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
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 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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