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
An exploration of the prior conceptual understanding of measurement of first year national certificate (vocational) Engineering students
- Authors: Vale, Pamela
- Date: 2017
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/8033 , vital:21337
- Description: Measurement is acknowledged to be a critical component in mathematics education and is particularly important for vocational Engineering students, for whom this is a key skill required in the workplace. The goal of this research was to explore the existing measurement conceptualisations of vocational Engineering students at the outset of their course, as evident in their engagement with mediated measurement tasks. The focus on students’ prior knowledge in measurement, was for the value that this awareness holds in understanding the learning needs of the students. Students participated in five measurement tasks. Four took the form of dynamically assessed task-based interviews, and the fifth was a written test assessing what they had learned during their Mathematics classes. Domains of measurement that were assessed in these tasks included length, area, surface area, volume and flow rate. The interviewer took the role of mediator and students were assessed according to the number of moments of mediation and the degree of mediation required to successfully complete the task. Students’ responsiveness to this mediation provided insight as to their conceptualisations of the measurements relevant to the task. This research was exploratory in nature and adopted an open and flexible approach to the data analysis. Critical incidents were identified and coded according to the mediation offered and the actions of the students during the measuring activity. This allowed patterns to emerge that revealed stable and emerging conceptualisations that related to embodied and symbolic aspects of measurement. Evidence was found that for many of these students the link between the embodied and symbolic aspects of the concept was broken. This insight allowed suggestions to be formulated about how better to facilitate these students’ learning of measurement.
- Full Text:
- Date Issued: 2017
- Authors: Vale, Pamela
- Date: 2017
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/8033 , vital:21337
- Description: Measurement is acknowledged to be a critical component in mathematics education and is particularly important for vocational Engineering students, for whom this is a key skill required in the workplace. The goal of this research was to explore the existing measurement conceptualisations of vocational Engineering students at the outset of their course, as evident in their engagement with mediated measurement tasks. The focus on students’ prior knowledge in measurement, was for the value that this awareness holds in understanding the learning needs of the students. Students participated in five measurement tasks. Four took the form of dynamically assessed task-based interviews, and the fifth was a written test assessing what they had learned during their Mathematics classes. Domains of measurement that were assessed in these tasks included length, area, surface area, volume and flow rate. The interviewer took the role of mediator and students were assessed according to the number of moments of mediation and the degree of mediation required to successfully complete the task. Students’ responsiveness to this mediation provided insight as to their conceptualisations of the measurements relevant to the task. This research was exploratory in nature and adopted an open and flexible approach to the data analysis. Critical incidents were identified and coded according to the mediation offered and the actions of the students during the measuring activity. This allowed patterns to emerge that revealed stable and emerging conceptualisations that related to embodied and symbolic aspects of measurement. Evidence was found that for many of these students the link between the embodied and symbolic aspects of the concept was broken. This insight allowed suggestions to be formulated about how better to facilitate these students’ learning of measurement.
- Full Text:
- Date Issued: 2017
Describing the relationship between the cognitive and linguistic complexity of a mathematical literacy examination and types of student errors
- Authors: Vale, Pamela
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Research -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa -- Evaluation Mathematics -- Study and teaching (Secondary) -- South Africa -- Evaluation Communication in foreign language education -- Research -- South Africa Communication in foreign language education -- Research -- South Africa Education, Secondary -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1397 , http://hdl.handle.net/10962/d1001774
- Description: Much prior research has shown that if students have a poor command of the language in which they are taught and assessed, they experience a complex and deep learning disadvantage (Barton & Neville-Barton, 2003). Abedi (2006) mentions, in particular, that unnecessary linguistic complexity can threaten the validity of examination items and thus compromises the fairness of the assessment for English language learners. In Clarkson’s (1991, p. 31) research it was found that for the English language learners in the study “comprehension errors [made] up a high proportion of the errors made when…students attempt[ed] to solve mathematical word problems”. In an attempt to explore whether this was the case for a group of National Certificate (Vocational) [NC(V)] students at an FET college, the research conducted in this study focused on describing the cognitive and linguistic complexity of Level 4 Mathematical Literacy examination items as well as the types of responses from a sample of students. A mixed-methods case study design was selected. Student errors were classified as either due to mathematical literacy-related sources, or language-related sources and the question was asked as to how the cognitive and linguistic complexity of items might be related to the types of errors made. Statistically significant correlations were found between the linguistic complexity of items and language-related errors, and between the cognitive complexity of items and all types of errors. It was also possible to identify which language features, in particular, were statistically significantly correlated with linguistic complexity, namely: prepositional phrases; words of 7 letters or more and complex/compound sentences. As was expected, the majority of errors were categorised as mathematical literacy-related. However, as many as 19.22% of all errors made were identified as language-related. While the scope of the study prevents any generalisations from being made, the results indicate a need for a larger-scale study of this nature to determine if the complex and deep learning disadvantage mentioned by Barton and Neville-Barton (2003) does exist with regard to the assessment of Mathematical Literacy for NC(V) students who are English language learners (Barton & Neville-Barton, 2003).
- Full Text:
- Date Issued: 2013
- Authors: Vale, Pamela
- Date: 2013
- Subjects: Mathematics -- Study and teaching (Secondary) -- Research -- South Africa Mathematics -- Study and teaching (Secondary) -- South Africa -- Evaluation Mathematics -- Study and teaching (Secondary) -- South Africa -- Evaluation Communication in foreign language education -- Research -- South Africa Communication in foreign language education -- Research -- South Africa Education, Secondary -- Research -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1397 , http://hdl.handle.net/10962/d1001774
- Description: Much prior research has shown that if students have a poor command of the language in which they are taught and assessed, they experience a complex and deep learning disadvantage (Barton & Neville-Barton, 2003). Abedi (2006) mentions, in particular, that unnecessary linguistic complexity can threaten the validity of examination items and thus compromises the fairness of the assessment for English language learners. In Clarkson’s (1991, p. 31) research it was found that for the English language learners in the study “comprehension errors [made] up a high proportion of the errors made when…students attempt[ed] to solve mathematical word problems”. In an attempt to explore whether this was the case for a group of National Certificate (Vocational) [NC(V)] students at an FET college, the research conducted in this study focused on describing the cognitive and linguistic complexity of Level 4 Mathematical Literacy examination items as well as the types of responses from a sample of students. A mixed-methods case study design was selected. Student errors were classified as either due to mathematical literacy-related sources, or language-related sources and the question was asked as to how the cognitive and linguistic complexity of items might be related to the types of errors made. Statistically significant correlations were found between the linguistic complexity of items and language-related errors, and between the cognitive complexity of items and all types of errors. It was also possible to identify which language features, in particular, were statistically significantly correlated with linguistic complexity, namely: prepositional phrases; words of 7 letters or more and complex/compound sentences. As was expected, the majority of errors were categorised as mathematical literacy-related. However, as many as 19.22% of all errors made were identified as language-related. While the scope of the study prevents any generalisations from being made, the results indicate a need for a larger-scale study of this nature to determine if the complex and deep learning disadvantage mentioned by Barton and Neville-Barton (2003) does exist with regard to the assessment of Mathematical Literacy for NC(V) students who are English language learners (Barton & Neville-Barton, 2003).
- Full Text:
- Date Issued: 2013
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