Marthie Van Der Walt - Academia.edu (original) (raw)

Papers by Marthie Van Der Walt

Research paper thumbnail of Developing a Basic Mathematics Questionnaire for Grades 4 to 7

Journal of Psychology in Africa, 2009

In this article, the authors report on the development of a basic mathematics questionnaire for G... more In this article, the authors report on the development of a basic mathematics questionnaire for Grades 4 to 7 (the BM(P)). The provisional instrument was completed by 1,103 Afrikaans-, English-and Tswana-speaking learners in Grades 4 to 7 in the North-West Province of South Africa. First-order factor analysis was carried out, item analysis was done, reliability coefficients and discrimination values were calculated, and norm tables were established. Weighted means were used to ensure that the results were proportional to the ratios of the language groups in the province. We (the authors) concluded that standardisation of the BM(P) yielded satisfactory results with regard to the determination of issues such as construct validity, reliability, validity and intercorrelations for Grade 4 to 7 learners in the North-West Province of South Africa.

Research paper thumbnail of Metacognitive awareness and the zone of proximal intermediate phase mathematics teachers’ professional development

Eurasia Journal of Mathematics, Science and Technology Education

This paper investigates in-service intermediate phase mathematics teachers' metacognitive awarene... more This paper investigates in-service intermediate phase mathematics teachers' metacognitive awareness based on their engagement in a professional development intervention in two ruraland one township school in South Africa. Professional teacher development interventions should be structured and collaborative as teachers tend to revert to traditional modes of teaching when interventions are brief and sporadic. This research was scaffolded across the zone of proximal teacher development (ZPTD) as conceptualized by Warford (2011). The aim of the study was to investigate how metacognitive awareness facilitated intermediate phase mathematics teachers' ZPTD, i.e., from their actual knowledge to "proximal development". 10 intermediate phase mathematics teachers participated in the qualitative research (n=10). The professional development intervention was conducted on two consecutive Saturdays, infused with an adapted lesson study approach. The data was collected through (i) individual interviews, (ii) reflective prompts, (iii) observations, and (iv) reflective journals. The data from each data source were coded and categorized and were triangulated to answer the research question. Participants deemed the professional development intervention and the accompanying materials as supportive and showed increased metacognitive awareness of their personal teaching praxis during and after the intervention, hence growth along the ZPTD occurred.

Research paper thumbnail of Puppetry as a pedagogy of play in the Intermediate Phase mathematics classroom: A case study

Perspectives in Education, 2021

Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, p... more Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, play affords a playful element that can optimise learning opportunities. However, many mathematics teachers are unfamiliar with the integration of pedagogy of play (PoP) (in this case, puppetry). The aim of this paper is to report on one participant's (an Intermediate Phase mathematics teacher [N=1]) lived experiences of teaching with puppets after a twoday intervention. A case study approach was followed and the participant constantly reflected on his experiences. Data were collected through (i) a semi-structured open-ended interview, (ii) reflective prompts and (iii) a reflective journal with prompts. The data revealed the participant's experiences of puppetry, how his metacognitive awareness developed and how he transferred new knowledge to his Intermediate Phase mathematics classroom. The data were analysed using content analysis. The results show that, although learners often deem mathematics "mundane" and "unexciting", puppetry allowed the participant's learners (according to his reflections) to experience this subject as enjoyable and creative, encouraging participation and liveliness, as the puppet was considered a peer in teaching-learning. The Intermediate Phase mathematics classroom became a space where content became meaningful, accessible and understandable to all learners.

Research paper thumbnail of Study Orientation Questionnaire in Mathematics (Primary)

Research paper thumbnail of rights in Africa

Poor mathematics performance in schools is both a national and an international concern. Teachers... more Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no math-ematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase student teachers in South Africa. To make recommendations for the drafting of such standards for final year Foundation Phase teachers, we com-pared different policy documents. We performed a document analysis on policy documents from South Africa, The Netherlands, Australia and North Carolina (United States of America), all of which addressed the number domain in mathematics. Our find-ings indicate that knowledge standards ought to include subject matter knowledge, while practice standards require pedagogical content knowledge, noting that neither of these are fulfilled in the education system in South Africa at present. Key words: founda...

Research paper thumbnail of List of tables

The reader is reminded of the following: ■ The referencing, as well as the editorial style as pre... more The reader is reminded of the following: ■ The referencing, as well as the editorial style as prescribed by the Publication Manual (5th edition) of the American Psychological Association (APA) was followed in this thesis. This practice is in line with the policy of the Programme in Industrial Psychology of the North-West University (Potchefstroom Campus) to use APA style in all scientific documents. ■ The thesis is submitted in the form of three research articles. ACKNOWLEDGEMENTS • Prof. Ian Rothmann for his support, motivation and patience, without which this would not have been possible. • All the participants in this study, as well as the organisation that took part in this study for their support and willingness to participate. • My family for all their support. • I extend my grateful appreciation to Mrs. M. Coetzee for the professional manner in which she conducted the language editing.

Research paper thumbnail of International comparisons of Foundation Phase number domain mathematics knowledge and practice standards

South African Journal of Education, 2015

Poor mathematics performance in schools is both a national and an international concern. Teachers... more Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase student teachers in South Africa. To make recommendations for the drafting of such standards for final year Foundation Phase teachers, we compared different policy documents. We performed a document analysis on policy documents from South Africa, The Netherlands, Australia and North Carolina (United States of America), all of which addressed the number domain in mathematics. Our findings indicate that knowledge standards ought to include subject matter knowledge, while practice standards require pedagogical content knowledge, noting that neither of these are fulfilled in the education system in South Africa at present.

Research paper thumbnail of Exploiting Metacognitive Networks Embedded in Narrative Focus Group Interviews Using NodeXL

The Qualitative Report, Oct 17, 2016

Development of metacognitive theory for changing pedagogy remains an essential research activity.... more Development of metacognitive theory for changing pedagogy remains an essential research activity. A lack of sufficient clear-cut qualitative analysis procedures extracting embedded metacognitive constructs from qualitative data (e.g., narrative focus group interviews) can hinder development of theory. An approach is therefore needed to analyse qualitative metacognitive data exploiting embedded metacognitive constructs for theory development. In an undergraduate fourth-year mathematics education module, two groups of students (Group A: n = 6; Group B: n = 5) participated in a series of focus group interviews. Participants designed and refined mathematics lessons about the concept of place value. We identified metacognitive networks as an embedded construct in students' metacognitive processes. Findings indicate that metacognitive networks of an individual, social and socially shared metacognitive nature are embedded in qualitative data, and can be exploited to develop new metacognitive theory. We offer a novel three-step process in this methodology paper to extract metacognitive networks using Microsoft Office, ATLAS.ti and NodeXL.

Research paper thumbnail of Potgieter, E. (2020). Pedagogies of play to develop intermediate phase mathematics teachers' metacognitive awareness. (Unpublished master's thesis). North-West University, Potchefstroom

Research paper thumbnail of Teaching mathematics: foundation to senior phase

Research paper thumbnail of Do mathematics learning facilitators implement metacognitive strategies

South African Journal of Education, 2007

It is widely accepted that mathematical skills are critically important in our technologically so... more It is widely accepted that mathematical skills are critically important in our technologically sophisticated world. Educators' metacognition directs, plans, monitors, evaluates and reflects their instructional behaviour and this can promote learners ' learning with und ers tanding. The p urpos e of this study was to investigate the exten t to which mathematics educators implemented and taught metacognit ive strategies. Res ults of the quantitative part of the study were triangulated with the results of the qualitative part. Results suggested that whereas mathematics educators may well have possess ed metacognitive skills and utilised them intuitively, thes e s kills were not implemented to a s atisfa ctory extent in the classes we observed.

Research paper thumbnail of The Affordances of Adapted Lesson Study in South Africa - Two Cases

Teacher education programmes are often criticised for not addressing the ‘theory-practice divide’... more Teacher education programmes are often criticised for not addressing the ‘theory-practice divide’. Student teachers are left underprepared for facing the 'coalface' of practice. Two of the possible reasons can be didactics modules being too theory-based and a lack of mentorship at the university or (WIL) schools. According to the Japanese lesson study model teachers collaboratively design, present, refine and re-present a lesson. Two different ways of implementing lesson study, at two South African universities that focused on the professional development of life sciences and mathematics student teachers, are shared by the authors. This qualitative research resulted in findings that highlight the affordances of lesson study approaches in the process of enculturation within a community of practice. Participants include 60 life sciences and 30 mathematics (either 4th year BEd or PGCE) student teachers. Data collection methods included individualand focus group interviews and r...

Research paper thumbnail of Consumer Studies student teachers’ affective experiences during project-based learning

Die implementering van projekgebaseerde leer het die potensiaal om affektiewe faktore in studente... more Die implementering van projekgebaseerde leer het die potensiaal om affektiewe faktore in studente positief te ontwikkel wat selfgerigte lewenslange leer kan bevorder. Lewenslange leer is ’n sleutelvereiste vir onderwysers om relevant kundig in hulle vakgebied te bly, asook om aan die vereistes te kan voldoen wat aan leerders en onderwysers in die 21ste eeu gestel word. Dit is veral belangrik vir onderwysers wat Verbruikerstudie, ’n dinamiese en waardevolle vak in Suid-Afrikaanse skole, aanbied. Die bevordering van selfgerigte lewenslange leer as deel van die opleiding van Verbruikerstudie-onderwysstudente is dus noodsaaklik. Verskillende affektiewe faktore, byvoorbeeld motivering, dra by tot die bevordering van leer wat ontwikkel kan word deur die keuse van gepaste onderrig-leerstrategiee. Affek kan leer deur geheueprosesse, leerprosesse, aandagspan, ervarings en motivering beinvloed. ’n Gevallestudie is onderneem om ondersoek in te stel op welke wyse projekgebaseerde leer in ’n opl...

Research paper thumbnail of Mathematics Confidence : Reflections on Problem-Solving Experiences

The purpose of this paper is to present the findings of a qualitative inquiry into Grade 8 and 9 ... more The purpose of this paper is to present the findings of a qualitative inquiry into Grade 8 and 9 learners’ mathematics confidence. Learners reflect on experiences with mathematics that have influenced their levels of confidence in the social, psychological and intellectual domains. A convenient purposive sample of four participants, individually interviewed with reflective questioning, provides insight into their reflective accounts on experiences with mathematics problem solving. Through content analysis, the researchers’ findings confirm the dimensionality of mathematics confidence and present sources of participants’ mathematics confidence.

Research paper thumbnail of Metacognitive Transference: What Portfolios Tell Us About Contextualized Mathematics

Recognising the value of ethnomathematics is an important aspect of education worldwide. While th... more Recognising the value of ethnomathematics is an important aspect of education worldwide. While the value of IK in education has been recognised, this recognition is yet to translate into practical curriculum processes. It is not clear how metacognition can drive the transference of knowledge and skills into the classroom while, at the same time, contextualising mathematics. One approach is to introduce teachers to viable ways of contextualising mathematics, through ethnomathematics, and equipping them with metacognitive strategies (e.g. planning, monitoring and evaluating) to do so. Metacognitive transference and its relationship with ethnomathematics is the subject of this paper as it reports on what the portfolios tell us about contextualising mathematics and how metacognition transference takes place. An interpretivist-qualitative approach as research design was employed. Data collection instruments included lesson plans, reflections and open-ended questions. Content analysis, ba...

Research paper thumbnail of Project-based learning in higher education : new skills set for consumer studies teacher education

Journal for new generation sciences, 2016

The changing expectations demanded of life and work in the 21st century require that employees, i... more The changing expectations demanded of life and work in the 21st century require that employees, including teachers, be properly prepared for situations that may arise in this day and age. This is especially true for teachers of Consumer Studies, who have to develop an expanding range of knowledge and skills in order to facilitate teaching-learning effectively in their subject. Project-based learning has been implemented in Consumer Studies and other disciplines as a teaching-learning strategy to develop 21st century career skills in students, but has not yet been reported on in relation to the preparation of pre-service Consumer Studies teachers. A qualitative case study was undertaken to determine how the implementation of project-based learning as a teaching-learning strategy would affect and contribute to the development of preferred skills in pre-service Consumer Studies teachers. The findings show that project-based learning could make various positive and constructive contribu...

Research paper thumbnail of The decolonisation of the curriculum project: The affordances of indigenous knowledge for self-directed learning

NWU Self-Directed Learning Series, 2019

Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book... more Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book Publishers Forum Best Practice for Peer Review of Scholarly Books'. The manuscript was subjected to a rigorous two-step peer review prior to publication, with the identities of the reviewers not revealed to the author(s). The reviewers were independent of the publisher and/or authors in question. The reviewers commented positively on the scholarly merits of the manuscript and recommended that the manuscript should be published. Where the reviewers recommended revision and/or improvements to the manuscript, the authors responded adequately to such recommendations. Research Justification This book is the result of a longitudinal research project (2016-2018) funded by the National Research Foundation and the Fuchs Foundation, and it disseminates original research. The project researched the affordances of indigenous knowledge in the school Science, Technology and Mathematics curricula. Short learning programmes (SLPs) were offered to Science, Technology, Engineering and Mathematics (STEM) teachers, during which they engaged in creative and inquiry-based teaching and learning strategies. Research shows that strategies such as problem-based and cooperative learning have the potential to enhance self-directed learning. This design-based research was conducted in several provinces in South Africa (North-West Province, the Northern Cape, Limpopo province, and Gauteng). Based on the data obtained after each intervention, design principles were formulated for redesigning of SLPs. The qualitative research focussed on teachers' lived experiences of the epistemological bordercrossing between Natural Science and indigenous knowledge, their views on the nature of science and indigenous knowledge, and the reformed teaching and learning that took place after the intervention in teachers' classrooms. Most of the chapters in the book report empirical data, with the exception of three chapters (Ch. 2, Ch. 10 and Ch. 11), that can be categorised as systematic reviews. The book is devoted to scholarship in the field of STEM education and teacher professional development, with a specific focus on research into the enhancement of self-directed learning. The target audience are scholars working in the fields of indigenous knowledge systems, STEM education, teacher professional development and self-directed learning. This book makes a unique contribution in terms of, firstly, its extensive use of third-generation Cultural-Historical Activity Theory (CHAT) as a research lens and, secondly, in drawing on research from the fields of neuroscience, science education philosophy, self-directed learning and indigenous knowledge systems, in arguing for such border-crossing. Chapter 1 shows how this research contributes to the development of fourthgeneration CHAT, which, owing to the complexity of the object (which Engeström refers to as 'runaway objects'), requires a focus on numerous activity systems. The book also explores the conundrum of research ethics during participatory action research with holders of indigenous knowledge. In accordance with the requirements of the Department of Higher Education and Training, this book contains more than 50% original content, and no part of the work has been plagiarised. Ethical clearance for the project was provided by the North

Research paper thumbnail of A mathematics vocabulary questionnaire for use in the intermediate phase

South African Journal of Education, 2008

Teachers and psychologists need an instrument to assess learners' language proficiency in mathema... more Teachers and psychologists need an instrument to assess learners' language proficiency in mathematics to enable them to plan and evaluate interventions and to facilitate best practice in mathematics classrooms. We describe the development of a mathematics vocabulary questionnaire to measure learners' language proficiency in mathematics in the intermediate phase. It covers all the steps from designing the preliminary questionnaire to standardising the final instrument. A sample of 1 103 Grades 4 to 7 Afrikaans-, English-and Tswana-speaking learners in North West Province completed the Mathematics Vocabulary questionnaire (Primary) (MV(P)), consisting of 12 items. We analysed the data by calculating discrimination values, performing a factor analysis, determining reliability coefficients, and investigating item bias by language, gender, and grade. We concluded that there was strong evidence of validity and reliability for the MV(P).

Research paper thumbnail of The affordances of technology for teaching indigenous knowledge

NWU Self-Directed Learning Series, 2019

Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book... more Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book Publishers Forum Best Practice for Peer Review of Scholarly Books'. The manuscript was subjected to a rigorous two-step peer review prior to publication, with the identities of the reviewers not revealed to the author(s). The reviewers were independent of the publisher and/or authors in question. The reviewers commented positively on the scholarly merits of the manuscript and recommended that the manuscript should be published. Where the reviewers recommended revision and/or improvements to the manuscript, the authors responded adequately to such recommendations. Research Justification This book is the result of a longitudinal research project (2016-2018) funded by the National Research Foundation and the Fuchs Foundation, and it disseminates original research. The project researched the affordances of indigenous knowledge in the school Science, Technology and Mathematics curricula. Short learning programmes (SLPs) were offered to Science, Technology, Engineering and Mathematics (STEM) teachers, during which they engaged in creative and inquiry-based teaching and learning strategies. Research shows that strategies such as problem-based and cooperative learning have the potential to enhance self-directed learning. This design-based research was conducted in several provinces in South Africa (North-West Province, the Northern Cape, Limpopo province, and Gauteng). Based on the data obtained after each intervention, design principles were formulated for redesigning of SLPs. The qualitative research focussed on teachers' lived experiences of the epistemological bordercrossing between Natural Science and indigenous knowledge, their views on the nature of science and indigenous knowledge, and the reformed teaching and learning that took place after the intervention in teachers' classrooms. Most of the chapters in the book report empirical data, with the exception of three chapters (Ch. 2, Ch. 10 and Ch. 11), that can be categorised as systematic reviews. The book is devoted to scholarship in the field of STEM education and teacher professional development, with a specific focus on research into the enhancement of self-directed learning. The target audience are scholars working in the fields of indigenous knowledge systems, STEM education, teacher professional development and self-directed learning. This book makes a unique contribution in terms of, firstly, its extensive use of third-generation Cultural-Historical Activity Theory (CHAT) as a research lens and, secondly, in drawing on research from the fields of neuroscience, science education philosophy, self-directed learning and indigenous knowledge systems, in arguing for such border-crossing. Chapter 1 shows how this research contributes to the development of fourthgeneration CHAT, which, owing to the complexity of the object (which Engeström refers to as 'runaway objects'), requires a focus on numerous activity systems. The book also explores the conundrum of research ethics during participatory action research with holders of indigenous knowledge. In accordance with the requirements of the Department of Higher Education and Training, this book contains more than 50% original content, and no part of the work has been plagiarised. Ethical clearance for the project was provided by the North

Research paper thumbnail of Metacognitive awareness and visualisation in the imagination: The case of the invisible circles

Pythagoras, 2018

Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the im... more Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental case studies. Understanding how mathematical objects are modelled in the mind may explain the transfer of the mathematical ideas between metacognitive awareness and the rigour of the imaginer’s mental images. From each school, a top achiever in mathematics was invited to an individual interview (n = 4) and was video-recorded while solving a mathematics word problem. Participants also had to identify metacognitive statements from a sample of statement cards (n = 15) which provided them the necessary vocabulary to express their thinking during the interview. During their attempts, participa...

Research paper thumbnail of Developing a Basic Mathematics Questionnaire for Grades 4 to 7

Journal of Psychology in Africa, 2009

In this article, the authors report on the development of a basic mathematics questionnaire for G... more In this article, the authors report on the development of a basic mathematics questionnaire for Grades 4 to 7 (the BM(P)). The provisional instrument was completed by 1,103 Afrikaans-, English-and Tswana-speaking learners in Grades 4 to 7 in the North-West Province of South Africa. First-order factor analysis was carried out, item analysis was done, reliability coefficients and discrimination values were calculated, and norm tables were established. Weighted means were used to ensure that the results were proportional to the ratios of the language groups in the province. We (the authors) concluded that standardisation of the BM(P) yielded satisfactory results with regard to the determination of issues such as construct validity, reliability, validity and intercorrelations for Grade 4 to 7 learners in the North-West Province of South Africa.

Research paper thumbnail of Metacognitive awareness and the zone of proximal intermediate phase mathematics teachers’ professional development

Eurasia Journal of Mathematics, Science and Technology Education

This paper investigates in-service intermediate phase mathematics teachers' metacognitive awarene... more This paper investigates in-service intermediate phase mathematics teachers' metacognitive awareness based on their engagement in a professional development intervention in two ruraland one township school in South Africa. Professional teacher development interventions should be structured and collaborative as teachers tend to revert to traditional modes of teaching when interventions are brief and sporadic. This research was scaffolded across the zone of proximal teacher development (ZPTD) as conceptualized by Warford (2011). The aim of the study was to investigate how metacognitive awareness facilitated intermediate phase mathematics teachers' ZPTD, i.e., from their actual knowledge to "proximal development". 10 intermediate phase mathematics teachers participated in the qualitative research (n=10). The professional development intervention was conducted on two consecutive Saturdays, infused with an adapted lesson study approach. The data was collected through (i) individual interviews, (ii) reflective prompts, (iii) observations, and (iv) reflective journals. The data from each data source were coded and categorized and were triangulated to answer the research question. Participants deemed the professional development intervention and the accompanying materials as supportive and showed increased metacognitive awareness of their personal teaching praxis during and after the intervention, hence growth along the ZPTD occurred.

Research paper thumbnail of Puppetry as a pedagogy of play in the Intermediate Phase mathematics classroom: A case study

Perspectives in Education, 2021

Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, p... more Research on puppets in Intermediate Phase mathematics is in its infancy. According to Vygotsky, play affords a playful element that can optimise learning opportunities. However, many mathematics teachers are unfamiliar with the integration of pedagogy of play (PoP) (in this case, puppetry). The aim of this paper is to report on one participant's (an Intermediate Phase mathematics teacher [N=1]) lived experiences of teaching with puppets after a twoday intervention. A case study approach was followed and the participant constantly reflected on his experiences. Data were collected through (i) a semi-structured open-ended interview, (ii) reflective prompts and (iii) a reflective journal with prompts. The data revealed the participant's experiences of puppetry, how his metacognitive awareness developed and how he transferred new knowledge to his Intermediate Phase mathematics classroom. The data were analysed using content analysis. The results show that, although learners often deem mathematics "mundane" and "unexciting", puppetry allowed the participant's learners (according to his reflections) to experience this subject as enjoyable and creative, encouraging participation and liveliness, as the puppet was considered a peer in teaching-learning. The Intermediate Phase mathematics classroom became a space where content became meaningful, accessible and understandable to all learners.

Research paper thumbnail of Study Orientation Questionnaire in Mathematics (Primary)

Research paper thumbnail of rights in Africa

Poor mathematics performance in schools is both a national and an international concern. Teachers... more Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no math-ematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase student teachers in South Africa. To make recommendations for the drafting of such standards for final year Foundation Phase teachers, we com-pared different policy documents. We performed a document analysis on policy documents from South Africa, The Netherlands, Australia and North Carolina (United States of America), all of which addressed the number domain in mathematics. Our find-ings indicate that knowledge standards ought to include subject matter knowledge, while practice standards require pedagogical content knowledge, noting that neither of these are fulfilled in the education system in South Africa at present. Key words: founda...

Research paper thumbnail of List of tables

The reader is reminded of the following: ■ The referencing, as well as the editorial style as pre... more The reader is reminded of the following: ■ The referencing, as well as the editorial style as prescribed by the Publication Manual (5th edition) of the American Psychological Association (APA) was followed in this thesis. This practice is in line with the policy of the Programme in Industrial Psychology of the North-West University (Potchefstroom Campus) to use APA style in all scientific documents. ■ The thesis is submitted in the form of three research articles. ACKNOWLEDGEMENTS • Prof. Ian Rothmann for his support, motivation and patience, without which this would not have been possible. • All the participants in this study, as well as the organisation that took part in this study for their support and willingness to participate. • My family for all their support. • I extend my grateful appreciation to Mrs. M. Coetzee for the professional manner in which she conducted the language editing.

Research paper thumbnail of International comparisons of Foundation Phase number domain mathematics knowledge and practice standards

South African Journal of Education, 2015

Poor mathematics performance in schools is both a national and an international concern. Teachers... more Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase student teachers in South Africa. To make recommendations for the drafting of such standards for final year Foundation Phase teachers, we compared different policy documents. We performed a document analysis on policy documents from South Africa, The Netherlands, Australia and North Carolina (United States of America), all of which addressed the number domain in mathematics. Our findings indicate that knowledge standards ought to include subject matter knowledge, while practice standards require pedagogical content knowledge, noting that neither of these are fulfilled in the education system in South Africa at present.

Research paper thumbnail of Exploiting Metacognitive Networks Embedded in Narrative Focus Group Interviews Using NodeXL

The Qualitative Report, Oct 17, 2016

Development of metacognitive theory for changing pedagogy remains an essential research activity.... more Development of metacognitive theory for changing pedagogy remains an essential research activity. A lack of sufficient clear-cut qualitative analysis procedures extracting embedded metacognitive constructs from qualitative data (e.g., narrative focus group interviews) can hinder development of theory. An approach is therefore needed to analyse qualitative metacognitive data exploiting embedded metacognitive constructs for theory development. In an undergraduate fourth-year mathematics education module, two groups of students (Group A: n = 6; Group B: n = 5) participated in a series of focus group interviews. Participants designed and refined mathematics lessons about the concept of place value. We identified metacognitive networks as an embedded construct in students' metacognitive processes. Findings indicate that metacognitive networks of an individual, social and socially shared metacognitive nature are embedded in qualitative data, and can be exploited to develop new metacognitive theory. We offer a novel three-step process in this methodology paper to extract metacognitive networks using Microsoft Office, ATLAS.ti and NodeXL.

Research paper thumbnail of Potgieter, E. (2020). Pedagogies of play to develop intermediate phase mathematics teachers' metacognitive awareness. (Unpublished master's thesis). North-West University, Potchefstroom

Research paper thumbnail of Teaching mathematics: foundation to senior phase

Research paper thumbnail of Do mathematics learning facilitators implement metacognitive strategies

South African Journal of Education, 2007

It is widely accepted that mathematical skills are critically important in our technologically so... more It is widely accepted that mathematical skills are critically important in our technologically sophisticated world. Educators' metacognition directs, plans, monitors, evaluates and reflects their instructional behaviour and this can promote learners ' learning with und ers tanding. The p urpos e of this study was to investigate the exten t to which mathematics educators implemented and taught metacognit ive strategies. Res ults of the quantitative part of the study were triangulated with the results of the qualitative part. Results suggested that whereas mathematics educators may well have possess ed metacognitive skills and utilised them intuitively, thes e s kills were not implemented to a s atisfa ctory extent in the classes we observed.

Research paper thumbnail of The Affordances of Adapted Lesson Study in South Africa - Two Cases

Teacher education programmes are often criticised for not addressing the ‘theory-practice divide’... more Teacher education programmes are often criticised for not addressing the ‘theory-practice divide’. Student teachers are left underprepared for facing the 'coalface' of practice. Two of the possible reasons can be didactics modules being too theory-based and a lack of mentorship at the university or (WIL) schools. According to the Japanese lesson study model teachers collaboratively design, present, refine and re-present a lesson. Two different ways of implementing lesson study, at two South African universities that focused on the professional development of life sciences and mathematics student teachers, are shared by the authors. This qualitative research resulted in findings that highlight the affordances of lesson study approaches in the process of enculturation within a community of practice. Participants include 60 life sciences and 30 mathematics (either 4th year BEd or PGCE) student teachers. Data collection methods included individualand focus group interviews and r...

Research paper thumbnail of Consumer Studies student teachers’ affective experiences during project-based learning

Die implementering van projekgebaseerde leer het die potensiaal om affektiewe faktore in studente... more Die implementering van projekgebaseerde leer het die potensiaal om affektiewe faktore in studente positief te ontwikkel wat selfgerigte lewenslange leer kan bevorder. Lewenslange leer is ’n sleutelvereiste vir onderwysers om relevant kundig in hulle vakgebied te bly, asook om aan die vereistes te kan voldoen wat aan leerders en onderwysers in die 21ste eeu gestel word. Dit is veral belangrik vir onderwysers wat Verbruikerstudie, ’n dinamiese en waardevolle vak in Suid-Afrikaanse skole, aanbied. Die bevordering van selfgerigte lewenslange leer as deel van die opleiding van Verbruikerstudie-onderwysstudente is dus noodsaaklik. Verskillende affektiewe faktore, byvoorbeeld motivering, dra by tot die bevordering van leer wat ontwikkel kan word deur die keuse van gepaste onderrig-leerstrategiee. Affek kan leer deur geheueprosesse, leerprosesse, aandagspan, ervarings en motivering beinvloed. ’n Gevallestudie is onderneem om ondersoek in te stel op welke wyse projekgebaseerde leer in ’n opl...

Research paper thumbnail of Mathematics Confidence : Reflections on Problem-Solving Experiences

The purpose of this paper is to present the findings of a qualitative inquiry into Grade 8 and 9 ... more The purpose of this paper is to present the findings of a qualitative inquiry into Grade 8 and 9 learners’ mathematics confidence. Learners reflect on experiences with mathematics that have influenced their levels of confidence in the social, psychological and intellectual domains. A convenient purposive sample of four participants, individually interviewed with reflective questioning, provides insight into their reflective accounts on experiences with mathematics problem solving. Through content analysis, the researchers’ findings confirm the dimensionality of mathematics confidence and present sources of participants’ mathematics confidence.

Research paper thumbnail of Metacognitive Transference: What Portfolios Tell Us About Contextualized Mathematics

Recognising the value of ethnomathematics is an important aspect of education worldwide. While th... more Recognising the value of ethnomathematics is an important aspect of education worldwide. While the value of IK in education has been recognised, this recognition is yet to translate into practical curriculum processes. It is not clear how metacognition can drive the transference of knowledge and skills into the classroom while, at the same time, contextualising mathematics. One approach is to introduce teachers to viable ways of contextualising mathematics, through ethnomathematics, and equipping them with metacognitive strategies (e.g. planning, monitoring and evaluating) to do so. Metacognitive transference and its relationship with ethnomathematics is the subject of this paper as it reports on what the portfolios tell us about contextualising mathematics and how metacognition transference takes place. An interpretivist-qualitative approach as research design was employed. Data collection instruments included lesson plans, reflections and open-ended questions. Content analysis, ba...

Research paper thumbnail of Project-based learning in higher education : new skills set for consumer studies teacher education

Journal for new generation sciences, 2016

The changing expectations demanded of life and work in the 21st century require that employees, i... more The changing expectations demanded of life and work in the 21st century require that employees, including teachers, be properly prepared for situations that may arise in this day and age. This is especially true for teachers of Consumer Studies, who have to develop an expanding range of knowledge and skills in order to facilitate teaching-learning effectively in their subject. Project-based learning has been implemented in Consumer Studies and other disciplines as a teaching-learning strategy to develop 21st century career skills in students, but has not yet been reported on in relation to the preparation of pre-service Consumer Studies teachers. A qualitative case study was undertaken to determine how the implementation of project-based learning as a teaching-learning strategy would affect and contribute to the development of preferred skills in pre-service Consumer Studies teachers. The findings show that project-based learning could make various positive and constructive contribu...

Research paper thumbnail of The decolonisation of the curriculum project: The affordances of indigenous knowledge for self-directed learning

NWU Self-Directed Learning Series, 2019

Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book... more Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book Publishers Forum Best Practice for Peer Review of Scholarly Books'. The manuscript was subjected to a rigorous two-step peer review prior to publication, with the identities of the reviewers not revealed to the author(s). The reviewers were independent of the publisher and/or authors in question. The reviewers commented positively on the scholarly merits of the manuscript and recommended that the manuscript should be published. Where the reviewers recommended revision and/or improvements to the manuscript, the authors responded adequately to such recommendations. Research Justification This book is the result of a longitudinal research project (2016-2018) funded by the National Research Foundation and the Fuchs Foundation, and it disseminates original research. The project researched the affordances of indigenous knowledge in the school Science, Technology and Mathematics curricula. Short learning programmes (SLPs) were offered to Science, Technology, Engineering and Mathematics (STEM) teachers, during which they engaged in creative and inquiry-based teaching and learning strategies. Research shows that strategies such as problem-based and cooperative learning have the potential to enhance self-directed learning. This design-based research was conducted in several provinces in South Africa (North-West Province, the Northern Cape, Limpopo province, and Gauteng). Based on the data obtained after each intervention, design principles were formulated for redesigning of SLPs. The qualitative research focussed on teachers' lived experiences of the epistemological bordercrossing between Natural Science and indigenous knowledge, their views on the nature of science and indigenous knowledge, and the reformed teaching and learning that took place after the intervention in teachers' classrooms. Most of the chapters in the book report empirical data, with the exception of three chapters (Ch. 2, Ch. 10 and Ch. 11), that can be categorised as systematic reviews. The book is devoted to scholarship in the field of STEM education and teacher professional development, with a specific focus on research into the enhancement of self-directed learning. The target audience are scholars working in the fields of indigenous knowledge systems, STEM education, teacher professional development and self-directed learning. This book makes a unique contribution in terms of, firstly, its extensive use of third-generation Cultural-Historical Activity Theory (CHAT) as a research lens and, secondly, in drawing on research from the fields of neuroscience, science education philosophy, self-directed learning and indigenous knowledge systems, in arguing for such border-crossing. Chapter 1 shows how this research contributes to the development of fourthgeneration CHAT, which, owing to the complexity of the object (which Engeström refers to as 'runaway objects'), requires a focus on numerous activity systems. The book also explores the conundrum of research ethics during participatory action research with holders of indigenous knowledge. In accordance with the requirements of the Department of Higher Education and Training, this book contains more than 50% original content, and no part of the work has been plagiarised. Ethical clearance for the project was provided by the North

Research paper thumbnail of A mathematics vocabulary questionnaire for use in the intermediate phase

South African Journal of Education, 2008

Teachers and psychologists need an instrument to assess learners' language proficiency in mathema... more Teachers and psychologists need an instrument to assess learners' language proficiency in mathematics to enable them to plan and evaluate interventions and to facilitate best practice in mathematics classrooms. We describe the development of a mathematics vocabulary questionnaire to measure learners' language proficiency in mathematics in the intermediate phase. It covers all the steps from designing the preliminary questionnaire to standardising the final instrument. A sample of 1 103 Grades 4 to 7 Afrikaans-, English-and Tswana-speaking learners in North West Province completed the Mathematics Vocabulary questionnaire (Primary) (MV(P)), consisting of 12 items. We analysed the data by calculating discrimination values, performing a factor analysis, determining reliability coefficients, and investigating item bias by language, gender, and grade. We concluded that there was strong evidence of validity and reliability for the MV(P).

Research paper thumbnail of The affordances of technology for teaching indigenous knowledge

NWU Self-Directed Learning Series, 2019

Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book... more Peer review declaration The publisher (AOSIS) endorses the South African 'National Scholarly Book Publishers Forum Best Practice for Peer Review of Scholarly Books'. The manuscript was subjected to a rigorous two-step peer review prior to publication, with the identities of the reviewers not revealed to the author(s). The reviewers were independent of the publisher and/or authors in question. The reviewers commented positively on the scholarly merits of the manuscript and recommended that the manuscript should be published. Where the reviewers recommended revision and/or improvements to the manuscript, the authors responded adequately to such recommendations. Research Justification This book is the result of a longitudinal research project (2016-2018) funded by the National Research Foundation and the Fuchs Foundation, and it disseminates original research. The project researched the affordances of indigenous knowledge in the school Science, Technology and Mathematics curricula. Short learning programmes (SLPs) were offered to Science, Technology, Engineering and Mathematics (STEM) teachers, during which they engaged in creative and inquiry-based teaching and learning strategies. Research shows that strategies such as problem-based and cooperative learning have the potential to enhance self-directed learning. This design-based research was conducted in several provinces in South Africa (North-West Province, the Northern Cape, Limpopo province, and Gauteng). Based on the data obtained after each intervention, design principles were formulated for redesigning of SLPs. The qualitative research focussed on teachers' lived experiences of the epistemological bordercrossing between Natural Science and indigenous knowledge, their views on the nature of science and indigenous knowledge, and the reformed teaching and learning that took place after the intervention in teachers' classrooms. Most of the chapters in the book report empirical data, with the exception of three chapters (Ch. 2, Ch. 10 and Ch. 11), that can be categorised as systematic reviews. The book is devoted to scholarship in the field of STEM education and teacher professional development, with a specific focus on research into the enhancement of self-directed learning. The target audience are scholars working in the fields of indigenous knowledge systems, STEM education, teacher professional development and self-directed learning. This book makes a unique contribution in terms of, firstly, its extensive use of third-generation Cultural-Historical Activity Theory (CHAT) as a research lens and, secondly, in drawing on research from the fields of neuroscience, science education philosophy, self-directed learning and indigenous knowledge systems, in arguing for such border-crossing. Chapter 1 shows how this research contributes to the development of fourthgeneration CHAT, which, owing to the complexity of the object (which Engeström refers to as 'runaway objects'), requires a focus on numerous activity systems. The book also explores the conundrum of research ethics during participatory action research with holders of indigenous knowledge. In accordance with the requirements of the Department of Higher Education and Training, this book contains more than 50% original content, and no part of the work has been plagiarised. Ethical clearance for the project was provided by the North

Research paper thumbnail of Metacognitive awareness and visualisation in the imagination: The case of the invisible circles

Pythagoras, 2018

Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the im... more Awareness of one’s own strengths and weaknesses during visualisation is often initiated by the imagination – the faculty for intuitively visualising and modelling an object. Towards exploring the role of metacognitive awareness and imagination in facilitating visualisation in solving a mathematics task, four secondary schools in the North West province of South Africa were selected for instrumental case studies. Understanding how mathematical objects are modelled in the mind may explain the transfer of the mathematical ideas between metacognitive awareness and the rigour of the imaginer’s mental images. From each school, a top achiever in mathematics was invited to an individual interview (n = 4) and was video-recorded while solving a mathematics word problem. Participants also had to identify metacognitive statements from a sample of statement cards (n = 15) which provided them the necessary vocabulary to express their thinking during the interview. During their attempts, participa...