An investigation into the use of visualisation processes as a teaching strategy to enhance number sense
- Authors: Griqua, Ronald Max
- Date: 2020
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics -- Study and teaching -- Psychological aspects , Visualization , Number concept , RUMEP (Rhodes University Mathematics Education Project)
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/147226 , vital:38606
- Description: The literature agrees that in order to improve learning outcomes, instruction in classrooms should be improved first. Mathematics educationists therefore advocate that schools should make extensive and deep efforts to rethink their instructional programmes. Research furthermore suggests that increasingly, indicators on school performance and teaching reveal largely unacknowledged problematic teaching of mathematics in the great majority of South African schools. This research study is therefore a contribution towards rethinking the teaching strategies within mathematics classrooms. The study examined the use of visualisation processes in order to understand how these interact with the pedagogy of selected mathematics teachers when they teach number sense after participating in an intervention programme. This study argues that the effective use of visualisation processes enhanced the teaching of number sense. The research study was framed as a case study that was grounded within the interpretive paradigm. The study was located in classrooms where the participating teachers promoted active learning after taking part in an intervention programme. A constructivist theoretical underpinning was therefore adopted. At the heart of the study was the Visualisation Intervention Programme (VIP), which involved seven Rhodes University Mathematics Education Project (RUMEP) teachers within the John Taolo Gaetsewe District of the Northern Cape Province. The content of the VIP was informed by initially working with five teachers of well-resourced schools within the Northern Cape who made interesting use of visualisation processes and manipulatives to teach number sense. With the assistance of these five teachers, the VIP was then implemented by seven selected RUMEP teachers to investigate the role of visualisation processes in the teaching of number sense understandings. The study employed a mixed method approach. Qualitative data was collected through observations and interviews, while quantitative data was collected with a series of pre- and post-tests. The analysis of the findings of this research study revealed that the effective use of visualisation processes was instrumental in enhancing the teaching of number sense understandings. Furthermore, the use of visualisation processes by the selected teachers fostered independent thought and conceptual understanding of number sense topics on the part of their learners.
- Full Text:
- Date Issued: 2020
- Authors: Griqua, Ronald Max
- Date: 2020
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics -- Study and teaching -- Psychological aspects , Visualization , Number concept , RUMEP (Rhodes University Mathematics Education Project)
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/147226 , vital:38606
- Description: The literature agrees that in order to improve learning outcomes, instruction in classrooms should be improved first. Mathematics educationists therefore advocate that schools should make extensive and deep efforts to rethink their instructional programmes. Research furthermore suggests that increasingly, indicators on school performance and teaching reveal largely unacknowledged problematic teaching of mathematics in the great majority of South African schools. This research study is therefore a contribution towards rethinking the teaching strategies within mathematics classrooms. The study examined the use of visualisation processes in order to understand how these interact with the pedagogy of selected mathematics teachers when they teach number sense after participating in an intervention programme. This study argues that the effective use of visualisation processes enhanced the teaching of number sense. The research study was framed as a case study that was grounded within the interpretive paradigm. The study was located in classrooms where the participating teachers promoted active learning after taking part in an intervention programme. A constructivist theoretical underpinning was therefore adopted. At the heart of the study was the Visualisation Intervention Programme (VIP), which involved seven Rhodes University Mathematics Education Project (RUMEP) teachers within the John Taolo Gaetsewe District of the Northern Cape Province. The content of the VIP was informed by initially working with five teachers of well-resourced schools within the Northern Cape who made interesting use of visualisation processes and manipulatives to teach number sense. With the assistance of these five teachers, the VIP was then implemented by seven selected RUMEP teachers to investigate the role of visualisation processes in the teaching of number sense understandings. The study employed a mixed method approach. Qualitative data was collected through observations and interviews, while quantitative data was collected with a series of pre- and post-tests. The analysis of the findings of this research study revealed that the effective use of visualisation processes was instrumental in enhancing the teaching of number sense understandings. Furthermore, the use of visualisation processes by the selected teachers fostered independent thought and conceptual understanding of number sense topics on the part of their learners.
- Full Text:
- Date Issued: 2020
Exploring National Certificate Vocational (NCV) level two learners’ misconceptions in algebraic functions through integrating GeoGebra during teaching and learning
- Authors: Ngwabe, Abongile
- Date: 2018
- Subjects: Mathematics -- Study and teaching -- South Africa , Algebraic functions -- Study and teaching , Algebraic fields , Mathematical analysis -- Data processing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10948/33671 , vital:32963
- Description: This study focuses on exploring NCV level two learners’ misconceptions in algebraic functions through integrating GeoGebra Dynamic Software during teaching and learning. The research investigates how the integration of GeoGebra during teaching and learning algebraic functions influenced learners’ misconceptions in algebraic functions. Vygotsky’s sociocultural view of learning underpinned the process of teaching and learning during the study. The research was carried out at the TVET College in Port Elizabeth. The data was collected by means of pre-test and post-test, focus group interviews, GeoGebra intervention and observations. Created GeoGebra applets and a worksheet was used during the integration process. The data collected was analyzed and used to answer the research questions of this study. Research findings showed that the integration of GeoGebra during teaching and learning enhanced learners’ conceptual understanding in algebraic functions. There was a significance increase in the number of learners who showed ability to interpret algebraic functions based concepts after the engagement with GeoGebra applets.
- Full Text:
- Date Issued: 2018
- Authors: Ngwabe, Abongile
- Date: 2018
- Subjects: Mathematics -- Study and teaching -- South Africa , Algebraic functions -- Study and teaching , Algebraic fields , Mathematical analysis -- Data processing
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10948/33671 , vital:32963
- Description: This study focuses on exploring NCV level two learners’ misconceptions in algebraic functions through integrating GeoGebra Dynamic Software during teaching and learning. The research investigates how the integration of GeoGebra during teaching and learning algebraic functions influenced learners’ misconceptions in algebraic functions. Vygotsky’s sociocultural view of learning underpinned the process of teaching and learning during the study. The research was carried out at the TVET College in Port Elizabeth. The data was collected by means of pre-test and post-test, focus group interviews, GeoGebra intervention and observations. Created GeoGebra applets and a worksheet was used during the integration process. The data collected was analyzed and used to answer the research questions of this study. Research findings showed that the integration of GeoGebra during teaching and learning enhanced learners’ conceptual understanding in algebraic functions. There was a significance increase in the number of learners who showed ability to interpret algebraic functions based concepts after the engagement with GeoGebra applets.
- Full Text:
- Date Issued: 2018
A case study of a pre-service mathematics education course to grow and develop proficient teaching in mathematics in the intermediate phase
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
- Authors: Lee, Amanda Jane
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , Mathematics -- Study and teaching (Elementary) -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:2004 , http://hdl.handle.net/10962/d1015664
- Description: This research study investigated the ways in which a mathematics module, informed by an enactivist philosophy, enabled pre-service teachers to unpack the reality of their teaching practice in terms of proficient teaching. Given the generally poor mathematics results in South Africa it is not enough for teachers to be merely proficient in Mathematics. They also need to be in a position to explain important mathematical concepts to children in a manner that will encourage and develop an understanding of the basic mathematical concepts. It was my intention with this study to determine whether a mathematics education module, that embraced the underlying themes of enactivism as part of its teaching pedagogy, could have the potential to develop and increase the skills of pre-service teachers’ teaching for proficiency in Mathematics. The mathematics module was underpinned by five themes of enactivism namely: autonomy, embodiment, emergence, sense-making and experience and was designed to supplement the pre-service teachers’ basic skills in Mathematics in the Intermediate Phase. This mathematics module was offered to fourth year pre-service teachers completing a B.Ed. in the Foundation Phase at a private institute specialising in the training of teachers. The theoretical framework was informed by enactivism and how the themes of enactivism could be used as a vehicle to develop teaching proficiency. The study was qualitative in nature and situated within an interpretivist paradigm. The specific perspectives of interpretivism that were used were hermeneutics, phenomenology and reflexivity. The research design was a case study that contained elements of action research and encompassed three phases of data collection. The first phase focused on the pre-service teachers’ approach to teaching Mathematics and what this brought forth in terms of the reality of their teaching practice and the problems they encountered. The second phase undertook to determine what growth and development of teaching proficiency in Mathematics had emerged over the research period. The final phase was undertaken after the pre-service teachers had graduated and were employed as full time teachers in the Intermediate Phase. The analytical framework and lens through which the data was analysed was that of Kilpatrick, Swafford and Findell’s (2001) strands of mathematical proficiency. The argument that I present is that the themes of enactivism did contribute to the growth of the pre-service teachers’ teaching for mathematical proficiency. The themes of embodiment and experience were major contributions in revealing that this was a reality for the pre-service teachers from a practical perspective and was what they would be able to take away with them. However the theme of emergence stood out as the principle that generated the most awareness and growth and which, in turn, affected the participants’ autonomy.
- Full Text:
- Date Issued: 2014
Integrating information and communications technology (ICT) into teaching and learning: the case of mathematics, science and technology education in one higher education institution
- Authors: Addam, Billey Bright Kwadwo
- Date: 2014
- Subjects: Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: vital:16224 , http://hdl.handle.net/10353/d1019736 , Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Description: This study explores the integration of Information and Communication Technologies (ICT) into teaching and learning within one Higher Education institution. The main question driving the study was: How is ICT integrated in the teaching and learning of mathematics, science and technology education (MSTE) in a Bachelor of Education programme? This is a case study of lecturers and students in Mathematics, Science and Technology Education. It makes use of questionnaires, interviews, field notes and document analyses to collect data. MSTE lecturers and students were assumed to be well versed in ICT usage and, therefore, well placed to assess its integration into teaching and learning. There were five main findings: First, that Mathematics, Science and Technology Education lecturers showed some ambivalence in their ontological and epistemological orientation to using ICT. Some leaned towards the instruction paradigm and used ICT as a tool for the transmission of knowledge; others leaned towards the learning paradigm, showing an awareness of the need to elicit discovery through ICT. Secondly, that lecturers’ understanding of ICT integration was oriented towards teaching and learning from technologies rather than with technologies. Thirdly, that processes of ‘pedagogical evolution’ were taking place, in terms of which there was a gradual but perceptible shift in the teaching and learning practice of both students and lecturers. Fourthly, there was no evidence to show that lecturers used ICT to promote innovative and creative teaching; in fact, students appeared to be more creative in using ICT resources, than lecturers. Fifthly, and finally, lecturers did not assign ICT-based tasks that promote conceptual understanding. They assigned tasks that asked students to extract and reproduce information from computers, without demonstrating understanding. When used in this way, ICT can, in fact, be de-skilling. From these findings, it can be concluded that ICT integration cannot be understood without exploring the ontological and epistemological orientations, as well as the theoretical orientations, at play in the teaching and learning situation. It is on the basis of these that people, that is, lecturers and students, make use of, ICTs to achieve desired goals. It is therefore recommended that, for the improvement of integration, there should be a greater emphasis on developing and sharing pedagogical expertise concerning ICT use in teaching and learning. It is recommended that a country-wide research survey should be undertaken, based on probability sampling and focussing on pedagogical issues in ICT integration in teaching and learning.
- Full Text:
- Date Issued: 2014
- Authors: Addam, Billey Bright Kwadwo
- Date: 2014
- Subjects: Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: vital:16224 , http://hdl.handle.net/10353/d1019736 , Educational teaching -- South Africa , Computer-assisted instruction -- South Africa , Mathematics -- Study and teaching -- South Africa , Science -- Study and teaching -- South Africa
- Description: This study explores the integration of Information and Communication Technologies (ICT) into teaching and learning within one Higher Education institution. The main question driving the study was: How is ICT integrated in the teaching and learning of mathematics, science and technology education (MSTE) in a Bachelor of Education programme? This is a case study of lecturers and students in Mathematics, Science and Technology Education. It makes use of questionnaires, interviews, field notes and document analyses to collect data. MSTE lecturers and students were assumed to be well versed in ICT usage and, therefore, well placed to assess its integration into teaching and learning. There were five main findings: First, that Mathematics, Science and Technology Education lecturers showed some ambivalence in their ontological and epistemological orientation to using ICT. Some leaned towards the instruction paradigm and used ICT as a tool for the transmission of knowledge; others leaned towards the learning paradigm, showing an awareness of the need to elicit discovery through ICT. Secondly, that lecturers’ understanding of ICT integration was oriented towards teaching and learning from technologies rather than with technologies. Thirdly, that processes of ‘pedagogical evolution’ were taking place, in terms of which there was a gradual but perceptible shift in the teaching and learning practice of both students and lecturers. Fourthly, there was no evidence to show that lecturers used ICT to promote innovative and creative teaching; in fact, students appeared to be more creative in using ICT resources, than lecturers. Fifthly, and finally, lecturers did not assign ICT-based tasks that promote conceptual understanding. They assigned tasks that asked students to extract and reproduce information from computers, without demonstrating understanding. When used in this way, ICT can, in fact, be de-skilling. From these findings, it can be concluded that ICT integration cannot be understood without exploring the ontological and epistemological orientations, as well as the theoretical orientations, at play in the teaching and learning situation. It is on the basis of these that people, that is, lecturers and students, make use of, ICTs to achieve desired goals. It is therefore recommended that, for the improvement of integration, there should be a greater emphasis on developing and sharing pedagogical expertise concerning ICT use in teaching and learning. It is recommended that a country-wide research survey should be undertaken, based on probability sampling and focussing on pedagogical issues in ICT integration in teaching and learning.
- Full Text:
- Date Issued: 2014
Learner perceptions on feedback received on performance tasks in mathematics in selected schools from the East London district in the Eastern Cape
- Authors: Ngudle, N G
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Effective teaching , Teacher effectiveness
- Language: English
- Type: Thesis , Masters , M Ed
- Identifier: vital:16213 , http://hdl.handle.net/10353/d1016499 , Mathematics -- Study and teaching -- South Africa , Effective teaching , Teacher effectiveness
- Description: Feedback has an important role to play in the performance of learners. This study looks to identify the challenges that the learners are faced with when the teachers provide them with feedback and the ways they would like like it to be used in order to see feedback assisting them in their learning and improve their performance. Feedback contributes a lot to assessment and has a close link with performance. The study used the qualitative approach to identify the challenges the learners experience when they receive the feedback from their teachers. The participants were sampled from grade 12 learners in the form of a focus group (seven to ten per school) and individual respondents. The method used semi-structured interviews and portfolio observations to collect the data from two high schools in East London (EL) district to look at the nature of the feedback provided to learners. The data was later analysed and interpreted. It has been identified that for both schools feedback conveyed certain messages to learners such motivation to do better, a need to do better and, lastly, affirmation that the learners are on the right track or they are neglected and left to figure out how to do the tasks. The study discovered that, according to Hattie and Timperley (2007)’ there are four levels of feedback. It was found that for the task level learners from school A mainly received oral feedback which was often seen as denigrating them; however, in school B learners received both the oral and written feedback. They felt that the feedback assisted them to understand the task at hand. They also saw this as a way of building up their confidence in all the tasks they come across. Secondly, in the process level, learners in school A did not report receiving feedback at this level but only oral feedback which does not show their mistakes step by step in the task, yet in school B they reported that they got feedback from their teacher individually to help them understand the task. Thirdly, for the self regulation level, in school A there was no data to confirm this. Regarding school B, learners were being assisted by the feedback they received from their teacher and this caused them to monitor their progress. The fourth and last level is the self or personal evaluation where in school A learners were not able to evaluate themselves because they did not receive written feedback, whereas in school B learners could do that freely referring to the written comments from their teacher. The research therefore concluded that in one of the schools the four levels that the study was looking at were not all addressed and thus no meaningful feedback was given. For school B the teacher gave them the feedback which has contributed a lot in their learning. The study recommends that feedback should not be used for right or wrong answers but it must also state clearly why the learner has obtained such mark or grade and what to do to correct the wrongs. Teachers should consider that learner errors also assist them to have a broader picture on what more they need to do in their subjects. It is also recommended that teachers should consider various strategies in giving feedback and the learners’ work has to be monitored timeously for the purpose of the learning process. Lastly, a good approach when feedback is provided is also important because it builds high self-esteem and develops the teacher-learner approach accordingly.
- Full Text:
- Date Issued: 2014
- Authors: Ngudle, N G
- Date: 2014
- Subjects: Mathematics -- Study and teaching -- South Africa , Effective teaching , Teacher effectiveness
- Language: English
- Type: Thesis , Masters , M Ed
- Identifier: vital:16213 , http://hdl.handle.net/10353/d1016499 , Mathematics -- Study and teaching -- South Africa , Effective teaching , Teacher effectiveness
- Description: Feedback has an important role to play in the performance of learners. This study looks to identify the challenges that the learners are faced with when the teachers provide them with feedback and the ways they would like like it to be used in order to see feedback assisting them in their learning and improve their performance. Feedback contributes a lot to assessment and has a close link with performance. The study used the qualitative approach to identify the challenges the learners experience when they receive the feedback from their teachers. The participants were sampled from grade 12 learners in the form of a focus group (seven to ten per school) and individual respondents. The method used semi-structured interviews and portfolio observations to collect the data from two high schools in East London (EL) district to look at the nature of the feedback provided to learners. The data was later analysed and interpreted. It has been identified that for both schools feedback conveyed certain messages to learners such motivation to do better, a need to do better and, lastly, affirmation that the learners are on the right track or they are neglected and left to figure out how to do the tasks. The study discovered that, according to Hattie and Timperley (2007)’ there are four levels of feedback. It was found that for the task level learners from school A mainly received oral feedback which was often seen as denigrating them; however, in school B learners received both the oral and written feedback. They felt that the feedback assisted them to understand the task at hand. They also saw this as a way of building up their confidence in all the tasks they come across. Secondly, in the process level, learners in school A did not report receiving feedback at this level but only oral feedback which does not show their mistakes step by step in the task, yet in school B they reported that they got feedback from their teacher individually to help them understand the task. Thirdly, for the self regulation level, in school A there was no data to confirm this. Regarding school B, learners were being assisted by the feedback they received from their teacher and this caused them to monitor their progress. The fourth and last level is the self or personal evaluation where in school A learners were not able to evaluate themselves because they did not receive written feedback, whereas in school B learners could do that freely referring to the written comments from their teacher. The research therefore concluded that in one of the schools the four levels that the study was looking at were not all addressed and thus no meaningful feedback was given. For school B the teacher gave them the feedback which has contributed a lot in their learning. The study recommends that feedback should not be used for right or wrong answers but it must also state clearly why the learner has obtained such mark or grade and what to do to correct the wrongs. Teachers should consider that learner errors also assist them to have a broader picture on what more they need to do in their subjects. It is also recommended that teachers should consider various strategies in giving feedback and the learners’ work has to be monitored timeously for the purpose of the learning process. Lastly, a good approach when feedback is provided is also important because it builds high self-esteem and develops the teacher-learner approach accordingly.
- Full Text:
- Date Issued: 2014
A value-based approach to promoting excellence in mathematics education
- Authors: Austin, Pamela Winifred
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:9482 , http://hdl.handle.net/10948/1656 , Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Description: This research study has emerged as a result of my concern regarding the apparent low self-efficacy amongst initial teacher education students in my mathematics education classes. It also reflects a reported renewed interest in values, and the promotion of excellence in education. The effects of a values-based approach to mathematics education towards improving students’ self-efficacy and promoting excellence have been investigated, grounded within my ontology of excellence in mathematics education, which incorporates the values of respect, fairness, accountability, honesty and compassion. An inquiry-based teaching and learning approach formed the framework within which the study took place. Notions of ‘new scholarship’, premised on the view that teaching is about engagement in participatory learning, and the development of communities of creative students, provided the theoretical framework. Both quantitative and qualitative data gathering methods were used. Data-collection tools included affective-disposition statements, interviews, journal entries, as well as a video recording of a mathematics education lesson. The quantitative and qualitative data generated suggest improved levels of self-efficacy amongst the students who participated in the study. The data also suggest that a valuesbased approach to teaching can be used as an effective approach by mathematics teachers – and mathematics teacher educators – for the purpose of promoting the pursuit of excellence. As teacher education worldwide is currently characterised by a lack of vitality in teacher preparation (Grossman, 2008), the findings of this study should provide insights for teacher educators, teachers and policy makers who wish to promote mathematics self-efficacy, excellence and facilitate enhanced vitality within the teaching profession.
- Full Text:
- Date Issued: 2010
- Authors: Austin, Pamela Winifred
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:9482 , http://hdl.handle.net/10948/1656 , Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa , Active learning -- South Africa , Effective teaching -- South Africa , Self-efficacy
- Description: This research study has emerged as a result of my concern regarding the apparent low self-efficacy amongst initial teacher education students in my mathematics education classes. It also reflects a reported renewed interest in values, and the promotion of excellence in education. The effects of a values-based approach to mathematics education towards improving students’ self-efficacy and promoting excellence have been investigated, grounded within my ontology of excellence in mathematics education, which incorporates the values of respect, fairness, accountability, honesty and compassion. An inquiry-based teaching and learning approach formed the framework within which the study took place. Notions of ‘new scholarship’, premised on the view that teaching is about engagement in participatory learning, and the development of communities of creative students, provided the theoretical framework. Both quantitative and qualitative data gathering methods were used. Data-collection tools included affective-disposition statements, interviews, journal entries, as well as a video recording of a mathematics education lesson. The quantitative and qualitative data generated suggest improved levels of self-efficacy amongst the students who participated in the study. The data also suggest that a valuesbased approach to teaching can be used as an effective approach by mathematics teachers – and mathematics teacher educators – for the purpose of promoting the pursuit of excellence. As teacher education worldwide is currently characterised by a lack of vitality in teacher preparation (Grossman, 2008), the findings of this study should provide insights for teacher educators, teachers and policy makers who wish to promote mathematics self-efficacy, excellence and facilitate enhanced vitality within the teaching profession.
- Full Text:
- Date Issued: 2010
Searching for common ground: developing mathematical reasoning through dialogue
- Authors: Webb, Marie Lynette
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9493 , http://hdl.handle.net/10948/1132 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Description: In the majority of the schools in the Eastern Cape, South Africa, teaching and learning takes place in the second language, English, of both teachers and learners. The purpose of this research was to elicit the perceptions of teachers in multilingual mathematics classes about language issues that they encounter and to ascertain whether they could experientially learn the theory of dialogic teaching through an intervention in order to introduce dialogue in practice in their classes. The effect of the intervention on teacher practices was qualitatively observed and the effect of the teacher practices on learner reasoning competence, numeracy competence and English language competence was quantitatively tested by using validated pre- and post-tests. The study follows a mixed method concurrent triangulation design with both quantitative and qualitative results. Two cohorts of students/teachers studying for qualifications at Nelson Mandela Metropolitan University centres throughout the Eastern Cape expressed their opinions about language challenges and solutions through questionnaires, reflective writing and poetry. A cohort of BEd Honours (Mathematics and Science) students experienced a semester long intervention on the theory and practice of dialogic teaching, particularly exploratory talk, and were tasked to introduce the practice into their multilingual mathematics classes in the form of reported action research. The next phase of the study focussed on the practices of three teachers and their grade seven multilingual mathematics learners who were observed and tested over a period of nine months. The following year the observations and testing were repeated with one teacher and his grade seven learners to ascertain whether the intervention would result in similar findings. iv The results enhance the validity of the Vygotskian claim concerning the relationship between language use, social interaction and reasoning development. In classes where there was evidence of dialogic practices the learners collaborated in groups using code-switching and their main language. Their reasoning, numeracy and English skills test scores improved statistically significantly. Teachers were able to give voice to their deep-felt emotions through poetry. They felt that the devaluing of isiXhosa had resulted in the loss of learners’ main language literacy competencies and consequent loss of cultural capital; however they considered it necessary to develop English competence in the learners, even if it was at the expense of developing mathematical competence. The introduction of exploratory talk in their home languages served the dual purpose of promoting the value of isiXhosa in an academic environment as well as enhancing mathematical reasoning. It appears that when teachers focus on developing language as a tool for reasoning, significant improvements in learners’ problem solving competences occur. When the language used is the main language of both teachers and learners both mathematical understanding and cultural identity are enhanced. The study concludes with a suggestion for a model for future interventions to train teachers to introduce dialogic practices in multilingual mathematics classes.
- Full Text:
- Date Issued: 2010
- Authors: Webb, Marie Lynette
- Date: 2010
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9493 , http://hdl.handle.net/10948/1132 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa , English language -- Usage -- South Africa
- Description: In the majority of the schools in the Eastern Cape, South Africa, teaching and learning takes place in the second language, English, of both teachers and learners. The purpose of this research was to elicit the perceptions of teachers in multilingual mathematics classes about language issues that they encounter and to ascertain whether they could experientially learn the theory of dialogic teaching through an intervention in order to introduce dialogue in practice in their classes. The effect of the intervention on teacher practices was qualitatively observed and the effect of the teacher practices on learner reasoning competence, numeracy competence and English language competence was quantitatively tested by using validated pre- and post-tests. The study follows a mixed method concurrent triangulation design with both quantitative and qualitative results. Two cohorts of students/teachers studying for qualifications at Nelson Mandela Metropolitan University centres throughout the Eastern Cape expressed their opinions about language challenges and solutions through questionnaires, reflective writing and poetry. A cohort of BEd Honours (Mathematics and Science) students experienced a semester long intervention on the theory and practice of dialogic teaching, particularly exploratory talk, and were tasked to introduce the practice into their multilingual mathematics classes in the form of reported action research. The next phase of the study focussed on the practices of three teachers and their grade seven multilingual mathematics learners who were observed and tested over a period of nine months. The following year the observations and testing were repeated with one teacher and his grade seven learners to ascertain whether the intervention would result in similar findings. iv The results enhance the validity of the Vygotskian claim concerning the relationship between language use, social interaction and reasoning development. In classes where there was evidence of dialogic practices the learners collaborated in groups using code-switching and their main language. Their reasoning, numeracy and English skills test scores improved statistically significantly. Teachers were able to give voice to their deep-felt emotions through poetry. They felt that the devaluing of isiXhosa had resulted in the loss of learners’ main language literacy competencies and consequent loss of cultural capital; however they considered it necessary to develop English competence in the learners, even if it was at the expense of developing mathematical competence. The introduction of exploratory talk in their home languages served the dual purpose of promoting the value of isiXhosa in an academic environment as well as enhancing mathematical reasoning. It appears that when teachers focus on developing language as a tool for reasoning, significant improvements in learners’ problem solving competences occur. When the language used is the main language of both teachers and learners both mathematical understanding and cultural identity are enhanced. The study concludes with a suggestion for a model for future interventions to train teachers to introduce dialogic practices in multilingual mathematics classes.
- Full Text:
- Date Issued: 2010
Investigating relationships between mathematics teachers' content knowledge, their pedagogical knowledge and their learnes' achievement in terms of functions and graphs
- Authors: Stewart, Joyce
- Date: 2009
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9515 , http://hdl.handle.net/10948/1100 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa
- Description: This study used diagnostic tests, questionnaires and interviews to investigate explore teachers’ subject content knowledge (SCK) and pedagogical subject knowledge (PCK). It also explored teachers’ and learners’ misconceptions within the topic of graphicacy and how teachers’ SCK and PCK possibly affect learner achievement. A small sample of teachers were drawn from the Keiskammahoek region; a deep rural area of the Eastern Cape. These teachers were part of the Nelson Mandela Metropolitan University (NMMU) Amathole Cluster Schools Project who were registered for a three-year BEd (FET) in-service programme in mathematics education. As part of the programme they studied mathematics 1 and 2 at university level and received quarterly non-formal workshops on teaching mathematics at FET level. The findings of this study suggest that teachers with insufficient SCK will probably have limited PCK, although the two are not entirely dependent on each other. In cases where teachers’ displayed low levels of SCK and PCK, their learners were more likely to perform poorly and their results often indicated similar misconceptions as displayed by their teachers. This implies that we have to look at what teachers know and what they need to know in terms of SCK and PCK if we are to plan effectively for effective teacher development aimed at improving learner performance.
- Full Text:
- Date Issued: 2009
- Authors: Stewart, Joyce
- Date: 2009
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9515 , http://hdl.handle.net/10948/1100 , Mathematics -- Study and teaching -- South Africa , Mathematics teachers -- Training of -- South Africa
- Description: This study used diagnostic tests, questionnaires and interviews to investigate explore teachers’ subject content knowledge (SCK) and pedagogical subject knowledge (PCK). It also explored teachers’ and learners’ misconceptions within the topic of graphicacy and how teachers’ SCK and PCK possibly affect learner achievement. A small sample of teachers were drawn from the Keiskammahoek region; a deep rural area of the Eastern Cape. These teachers were part of the Nelson Mandela Metropolitan University (NMMU) Amathole Cluster Schools Project who were registered for a three-year BEd (FET) in-service programme in mathematics education. As part of the programme they studied mathematics 1 and 2 at university level and received quarterly non-formal workshops on teaching mathematics at FET level. The findings of this study suggest that teachers with insufficient SCK will probably have limited PCK, although the two are not entirely dependent on each other. In cases where teachers’ displayed low levels of SCK and PCK, their learners were more likely to perform poorly and their results often indicated similar misconceptions as displayed by their teachers. This implies that we have to look at what teachers know and what they need to know in terms of SCK and PCK if we are to plan effectively for effective teacher development aimed at improving learner performance.
- Full Text:
- Date Issued: 2009
The identification of criteria to be utilised in mathematical diagnostic tests
- Authors: Wagner-Welsh, Shirley Joy
- Date: 2008
- Subjects: Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:10501 , http://hdl.handle.net/10948/708 , Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Description: School-related mistakes and low pass rates have led this researcher to perceive that some students are not adequately prepared for Mathematics 1. To address the problem of under-preparedness overseas universities use placement or diagnostic tests. Diagnostic testing identifies areas of weakness and provides information to guide the development of appropriate remedial support. This researcher embarked on a study to identify the sub-domains (criteria) that should be included in a diagnostic Mathematics test battery at the NMMU. An analysis of first-year curricula was undertaken to determine the required Mathematical pre-knowledge and skills entry-level students should have. Thereafter, the required pre-knowledge and skills were reflected against the standard grade school syllabi. From this it was determined that the school learners should acquire the necessary pre-knowledge and skills for university success as part of the school syllabus. However, in reality this is not the case as the researcher and other Mathematics lecturers identified a number of basic errors that incoming students make. This suggests that they have not developed all the required knowledge and skills. Furthermore, their performance in the matriculation examinations does not provide an adequate measure of the requisite Mathematical pre-knowledge and skills necessary for success at university-level Mathematics. No suitable existing diagnostic Mathematics test could be found. By utilizing both an action research as well as a test development methodology, the researcher thus proceeded to delineate the sub-domains that should be included in a diagnostic Mathematics test battery. Thereafter, test specifications were developed for two pilot tests and items were developed or sourced. The constructed response item-type was chosen for the pilot tests as it was argued that this item-type was more useful to use in a diagnostic test than a multiple-choice item format, for example. The pilot test battery, which consisted of a pilot Arithmetic and Algebra and Calculus tests, was administered to a sample of first-year students at the NMMU in 2004 and their performance in Mathematics at the end of the first year was tracked. Tests were scored holistically and analytically to provide a rich source of information. Thereafter, the test results were analysed to obtain evidence on the content validity of the pilot tests, including the item difficulty values and the item-total correlations; to determine the predictive validity of performance on the pilot tests with respect to final first-year Mathematics marks; and their reliability was determined using the Cronbach’s Alpha statistic. These findings suggest that appropriate sub-domains (criteria) were delineated and the items appropriately covered these sub-domains (i.e. the content validity of the pilot tests is acceptable). Furthermore, the predictive validity of the pilot ix tests was found to be acceptable in that significant correlations were found between the pilot tests and performance in first-year Mathematics. Finally, the pilot tests were found to be reliable. Based on the results, suggestions are made regarding how to refine the diagnostic test battery and the research related to it. The final diagnostic Mathematics test battery holds much potential to be able to assist in the early identification of at-risk students who can be timeously placed in developmentally appropriate Mathematics modules or provided with appropriate remedial intervention.
- Full Text:
- Date Issued: 2008
- Authors: Wagner-Welsh, Shirley Joy
- Date: 2008
- Subjects: Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Language: English
- Type: Thesis , Doctoral , DPhil
- Identifier: vital:10501 , http://hdl.handle.net/10948/708 , Educational tests and measurements -- South Africa -- Port Elizabeth , Mathematical ability -- Testing , Ability -- Testing , Guidance test battery for secondary pupils , Mathematics -- Study and teaching -- South Africa
- Description: School-related mistakes and low pass rates have led this researcher to perceive that some students are not adequately prepared for Mathematics 1. To address the problem of under-preparedness overseas universities use placement or diagnostic tests. Diagnostic testing identifies areas of weakness and provides information to guide the development of appropriate remedial support. This researcher embarked on a study to identify the sub-domains (criteria) that should be included in a diagnostic Mathematics test battery at the NMMU. An analysis of first-year curricula was undertaken to determine the required Mathematical pre-knowledge and skills entry-level students should have. Thereafter, the required pre-knowledge and skills were reflected against the standard grade school syllabi. From this it was determined that the school learners should acquire the necessary pre-knowledge and skills for university success as part of the school syllabus. However, in reality this is not the case as the researcher and other Mathematics lecturers identified a number of basic errors that incoming students make. This suggests that they have not developed all the required knowledge and skills. Furthermore, their performance in the matriculation examinations does not provide an adequate measure of the requisite Mathematical pre-knowledge and skills necessary for success at university-level Mathematics. No suitable existing diagnostic Mathematics test could be found. By utilizing both an action research as well as a test development methodology, the researcher thus proceeded to delineate the sub-domains that should be included in a diagnostic Mathematics test battery. Thereafter, test specifications were developed for two pilot tests and items were developed or sourced. The constructed response item-type was chosen for the pilot tests as it was argued that this item-type was more useful to use in a diagnostic test than a multiple-choice item format, for example. The pilot test battery, which consisted of a pilot Arithmetic and Algebra and Calculus tests, was administered to a sample of first-year students at the NMMU in 2004 and their performance in Mathematics at the end of the first year was tracked. Tests were scored holistically and analytically to provide a rich source of information. Thereafter, the test results were analysed to obtain evidence on the content validity of the pilot tests, including the item difficulty values and the item-total correlations; to determine the predictive validity of performance on the pilot tests with respect to final first-year Mathematics marks; and their reliability was determined using the Cronbach’s Alpha statistic. These findings suggest that appropriate sub-domains (criteria) were delineated and the items appropriately covered these sub-domains (i.e. the content validity of the pilot tests is acceptable). Furthermore, the predictive validity of the pilot ix tests was found to be acceptable in that significant correlations were found between the pilot tests and performance in first-year Mathematics. Finally, the pilot tests were found to be reliable. Based on the results, suggestions are made regarding how to refine the diagnostic test battery and the research related to it. The final diagnostic Mathematics test battery holds much potential to be able to assist in the early identification of at-risk students who can be timeously placed in developmentally appropriate Mathematics modules or provided with appropriate remedial intervention.
- Full Text:
- Date Issued: 2008
The family maths programme: facilitators' ability to implement inquiry-based teaching and learning with learners and parents
- Authors: Austin, Pamela Winifred
- Date: 2007
- Subjects: Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9483 , http://hdl.handle.net/10948/471 , Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa
- Description: Despite the fact that the facilitation of inquiry learning is a core methodology in the General Education and Training (GET) band of the South African National Curriculum Statement, rote learning and memorization of algorithms remains common practice in many mathematics classrooms. The inquiry-based Family Maths professional development programme, offered by the Nelson Mandela Metropolitan University, attempts not only to support the transformative education practices targeted by the South African National Department of Education, but also to extend them beyond the school walls to the community at large. This study investigates the extent to which the Family Maths professional development programme develops facilitators’ ability to implement inquiry-based learning. It also seeks to explore which aspects of the programme are effective in developing an inquiry-based approach. The research undertaken is an empirical study of 39 facilitators and uses both qualitative and quantitative methods. The facilitators’ inquiry beliefs and ability to implement inquiry learning was measured by means of questionnaires, observation schedules and interviews. As the ‘teacher as facilitator of inquiry-based teaching and learning’ is a requirement of all South African teachers, the findings of this research should make a meaningful contribution to the field of mathematics teacher education in the South African context.
- Full Text:
- Date Issued: 2007
- Authors: Austin, Pamela Winifred
- Date: 2007
- Subjects: Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9483 , http://hdl.handle.net/10948/471 , Mathematics -- Study and teaching -- South Africa , Inquiry-based learning -- South Africa
- Description: Despite the fact that the facilitation of inquiry learning is a core methodology in the General Education and Training (GET) band of the South African National Curriculum Statement, rote learning and memorization of algorithms remains common practice in many mathematics classrooms. The inquiry-based Family Maths professional development programme, offered by the Nelson Mandela Metropolitan University, attempts not only to support the transformative education practices targeted by the South African National Department of Education, but also to extend them beyond the school walls to the community at large. This study investigates the extent to which the Family Maths professional development programme develops facilitators’ ability to implement inquiry-based learning. It also seeks to explore which aspects of the programme are effective in developing an inquiry-based approach. The research undertaken is an empirical study of 39 facilitators and uses both qualitative and quantitative methods. The facilitators’ inquiry beliefs and ability to implement inquiry learning was measured by means of questionnaires, observation schedules and interviews. As the ‘teacher as facilitator of inquiry-based teaching and learning’ is a requirement of all South African teachers, the findings of this research should make a meaningful contribution to the field of mathematics teacher education in the South African context.
- Full Text:
- Date Issued: 2007
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