2023
How Pre-service Teachers Reflect on their own Mathematics Teaching Practice Compared with the Practice of Others
- Chikiwa, Samukeliso, Graven, Mellony
- Authors: Chikiwa, Samukeliso , Graven, Mellony
- Date: 2021
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482399 , vital:78647 , https://doi.org/10.1080/18117295.2021.1968164
- Description: Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university – in the process of learning to reflect on practice through analysing video-recorded lessons – reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher’s practice while the other was based on a video-recording of their own practice. The study found that the PSTs’ reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers’ reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers.
- Full Text:
- Date Issued: 2021
- Authors: Chikiwa, Samukeliso , Graven, Mellony
- Date: 2021
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482399 , vital:78647 , https://doi.org/10.1080/18117295.2021.1968164
- Description: Reflective practice is a crucial element of professional growth that is gaining in popularity in teacher education, yet the ability to reflect is a skill that is neither natural nor easy to develop. This paper reports on an investigation that sought to establish if pre-service teachers at a South African university – in the process of learning to reflect on practice through analysing video-recorded lessons – reflected differently when reflecting on their own practice from the way they reflected on the practice of other teachers. Pre-service teachers were introduced to the Six Lens Framework as a tool to aid reflection on mathematics teaching. The authors compared two sets of reflections written by four pre-service teachers (PSTs) who participated in the study. One set was based on a video-recorded lesson of another teacher’s practice while the other was based on a video-recording of their own practice. The study found that the PSTs’ reflections in both cases were generally at the lowest level of the reflection spectrum. They mostly described classroom events rather than analysing the lessons to provide explanation suggestions, or reflectivity. We found, however, that all four PSTs reflected at substantially greater length on their own lessons than on those of other teachers. Furthermore, three of the four teachers’ reflections on their own practice focused on mathematical rather than general aspects and provided more suggestions for improvement than their reflections on the practice of other teachers.
- Full Text:
- Date Issued: 2021
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
Partnering with Districts to Expand an After-School Maths Club Programme
- Stott, Deborah A, Baart, Noluntu, Graven, Mellony
- Authors: Stott, Deborah A , Baart, Noluntu , Graven, Mellony
- Date: 2019
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482441 , vital:78652 , https://doi.org/10.1080/18146627.2018.1464690
- Description: A key intervention of the South African Numeracy Chair Project (SANCP) since 2011 has been the introduction of mathematics (or maths) clubs, which occur in the out-of-school time space. In 2016 the maths club concept was developed into a 15-week Pushing for Progression (PfP) teacher development programme which supports primary school mathematics teachers to run clubs beyond the SANCP local area. Expanding intervention models beyond local schools is imperative in the second phase of the SANCP (2016–2020). Working from a mixed methods methodological approach, the researchers collected pre- and post-data for a 4-operations assessment of the entire PfP programme. In this article they share learner data from one of the nine teachers who participated in the PfP maths club programme in the Uitenhague District, Eastern Cape, South Africa, to illuminate how partnerships between academics, district officials and teachers can enable powerful student learning in the club space. They argue further that within the tightly focused development programme run by teachers in this one district, it is possible for learners to make substantive progress in mathematical proficiency (MP) (especially procedural fluency and conceptual understanding) when comparing scores and learner methods between a pre- and post- assessment.
- Full Text:
- Date Issued: 2019
- Authors: Stott, Deborah A , Baart, Noluntu , Graven, Mellony
- Date: 2019
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482441 , vital:78652 , https://doi.org/10.1080/18146627.2018.1464690
- Description: A key intervention of the South African Numeracy Chair Project (SANCP) since 2011 has been the introduction of mathematics (or maths) clubs, which occur in the out-of-school time space. In 2016 the maths club concept was developed into a 15-week Pushing for Progression (PfP) teacher development programme which supports primary school mathematics teachers to run clubs beyond the SANCP local area. Expanding intervention models beyond local schools is imperative in the second phase of the SANCP (2016–2020). Working from a mixed methods methodological approach, the researchers collected pre- and post-data for a 4-operations assessment of the entire PfP programme. In this article they share learner data from one of the nine teachers who participated in the PfP maths club programme in the Uitenhague District, Eastern Cape, South Africa, to illuminate how partnerships between academics, district officials and teachers can enable powerful student learning in the club space. They argue further that within the tightly focused development programme run by teachers in this one district, it is possible for learners to make substantive progress in mathematical proficiency (MP) (especially procedural fluency and conceptual understanding) when comparing scores and learner methods between a pre- and post- assessment.
- Full Text:
- Date Issued: 2019
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
Exploring South African mathematics teachers’ experiences of learner migration
- Robertson, Sally-Ann, Graven, Mellony
- Authors: Robertson, Sally-Ann , Graven, Mellony
- Date: 2015
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482377 , vital:78645 , https://doi.org/10.1080/14675986.2015.1071754
- Description: This paper focuses on patterns of post-apartheid learner migration between schools previously segregated along racial lines. South Africa’s shift away from cultural and linguistic isolationism and the ways this has impacted educational arrangements in this country, most particularly in relation to the language of learning and teaching, affects mathematics teaching and learning in complex ways. We focus on how changes in the demographic make-up of some schools have affected the teaching and learning of mathematics by drawing on two case study vignettes in historically different schools. The vignettes are used to illuminate our discussion and to raise key questions requiring further research.
- Full Text:
- Date Issued: 2015
- Authors: Robertson, Sally-Ann , Graven, Mellony
- Date: 2015
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482377 , vital:78645 , https://doi.org/10.1080/14675986.2015.1071754
- Description: This paper focuses on patterns of post-apartheid learner migration between schools previously segregated along racial lines. South Africa’s shift away from cultural and linguistic isolationism and the ways this has impacted educational arrangements in this country, most particularly in relation to the language of learning and teaching, affects mathematics teaching and learning in complex ways. We focus on how changes in the demographic make-up of some schools have affected the teaching and learning of mathematics by drawing on two case study vignettes in historically different schools. The vignettes are used to illuminate our discussion and to raise key questions requiring further research.
- Full Text:
- Date Issued: 2015
Primary Teachers’ Experiences Relating to the Administration Processes of High-stakes Testing The Case of Mathematics Annual National Assessments
- Graven, Mellony, Venkat, Hamsa
- Authors: Graven, Mellony , Venkat, Hamsa
- Date: 2014
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482466 , vital:78654 , https://doi.org/10.1080/10288457.2014.965406
- Description: In this paper we highlight teacher experiences of the administration of high-stakes testing, in particular, of the 2012 Annual National Assessments (ANAs). The exploration is based on data gathered across two primary numeracy teacher development projects in the Eastern Cape and Gauteng in the form of open-ended questionnaires designed to elicit teacher experiences of the 2012 Numeracy ANAs (at Grades 1–3) and Mathematics ANAs (Grades 4–6). Fifty-four teachers across 21 schools (including fee-paying and non-fee-paying schools) completed the questionnaire. Using a grounded approach to the analysis of data, we note that, while teachers state support for the purpose of the ANAs ,several concerns emerge in relation to their administration. These concerns fall largely into two categories: concern for learner experiences and concern for the implications of the administration processes (including the use of exemplars and the marking process) for teacher practices. The primary purpose of the paper is to raise awareness of the need for further discussion and research into the way in which ANAs result in possible unintended consequences.
- Full Text:
- Date Issued: 2014
- Authors: Graven, Mellony , Venkat, Hamsa
- Date: 2014
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482466 , vital:78654 , https://doi.org/10.1080/10288457.2014.965406
- Description: In this paper we highlight teacher experiences of the administration of high-stakes testing, in particular, of the 2012 Annual National Assessments (ANAs). The exploration is based on data gathered across two primary numeracy teacher development projects in the Eastern Cape and Gauteng in the form of open-ended questionnaires designed to elicit teacher experiences of the 2012 Numeracy ANAs (at Grades 1–3) and Mathematics ANAs (Grades 4–6). Fifty-four teachers across 21 schools (including fee-paying and non-fee-paying schools) completed the questionnaire. Using a grounded approach to the analysis of data, we note that, while teachers state support for the purpose of the ANAs ,several concerns emerge in relation to their administration. These concerns fall largely into two categories: concern for learner experiences and concern for the implications of the administration processes (including the use of exemplars and the marking process) for teacher practices. The primary purpose of the paper is to raise awareness of the need for further discussion and research into the way in which ANAs result in possible unintended consequences.
- Full Text:
- Date Issued: 2014
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
The Evolution of an Instrument for Researching Young Mathematical Dispositions
- Graven, Mellony, Hewana, Deliza, Stott, Deborah A
- Authors: Graven, Mellony , Hewana, Deliza , Stott, Deborah A
- Date: 2013
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482508 , vital:78658 , https://doi.org/10.1080/10288457.2013.826968
- Description: In this paper, we share our experience of searching for ways in which to access learner dispositions and the evolution of an instrument that we have used as both a written and an interview instrument. We argue for the importance of understanding young learner mathematical learning dispositions in order to inform ways in which to support learning. As researchers, finding ways in which to access learner mathematical dispositions can be difficult, especially with young learners who struggle to articulate their stories. Mathematical learning dispositions are taken to include what learners say about learning and how they act when they learn. The focus of this paper is on gathering data in relation to the former. In order to illuminate what the instrument allows us to see we share some preliminary findings from our research. Our findings draw on evidence gathered, in interview form, from 16 learners in two grade 3 after school maths clubs and evidence gathered, in written form, from 614 grade 4 learners across 10 schools in the broader Grahamstown area. We interrogate the extent to which these articulated dispositions indicate constrained learning opportunities. The preliminary findings shared in this paper illuminate both what the instrument allows one to see as well as the limitations of the instrument.
- Full Text:
- Date Issued: 2013
- Authors: Graven, Mellony , Hewana, Deliza , Stott, Deborah A
- Date: 2013
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/482508 , vital:78658 , https://doi.org/10.1080/10288457.2013.826968
- Description: In this paper, we share our experience of searching for ways in which to access learner dispositions and the evolution of an instrument that we have used as both a written and an interview instrument. We argue for the importance of understanding young learner mathematical learning dispositions in order to inform ways in which to support learning. As researchers, finding ways in which to access learner mathematical dispositions can be difficult, especially with young learners who struggle to articulate their stories. Mathematical learning dispositions are taken to include what learners say about learning and how they act when they learn. The focus of this paper is on gathering data in relation to the former. In order to illuminate what the instrument allows us to see we share some preliminary findings from our research. Our findings draw on evidence gathered, in interview form, from 16 learners in two grade 3 after school maths clubs and evidence gathered, in written form, from 614 grade 4 learners across 10 schools in the broader Grahamstown area. We interrogate the extent to which these articulated dispositions indicate constrained learning opportunities. The preliminary findings shared in this paper illuminate both what the instrument allows one to see as well as the limitations of the instrument.
- 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
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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