An analysis of how visualisation capabilities in dynamic geometric software develop meaning-making of mathematical concepts in selected Grade 11 learners
- Authors: Mavani, Deepack Pravin
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Mathematics -- Computer programs , Mathematics -- Study and teaching (Secondary) -- South Africa -- Case studies , Mathematics -- Study and teaching -- Activity programs , Educational technology , Visualization
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/143213 , vital:38211
- Description: Visualisation plays a central role in developing mathematical ideas because it can be used to make these ideas explicit and visible, and thus has the potential to advance understanding. This study centred around the GeoGebra Literacy Initiative Project (GLIP), a teacher development initiative in Mthatha that aimed to grow and develop appropriate Information and Communication Technology (ICT) skills in teachers, to harness the teaching and learning potential of GeoGebra. GeoGebra is a dynamic geometric software package that is very interactive and makes use of powerful features to create images which can be moved around the computer screen for mathematical exploration. This research project was located within GLIP and analysed how GeoGebra applets develop conceptual and procedural understanding in selected Grade 11 learners. One aspect of GLIP was for teachers to use GeoGebra applets that they had developed themselves and implemented in their classrooms in pre-determined cycles that were aligned to the curriculum. My study specifically focused on how the selected learners made use of these applets and explored how learning had taken place in terms of developing mathematical meaning-making. This interpretive research study was designed as a case study. The case was a cohort of selected Grade 11 learners who had been taught by GLIP teachers, and my unit of analysis was the learners’ interaction with the applets. A screen capturing software package was used to capture learners’ interactions with the GeoGebra. My data consisted mainly of recorded observations and interviews. An analytical framework derived from the works of Kilpatrick, Swafford, and Findell (2001) and Carter et al. (2009) guided and informed the data analysis of the learners’ activities with the GeoGebra. The theoretical orientation of this study was constructivist learning. An in-depth analysis and detailed descriptions of the participants’ interactions enabled me to gain a comprehensive understanding of their meaning-making processes in a technological classroom context. An analysis across the participants identified distinguishable patterns or differences in the development of the learners’ mathematical proficiency and making sense of mathematical ideas. The research argued that technology enabled visualisation was a powerful tool to not only enrich mathematically activities, but to also enrich conceptual and procedural understanding. The findings recognised that exploration of, or manipulation on mathematical objects in GeoGebra was a key activity in the participants’ meaning-making process. It also enabled learners to offer self-proclaimed theories
- Full Text:
- Authors: Mavani, Deepack Pravin
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Mathematics -- Computer programs , Mathematics -- Study and teaching (Secondary) -- South Africa -- Case studies , Mathematics -- Study and teaching -- Activity programs , Educational technology , Visualization
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/143213 , vital:38211
- Description: Visualisation plays a central role in developing mathematical ideas because it can be used to make these ideas explicit and visible, and thus has the potential to advance understanding. This study centred around the GeoGebra Literacy Initiative Project (GLIP), a teacher development initiative in Mthatha that aimed to grow and develop appropriate Information and Communication Technology (ICT) skills in teachers, to harness the teaching and learning potential of GeoGebra. GeoGebra is a dynamic geometric software package that is very interactive and makes use of powerful features to create images which can be moved around the computer screen for mathematical exploration. This research project was located within GLIP and analysed how GeoGebra applets develop conceptual and procedural understanding in selected Grade 11 learners. One aspect of GLIP was for teachers to use GeoGebra applets that they had developed themselves and implemented in their classrooms in pre-determined cycles that were aligned to the curriculum. My study specifically focused on how the selected learners made use of these applets and explored how learning had taken place in terms of developing mathematical meaning-making. This interpretive research study was designed as a case study. The case was a cohort of selected Grade 11 learners who had been taught by GLIP teachers, and my unit of analysis was the learners’ interaction with the applets. A screen capturing software package was used to capture learners’ interactions with the GeoGebra. My data consisted mainly of recorded observations and interviews. An analytical framework derived from the works of Kilpatrick, Swafford, and Findell (2001) and Carter et al. (2009) guided and informed the data analysis of the learners’ activities with the GeoGebra. The theoretical orientation of this study was constructivist learning. An in-depth analysis and detailed descriptions of the participants’ interactions enabled me to gain a comprehensive understanding of their meaning-making processes in a technological classroom context. An analysis across the participants identified distinguishable patterns or differences in the development of the learners’ mathematical proficiency and making sense of mathematical ideas. The research argued that technology enabled visualisation was a powerful tool to not only enrich mathematically activities, but to also enrich conceptual and procedural understanding. The findings recognised that exploration of, or manipulation on mathematical objects in GeoGebra was a key activity in the participants’ meaning-making process. It also enabled learners to offer self-proclaimed theories
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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:
- 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:
Investigating conceptual teaching of word problems through visualisation processes: a case of selected Grad 9 mathematics teachers
- Authors: John, Ssennyomo Bernard
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Pythagorean theorem -- Study and teaching (Secondary) , Mathematics teachers -- South Africa , Visualization
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/167497 , vital:41486
- Description: This study investigated how selected grade 9 mathematics teachers used visualisation strategies to conceptually teach Pythagoras' theorem word problems as a result of an intervention program. This research project is an integral component of the ViProMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. This case study of mathematics teachers in the John Taolo Gaetsewe (JTG) District in the Northern Cape Province, used a social constructivist theory. The study is grounded within an interpretive paradigm and used an explanatory sequential mixed methods design. It surveyed eighty-seven mathematics teachers from all the secondary schools in the JTG District, focusing on their experiences when using visualisation approaches to teach Pythagoras’ theorem word problems. After the survey, three teachers purposively selected from three different schools in the district took part in the intervention programme. I used a survey questionnaire, classroom observations and interviews to collect the data from the study participants. The data were analysed quantitatively and qualitatively. The findings from survey data revealed that while teachers in the JTG District acknowledge the importance and value of visualisation strategies in the teaching of Pythagoras’ theorem word problems, many of them are either using visuals minimally or not using them at all. Challenges such as lack of resources in schools, time constrains, a lack of support from subject advisers, among others were noted. This thus necessitated a need for an intervention with some teachers in the district, specifically focusing on the use of visualisation tools and skills to teach Pythagoras’ theorem word problems for conceptual understanding. Lessons observations showed that all observed teachers used visual models to generate images and used the models to develop mathematical ideas. The teachers used the images to create platforms for classroom discussions. The discussions were driven by questions which teachers asked both for ascertaining learners’ prior knowledge and for finding out if they understood what the teachers were teaching. Interviews revealed that teachers’ perceptions had changed because they now know how to make and use different models to build on learners’ prior knowledge, extend what they are teaching to real life and make sense of Pythagoras’ proposition in multiple ways and to establish connections among a rich set of mathematics concepts when teaching Pythagoras’ theorem word problems. This study concludes that the use of visual strategies has the potential of enhancing conceptual teaching of Pythagoras’ theorem word problems. The implications for teachers are that learners need to be taught how to create visual representations (both internally and externally) of the relations between objects in a word problem as this will help them in maximising understanding. Furthermore, it is hoped that the results of this study could be used by various stake holders who include inter alia, mathematics subject advisers and teacher training institutions to improve the teaching of Pythagoras’ theorem word problems.
- Full Text:
- Authors: John, Ssennyomo Bernard
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Pythagorean theorem -- Study and teaching (Secondary) , Mathematics teachers -- South Africa , Visualization
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/167497 , vital:41486
- Description: This study investigated how selected grade 9 mathematics teachers used visualisation strategies to conceptually teach Pythagoras' theorem word problems as a result of an intervention program. This research project is an integral component of the ViProMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. This case study of mathematics teachers in the John Taolo Gaetsewe (JTG) District in the Northern Cape Province, used a social constructivist theory. The study is grounded within an interpretive paradigm and used an explanatory sequential mixed methods design. It surveyed eighty-seven mathematics teachers from all the secondary schools in the JTG District, focusing on their experiences when using visualisation approaches to teach Pythagoras’ theorem word problems. After the survey, three teachers purposively selected from three different schools in the district took part in the intervention programme. I used a survey questionnaire, classroom observations and interviews to collect the data from the study participants. The data were analysed quantitatively and qualitatively. The findings from survey data revealed that while teachers in the JTG District acknowledge the importance and value of visualisation strategies in the teaching of Pythagoras’ theorem word problems, many of them are either using visuals minimally or not using them at all. Challenges such as lack of resources in schools, time constrains, a lack of support from subject advisers, among others were noted. This thus necessitated a need for an intervention with some teachers in the district, specifically focusing on the use of visualisation tools and skills to teach Pythagoras’ theorem word problems for conceptual understanding. Lessons observations showed that all observed teachers used visual models to generate images and used the models to develop mathematical ideas. The teachers used the images to create platforms for classroom discussions. The discussions were driven by questions which teachers asked both for ascertaining learners’ prior knowledge and for finding out if they understood what the teachers were teaching. Interviews revealed that teachers’ perceptions had changed because they now know how to make and use different models to build on learners’ prior knowledge, extend what they are teaching to real life and make sense of Pythagoras’ proposition in multiple ways and to establish connections among a rich set of mathematics concepts when teaching Pythagoras’ theorem word problems. This study concludes that the use of visual strategies has the potential of enhancing conceptual teaching of Pythagoras’ theorem word problems. The implications for teachers are that learners need to be taught how to create visual representations (both internally and externally) of the relations between objects in a word problem as this will help them in maximising understanding. Furthermore, it is hoped that the results of this study could be used by various stake holders who include inter alia, mathematics subject advisers and teacher training institutions to improve the teaching of Pythagoras’ theorem word problems.
- Full Text:
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