The present study explores undergraduate students' productive struggles in a Quantitative Literac... more The present study explores undergraduate students' productive struggles in a Quantitative Literacy (QL) course, when doing exercises on the statistical concept of confidence intervals (CIs) within the context of odds ratios (ORs), embedded in everyday authentic contexts. The research methodology employed in this study is lesson study, in which tutors and researchers work together to plan the research tutorial, observe and teach it, and reflect on the instruction in general within the research tutorial. Data for this study comprises video-and audio-recorded transcriptions of the observation and teaching, and reflections of tutors on research tutorials. In addition, samples of students' work and their achievements in assessments were analysed. Results from the study showed that the students' struggles were initiated when their prior knowledge was not sufficient for them to understand the concept of CIs in relation to ORs. The results also highlight some of the ways in which tutors can notice and address students' productive struggles during tutorials. Future researchers should focus on identifying which instructional approaches can promote and support prolific productive struggles for students during tutoring.
In the past two decades many studies have been carried out on the tutor-student interactions in h... more In the past two decades many studies have been carried out on the tutor-student interactions in higher education courses, particularly in undergraduate courses with the foci on exploring students' deep learning. However, few studies have focussed on the role of tutors' in "mathematical noticing" during classroom activities. Therefore, this study using the topic on time value of money seeks to explore the roles tutors play during mathematical noticing when facilitating a Quantitative Literacy undergraduate course. Data was collected from transcriptions of two videorecorded tutorials; documentary analysis from students' written work; and quantitative analysis of the students' scores from tests and an examination. The findings show that the conceptual issues that students struggle with during the classroom tutorials, remained unresolved as evidenced from the analyses of the students' written work from the tests and examination. Further research is required to establish the connections between the tutors' abilities for mathematical noticing and their mathematical knowledge for teaching.
Pedagogy in Basic and Higher Education - Current Developments and Challenges, 2020
Using a predetermined framework on students' productive struggles, the purpose of this study is t... more Using a predetermined framework on students' productive struggles, the purpose of this study is to explore high school students' productive struggles during the simplification of rational algebraic expressions in a high school mathematics classroom. This study is foregrounded in the anthropological theory of the didactic, and its central notion of a "praxeology"-a praxeology refers to the study of human action, based on the notion that humans engage in purposeful behavior of which the simplification of rational algebraic expressions is an example. The research methodology comprised a lesson study involving a sample of 28 students, and the productive struggle framework was used for data analysis. Findings show that the productive struggle framework is a useful tool that can be used to analyze students' thinking processes during the simplification of rational algebraic expressions. Further research is required on the roles that noticing and questioning can play for mathematics teachers to respond to and effectively support the students' struggles during teaching and learning.
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2021
This chapter reports from a study investigating the use of a modelling task that was given to six... more This chapter reports from a study investigating the use of a modelling task that was given to sixty-two Grade 11 students from two schools in low socio-economic areas in South Africa. The Modelling Activity Diagram (MAD) framework was used to characterise students’ mathematical thinking style when working on a real-world problem on geometrical constructions. Although students were able to find solutions to the scaffolded questions, they had problems with identifying key mathematical concepts required during the mathematisation process and assumptions required to solve the modelling task. Only 16% of the students successfully completed the modelling task.
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2021
Consistent with international trends, mathematical modelling is heralded and has been documented ... more Consistent with international trends, mathematical modelling is heralded and has been documented as a construct that is imperative for the teaching and learning of mathematics in South African schools. The study discussed in this chapter explored the immediate implications of using mathematical modelling as a framework for the teaching and learning of powerful mathematical concepts such as proportional reasoning in South African schools located in under-resourced low socio-economic areas. Results show that the initial apprehension that students experienced when exposed for the first time to a model-eliciting activity was soon transformed into a diverse range of creative mathematical approaches, when they learned that the activity is open-ended by default.
This chapter provides a theoretical perspective of how the South African Mathematical Literacy cu... more This chapter provides a theoretical perspective of how the South African Mathematical Literacy curriculum differs from the definition of Mathematical Literacy given by the Organisation for Economic Co-operation and Development. Through unpacking this definition, and the South African Mathematical Literacy curriculum definition, I demonstrate through the use of examples that mathematical modelling is the missing cog in the South African Mathematical Literacy curriculum context. I argue that this difference is significant, insofar as students’ acquisition of mathematical skills and competencies needed in the real world of work and as active participating citizens of a democratic country. I also argue that the teaching of Mathematical Literacy should focus on the development of key mathematical and statistical skills.
In South Africa's post-apartheid era, there is growing evidence of an increase in government ... more In South Africa's post-apartheid era, there is growing evidence of an increase in government support for intervention programs, particularly those aimed at preschool education in poor to low-income communities. This study argues that whilst there is consensus with regard to the rationale of implementing an early childhood mathematics intervention curriculum, not much research has focused on the actual constructs of mathematics teaching and the mathematics curriculum at pre-school level, hence not much is known about them. In this study, I also explore, and operationalise through an example, what could constitute a balanced mathematics intervention curriculum for pre-schoolers in poor to low-income communities. Data for this study was collected by analysing video-recorded episodes of pre-schoolers engaged in mathematical activities in a pre-school setting. The findings show that pre-schoolers can be taught and are capable of learning mathematics in a similar way as older children...
The study reports on the challenges lower primary numeracy teachers in the Zambezi Region face wh... more The study reports on the challenges lower primary numeracy teachers in the Zambezi Region face when using Silozi language as a medium of instruction. The use of Silozi language as a medium of instruction is part of the Namibian language policy in schools. In the Zambezi Region, Silozi, a lingua franca is considered predominant. The findings of the study show that teachers were unable to interpret the concepts in the curriculum and learners could not express their ideas using the lingua franca. However, when Numeracy questions were presented to the learners in symbolic form and in their mother tongue, they did not face challenges in understanding the questions. The study uses the socio-cultural theory as theoretical framework.
African Indigenous Knowledge System (IKS) is the body of knowledge embedded in the African ways o... more African Indigenous Knowledge System (IKS) is the body of knowledge embedded in the African ways of knowing and social practices which have been in existence and have evolved over the past many thousands of years. Within the sub-Sahara African region, IKS could provide alternative ways to promote sustainable development in poor rural communities (Briggs, 2005) – the challenge is on how to promote IKS within the communities, particularly among the younger generations.
African Journal of Research in Mathematics, Science and Technology Education, 2018
The use of technology in teaching mathematics in higher education has received much attention in ... more The use of technology in teaching mathematics in higher education has received much attention in education research lately. Using Roger’s Diffusion of Innovation theory (DOI) as a framework, this study sought to explore how the attributes of technology affect its adoption by mathematics teachers of a bridging course at an institution of higher learning. A qualitative research methodology was used to obtain detailed descriptions and narratives from the five mathematics teachers who participated in the study, to ascertain how, if at all, they adopted technology in their teaching in higher education. Data were collected through semi-structured individual interviews so that the teachers’ unique answers could be captured. ATLAS.ti software was used to analyse the data deductively. The results showed that some teachers were of the view that technology was disruptive, and that it exposed students to the wrong problem-solving methods during the teaching and learning of mathematics in higher education. The traditional ‘pen and paper’ method is seen not only as being essential, but also as critical in the instruction of students. The findings of this study also show the importance of the DOI theory in explaining reasons for the adoption of technology by mathematics teachers in higher education.
This article is based on a study that compared the FET (further education and training) phase mat... more This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison between the two curricula, views of 355 participants comprising of mathematics and mathematical literacy teachers, mathematics and mathematical literacy subject advisors and heads of departments at the MST (mathematics, science and technology) units were sought. The findings of the study revealed that both curricula have similar learning outcomes, but different assessment standards. Factors that hinder the learning and teaching of mathematics in both curricula, such as lack of qualified mathematics teachers, lack of parental support, negative societal attitudes towards mathematics and lack of support from the Department of Education among others, were identified by the study. Intervention mechanisms, such as the use of information technology as an instructional tool, contextualized teaching and learning materials for mathematics, recruiting and training mathematics teachers and continuous professional development, were suggested. Further research is necessary for exploring the benefits of cross-curriculum teaching and learning of mathematical literacy as a way of enhancing the acquisition of mathematical skills at the FET phase.
This study, situated in the context of higher education, seeks to track the performance of studen... more This study, situated in the context of higher education, seeks to track the performance of students whose National Benchmark Tests (NBT) performance is known in a Quantitative Literacy intervention course. The study used the repeated measures Analysis of Variance and t-tests in tracking the performance of students. Furthermore, student-test answer sheets were used to understand the challenges they were facing in the intervention course. The results show that the trajectory of the students' performances from the NBT Quantitative Literacy test to the end of semester Quantitative Literacy course examination scores had an upward trend. These findings provide a starting point for understanding students' experiences as they transit from NBT Quantitative Literacy to the final examination of Quantitative Literacy intervention course.
The National Senior Certificate examination is the most important school examination in South Afr... more The National Senior Certificate examination is the most important school examination in South Africa. Analysis of learners’ performance in Mathematics in this examination is normally carried out and presented in terms of the percentage of learners who succeeded in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics, such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study that, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked...
This theoretical paper focuses on how school-based continuous professional development (CPD) for ... more This theoretical paper focuses on how school-based continuous professional development (CPD) for mathematics teachers in schools located in disadvantaged areas can be carried out using the lesson study approach. School-based CPD is based on the notion that teachers need real-time and on-site professional training tailored to improve the instructional practices unique to their school and classroom contexts. The paper seeks to address the research question: How can a lesson study [or research lesson] be used in the school-based CPD of mathematics teachers in schools located in disadvantaged areas? Empirical evidence from lesson study research suggests that it is an effective tool for CPD activities because it is school-centred, focuses on learner learning, and draws on the collective and collaborative experiences of teachers working in the same school mathematics department. Therefore, this paper significantly contributes to theoretical and practical debates on school-based CPD activities in schools located in disadvantaged areas, using lesson study. Further research would necessitate a focus on understanding how the social learning processes within school-based CPD can be linked to school contexts.
Pedagogy in Basic and Higher Education - Current Developments and Challenges, Feb 19, 2020
This chapter is part of a larger research project that seeks to investigate sustainable ways of i... more This chapter is part of a larger research project that seeks to investigate sustainable ways of improving group-based tutoring in higher education courses. A growing body of research into teaching and learning in higher education acknowledges that higher education institutions are regarded as bastions of active teaching and learning that encourage students' deep learning and critical engagement. However, existing research also suggests that there is a lack of active participation by students during learning activities in tutorials; one of the reasons is the poor quality of the interactions between tutors and students during tutorials. Postgraduate students, who make up the majority of tutors, receive little formal training and lack sophisticated instructional skills on how to facilitate tutorials. By using an example, this chapter argues for the use of a research tutorial as a training strategy for tutor professional development (TPD) in an undergraduate Quantitative Literacy (QL) intervention course. The research methodology employed in this study is the lesson study. A research tutorial is a tutorial designed by both tutors and researchers that is used for TPD purposes. Suggestions for future research include focussing on how tutors notice, and attend to, the students' productive struggles during an undergraduate QL tutorial.
This article examines an 'unstated' belief that as the content of a given Quantitative Literacy c... more This article examines an 'unstated' belief that as the content of a given Quantitative Literacy course grows progressively more complex, the activities relating to social justice issues will surface at a higher cognitive level than those activities lacking social justice issues of social justice. Through the lens of the cognitive apprenticeship model and by means of a four-domain framework, an analysis was conducted of the contribution of the course materials to strengthening student awareness of social justice issues affecting their society. Results show that the expectation that activities relating to social justice outside the classroom would become more abundant as the course evolved over the semester did not materialise. Nonetheless, results did show that activities, which had a social justice agenda, were rated more highly on a cognitive level, than activities without social justice traits. This suggests that the course could thus still achieve its hidden aim of making students more aware of the societal issues in their communities.
The purpose of this study is to report on science teachers' indigenous knowledge (IK) identities,... more The purpose of this study is to report on science teachers' indigenous knowledge (IK) identities, in relation to the teacher professional development program whose aims were: to research IK, to produce teaching and learning materials on the integration of IK and science, and to introduce pre-service and in-service teachers to the construct of multicultural science learning and teaching environments. The formation of a teacher identity in multicultural science teaching environments is a complex construct because of the existence of the multicultural environment. It is important to understand the effectiveness of the current teacher preparation and professional development programs; these have important implications for educational success, access to education, and the effectiveness of such education, which could ultimately lead to sustainable development in developing countries. The trajectory of the transition of science teachers' IK portraits and formations, based on the findings of this study of six teachers, provides a rich yet sobering account of the potential challenges and pitfalls that teachers working with multicultural science classes can experience -especially when students bring their own IK from their communities into the science classrooms.
Abstract
The National Senior Certificate examination is the most important school examination in ... more Abstract The National Senior Certificate examination is the most important school examination in South Africa. Analyses of learners’ performance in Mathematics in this examination is normally done and presented in terms of percentage learners’ achievement in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study which, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analyses. The findings indicate that learners perform differently on sub-sections of topics, herein referred to as items, and that focussing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibited in these sub-sections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees run counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of ‘familiarity with problem types through repeated productive practice’ is used to account for the manifested hierarchy of difficulty of the items.
The present study explores undergraduate students' productive struggles in a Quantitative Literac... more The present study explores undergraduate students' productive struggles in a Quantitative Literacy (QL) course, when doing exercises on the statistical concept of confidence intervals (CIs) within the context of odds ratios (ORs), embedded in everyday authentic contexts. The research methodology employed in this study is lesson study, in which tutors and researchers work together to plan the research tutorial, observe and teach it, and reflect on the instruction in general within the research tutorial. Data for this study comprises video-and audio-recorded transcriptions of the observation and teaching, and reflections of tutors on research tutorials. In addition, samples of students' work and their achievements in assessments were analysed. Results from the study showed that the students' struggles were initiated when their prior knowledge was not sufficient for them to understand the concept of CIs in relation to ORs. The results also highlight some of the ways in which tutors can notice and address students' productive struggles during tutorials. Future researchers should focus on identifying which instructional approaches can promote and support prolific productive struggles for students during tutoring.
In the past two decades many studies have been carried out on the tutor-student interactions in h... more In the past two decades many studies have been carried out on the tutor-student interactions in higher education courses, particularly in undergraduate courses with the foci on exploring students' deep learning. However, few studies have focussed on the role of tutors' in "mathematical noticing" during classroom activities. Therefore, this study using the topic on time value of money seeks to explore the roles tutors play during mathematical noticing when facilitating a Quantitative Literacy undergraduate course. Data was collected from transcriptions of two videorecorded tutorials; documentary analysis from students' written work; and quantitative analysis of the students' scores from tests and an examination. The findings show that the conceptual issues that students struggle with during the classroom tutorials, remained unresolved as evidenced from the analyses of the students' written work from the tests and examination. Further research is required to establish the connections between the tutors' abilities for mathematical noticing and their mathematical knowledge for teaching.
Pedagogy in Basic and Higher Education - Current Developments and Challenges, 2020
Using a predetermined framework on students' productive struggles, the purpose of this study is t... more Using a predetermined framework on students' productive struggles, the purpose of this study is to explore high school students' productive struggles during the simplification of rational algebraic expressions in a high school mathematics classroom. This study is foregrounded in the anthropological theory of the didactic, and its central notion of a "praxeology"-a praxeology refers to the study of human action, based on the notion that humans engage in purposeful behavior of which the simplification of rational algebraic expressions is an example. The research methodology comprised a lesson study involving a sample of 28 students, and the productive struggle framework was used for data analysis. Findings show that the productive struggle framework is a useful tool that can be used to analyze students' thinking processes during the simplification of rational algebraic expressions. Further research is required on the roles that noticing and questioning can play for mathematics teachers to respond to and effectively support the students' struggles during teaching and learning.
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2021
This chapter reports from a study investigating the use of a modelling task that was given to six... more This chapter reports from a study investigating the use of a modelling task that was given to sixty-two Grade 11 students from two schools in low socio-economic areas in South Africa. The Modelling Activity Diagram (MAD) framework was used to characterise students’ mathematical thinking style when working on a real-world problem on geometrical constructions. Although students were able to find solutions to the scaffolded questions, they had problems with identifying key mathematical concepts required during the mathematisation process and assumptions required to solve the modelling task. Only 16% of the students successfully completed the modelling task.
International Perspectives on the Teaching and Learning of Mathematical Modelling, 2021
Consistent with international trends, mathematical modelling is heralded and has been documented ... more Consistent with international trends, mathematical modelling is heralded and has been documented as a construct that is imperative for the teaching and learning of mathematics in South African schools. The study discussed in this chapter explored the immediate implications of using mathematical modelling as a framework for the teaching and learning of powerful mathematical concepts such as proportional reasoning in South African schools located in under-resourced low socio-economic areas. Results show that the initial apprehension that students experienced when exposed for the first time to a model-eliciting activity was soon transformed into a diverse range of creative mathematical approaches, when they learned that the activity is open-ended by default.
This chapter provides a theoretical perspective of how the South African Mathematical Literacy cu... more This chapter provides a theoretical perspective of how the South African Mathematical Literacy curriculum differs from the definition of Mathematical Literacy given by the Organisation for Economic Co-operation and Development. Through unpacking this definition, and the South African Mathematical Literacy curriculum definition, I demonstrate through the use of examples that mathematical modelling is the missing cog in the South African Mathematical Literacy curriculum context. I argue that this difference is significant, insofar as students’ acquisition of mathematical skills and competencies needed in the real world of work and as active participating citizens of a democratic country. I also argue that the teaching of Mathematical Literacy should focus on the development of key mathematical and statistical skills.
In South Africa's post-apartheid era, there is growing evidence of an increase in government ... more In South Africa's post-apartheid era, there is growing evidence of an increase in government support for intervention programs, particularly those aimed at preschool education in poor to low-income communities. This study argues that whilst there is consensus with regard to the rationale of implementing an early childhood mathematics intervention curriculum, not much research has focused on the actual constructs of mathematics teaching and the mathematics curriculum at pre-school level, hence not much is known about them. In this study, I also explore, and operationalise through an example, what could constitute a balanced mathematics intervention curriculum for pre-schoolers in poor to low-income communities. Data for this study was collected by analysing video-recorded episodes of pre-schoolers engaged in mathematical activities in a pre-school setting. The findings show that pre-schoolers can be taught and are capable of learning mathematics in a similar way as older children...
The study reports on the challenges lower primary numeracy teachers in the Zambezi Region face wh... more The study reports on the challenges lower primary numeracy teachers in the Zambezi Region face when using Silozi language as a medium of instruction. The use of Silozi language as a medium of instruction is part of the Namibian language policy in schools. In the Zambezi Region, Silozi, a lingua franca is considered predominant. The findings of the study show that teachers were unable to interpret the concepts in the curriculum and learners could not express their ideas using the lingua franca. However, when Numeracy questions were presented to the learners in symbolic form and in their mother tongue, they did not face challenges in understanding the questions. The study uses the socio-cultural theory as theoretical framework.
African Indigenous Knowledge System (IKS) is the body of knowledge embedded in the African ways o... more African Indigenous Knowledge System (IKS) is the body of knowledge embedded in the African ways of knowing and social practices which have been in existence and have evolved over the past many thousands of years. Within the sub-Sahara African region, IKS could provide alternative ways to promote sustainable development in poor rural communities (Briggs, 2005) – the challenge is on how to promote IKS within the communities, particularly among the younger generations.
African Journal of Research in Mathematics, Science and Technology Education, 2018
The use of technology in teaching mathematics in higher education has received much attention in ... more The use of technology in teaching mathematics in higher education has received much attention in education research lately. Using Roger’s Diffusion of Innovation theory (DOI) as a framework, this study sought to explore how the attributes of technology affect its adoption by mathematics teachers of a bridging course at an institution of higher learning. A qualitative research methodology was used to obtain detailed descriptions and narratives from the five mathematics teachers who participated in the study, to ascertain how, if at all, they adopted technology in their teaching in higher education. Data were collected through semi-structured individual interviews so that the teachers’ unique answers could be captured. ATLAS.ti software was used to analyse the data deductively. The results showed that some teachers were of the view that technology was disruptive, and that it exposed students to the wrong problem-solving methods during the teaching and learning of mathematics in higher education. The traditional ‘pen and paper’ method is seen not only as being essential, but also as critical in the instruction of students. The findings of this study also show the importance of the DOI theory in explaining reasons for the adoption of technology by mathematics teachers in higher education.
This article is based on a study that compared the FET (further education and training) phase mat... more This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison between the two curricula, views of 355 participants comprising of mathematics and mathematical literacy teachers, mathematics and mathematical literacy subject advisors and heads of departments at the MST (mathematics, science and technology) units were sought. The findings of the study revealed that both curricula have similar learning outcomes, but different assessment standards. Factors that hinder the learning and teaching of mathematics in both curricula, such as lack of qualified mathematics teachers, lack of parental support, negative societal attitudes towards mathematics and lack of support from the Department of Education among others, were identified by the study. Intervention mechanisms, such as the use of information technology as an instructional tool, contextualized teaching and learning materials for mathematics, recruiting and training mathematics teachers and continuous professional development, were suggested. Further research is necessary for exploring the benefits of cross-curriculum teaching and learning of mathematical literacy as a way of enhancing the acquisition of mathematical skills at the FET phase.
This study, situated in the context of higher education, seeks to track the performance of studen... more This study, situated in the context of higher education, seeks to track the performance of students whose National Benchmark Tests (NBT) performance is known in a Quantitative Literacy intervention course. The study used the repeated measures Analysis of Variance and t-tests in tracking the performance of students. Furthermore, student-test answer sheets were used to understand the challenges they were facing in the intervention course. The results show that the trajectory of the students' performances from the NBT Quantitative Literacy test to the end of semester Quantitative Literacy course examination scores had an upward trend. These findings provide a starting point for understanding students' experiences as they transit from NBT Quantitative Literacy to the final examination of Quantitative Literacy intervention course.
The National Senior Certificate examination is the most important school examination in South Afr... more The National Senior Certificate examination is the most important school examination in South Africa. Analysis of learners’ performance in Mathematics in this examination is normally carried out and presented in terms of the percentage of learners who succeeded in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics, such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study that, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked...
This theoretical paper focuses on how school-based continuous professional development (CPD) for ... more This theoretical paper focuses on how school-based continuous professional development (CPD) for mathematics teachers in schools located in disadvantaged areas can be carried out using the lesson study approach. School-based CPD is based on the notion that teachers need real-time and on-site professional training tailored to improve the instructional practices unique to their school and classroom contexts. The paper seeks to address the research question: How can a lesson study [or research lesson] be used in the school-based CPD of mathematics teachers in schools located in disadvantaged areas? Empirical evidence from lesson study research suggests that it is an effective tool for CPD activities because it is school-centred, focuses on learner learning, and draws on the collective and collaborative experiences of teachers working in the same school mathematics department. Therefore, this paper significantly contributes to theoretical and practical debates on school-based CPD activities in schools located in disadvantaged areas, using lesson study. Further research would necessitate a focus on understanding how the social learning processes within school-based CPD can be linked to school contexts.
Pedagogy in Basic and Higher Education - Current Developments and Challenges, Feb 19, 2020
This chapter is part of a larger research project that seeks to investigate sustainable ways of i... more This chapter is part of a larger research project that seeks to investigate sustainable ways of improving group-based tutoring in higher education courses. A growing body of research into teaching and learning in higher education acknowledges that higher education institutions are regarded as bastions of active teaching and learning that encourage students' deep learning and critical engagement. However, existing research also suggests that there is a lack of active participation by students during learning activities in tutorials; one of the reasons is the poor quality of the interactions between tutors and students during tutorials. Postgraduate students, who make up the majority of tutors, receive little formal training and lack sophisticated instructional skills on how to facilitate tutorials. By using an example, this chapter argues for the use of a research tutorial as a training strategy for tutor professional development (TPD) in an undergraduate Quantitative Literacy (QL) intervention course. The research methodology employed in this study is the lesson study. A research tutorial is a tutorial designed by both tutors and researchers that is used for TPD purposes. Suggestions for future research include focussing on how tutors notice, and attend to, the students' productive struggles during an undergraduate QL tutorial.
This article examines an 'unstated' belief that as the content of a given Quantitative Literacy c... more This article examines an 'unstated' belief that as the content of a given Quantitative Literacy course grows progressively more complex, the activities relating to social justice issues will surface at a higher cognitive level than those activities lacking social justice issues of social justice. Through the lens of the cognitive apprenticeship model and by means of a four-domain framework, an analysis was conducted of the contribution of the course materials to strengthening student awareness of social justice issues affecting their society. Results show that the expectation that activities relating to social justice outside the classroom would become more abundant as the course evolved over the semester did not materialise. Nonetheless, results did show that activities, which had a social justice agenda, were rated more highly on a cognitive level, than activities without social justice traits. This suggests that the course could thus still achieve its hidden aim of making students more aware of the societal issues in their communities.
The purpose of this study is to report on science teachers' indigenous knowledge (IK) identities,... more The purpose of this study is to report on science teachers' indigenous knowledge (IK) identities, in relation to the teacher professional development program whose aims were: to research IK, to produce teaching and learning materials on the integration of IK and science, and to introduce pre-service and in-service teachers to the construct of multicultural science learning and teaching environments. The formation of a teacher identity in multicultural science teaching environments is a complex construct because of the existence of the multicultural environment. It is important to understand the effectiveness of the current teacher preparation and professional development programs; these have important implications for educational success, access to education, and the effectiveness of such education, which could ultimately lead to sustainable development in developing countries. The trajectory of the transition of science teachers' IK portraits and formations, based on the findings of this study of six teachers, provides a rich yet sobering account of the potential challenges and pitfalls that teachers working with multicultural science classes can experience -especially when students bring their own IK from their communities into the science classrooms.
Abstract
The National Senior Certificate examination is the most important school examination in ... more Abstract The National Senior Certificate examination is the most important school examination in South Africa. Analyses of learners’ performance in Mathematics in this examination is normally done and presented in terms of percentage learners’ achievement in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study which, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analyses. The findings indicate that learners perform differently on sub-sections of topics, herein referred to as items, and that focussing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibited in these sub-sections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees run counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of ‘familiarity with problem types through repeated productive practice’ is used to account for the manifested hierarchy of difficulty of the items.
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Papers by Duncan Mhakure
The National Senior Certificate examination is the most important school examination in South Africa. Analyses of learners’ performance in Mathematics in this examination is normally done and presented in terms of percentage learners’ achievement in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study which, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analyses. The findings indicate that learners perform differently on sub-sections of topics, herein referred to as items, and that focussing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibited in these sub-sections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees run counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of ‘familiarity with problem types through repeated productive practice’ is used to account for the manifested hierarchy of difficulty of the items.
The National Senior Certificate examination is the most important school examination in South Africa. Analyses of learners’ performance in Mathematics in this examination is normally done and presented in terms of percentage learners’ achievement in the different bands of achievement. In some cases item difficulties are presented – item refers to the subsection of each examination question. Very little attention is paid to other diagnostic statistics such as the discrimination indices and item difficulties taking into consideration partial scores examinees achieve on items. In this article we report on a study which, in addition to the usual item difficulties, includes a discrimination index of item difficulties taking into account partial scores examinees achieved. The items, considered individually, are analysed in relation to the other items on the test. The focus is on the topic sequences and series and the data were obtained from a stratified sample of the marked scripts of the candidates who wrote the National Senior Certificate examination in Mathematics in November 2010. Rasch procedures were used for the analyses. The findings indicate that learners perform differently on sub-sections of topics, herein referred to as items, and that focussing on scores for full topics potentially mask these differences. Mathematical explanations are attempted to account for difficulties learners exhibited in these sub-sections, using a hierarchy of scale. The findings and our analysis indicate that a form of measurement driven testing could have beneficial results for teaching. Also, for some items the difficulty obtained from the work of examinees run counter to the commonly perceived wisdom that an examination ought to be structured in such a way that the less difficult items are at the start of a topic. An explanatory device anchored around the construct of ‘familiarity with problem types through repeated productive practice’ is used to account for the manifested hierarchy of difficulty of the items.