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:
- Date Issued: 2020
- 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:
- Date Issued: 2020
Patterns and Pattern Languages for Mobile Augmented Reality
- Authors: Munro, Donald
- Date: 2020
- Subjects: Augmented reality , Educational technology
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10948/48510 , vital:40883
- Description: Mixed Reality is a relatively new field in computer science which uses technology as a medium to provide modified or enhanced views of reality or to virtually generate a new reality. Augmented Reality is a branch of Mixed Reality which blends the real-world as viewed through a computer interface with virtual objects generated by a computer. The 21st century commodification of mobile devices with multi-core Central Processing Units, Graphics Processing Units, high definition displays and multiple sensors controlled by capable Operating Systems such as Android and iOS means that Mobile Augmented Reality applications have become increasingly feasible. Mobile Augmented Reality is a multi-disciplinary field requiring a synthesis of many technologies such as computer graphics, computer vision, machine learning and mobile device programming while also requiring theoretical knowledge of diverse fields such as Linear Algebra, Projective and Differential Geometry, Probability and Optimisation. This multi-disciplinary nature has led to a fragmentation of knowledge into various specialisations, making it difficult to integrate different solution components into a coherent architecture. Software design patterns provide a solution space of tried and tested best practices for a specified problem within a given context. The solution space is non-prescriptive and is described in terms of relationships between roles that can be assigned to software components. Architectural patterns are used to specify high level designs of complete systems, as opposed to domain or tactical level patterns that address specific lower level problem areas. Pattern Languages comprise multiple software patterns combining in multiple possible sequences to form a language with the individual patterns forming the language vocabulary while the valid sequences through the patterns define the grammar. Pattern Languages provide flexible generalised solutions within a particular domain that can be customised to solve problems of differing characteristics and levels of iii complexity within the domain. The specification of one or more Pattern Languages tailored to the Mobile Augmented Reality domain can therefore provide a generalised guide for the design and architecture of Mobile Augmented Reality applications from an architectural level down to the ”nuts-and-bolts” implementation level. While there is a large body of research into the technical specialisations pertaining to Mobile Augmented Reality, there is a dearth of up-to-date literature covering Mobile Augmented Reality design. This thesis fills this vacuum by: 1. Providing architectural patterns that provide the spine on which the design of Mobile Augmented Reality artefacts can be based; 2. Documenting existing patterns within the context of Mobile Augmented Reality; 3. Identifying new patterns specific to Mobile Augmented Reality; and 4. Combining the patterns into Pattern Languages for Detection & Tracking, Rendering & Interaction and Data Access for Mobile Augmented Reality. The resulting Pattern Languages support design at multiple levels of complexity from an object-oriented framework down to specific one-off Augmented Reality applications. The practical contribution of this thesis is the specification of architectural patterns and Pattern Language that provide a unified design approach for both the overall architecture and the detailed design of Mobile Augmented Reality artefacts. The theoretical contribution is a design theory for Mobile Augmented Reality gleaned from the extraction of patterns and creation of a pattern language or languages.
- Full Text:
- Date Issued: 2020
- Authors: Munro, Donald
- Date: 2020
- Subjects: Augmented reality , Educational technology
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10948/48510 , vital:40883
- Description: Mixed Reality is a relatively new field in computer science which uses technology as a medium to provide modified or enhanced views of reality or to virtually generate a new reality. Augmented Reality is a branch of Mixed Reality which blends the real-world as viewed through a computer interface with virtual objects generated by a computer. The 21st century commodification of mobile devices with multi-core Central Processing Units, Graphics Processing Units, high definition displays and multiple sensors controlled by capable Operating Systems such as Android and iOS means that Mobile Augmented Reality applications have become increasingly feasible. Mobile Augmented Reality is a multi-disciplinary field requiring a synthesis of many technologies such as computer graphics, computer vision, machine learning and mobile device programming while also requiring theoretical knowledge of diverse fields such as Linear Algebra, Projective and Differential Geometry, Probability and Optimisation. This multi-disciplinary nature has led to a fragmentation of knowledge into various specialisations, making it difficult to integrate different solution components into a coherent architecture. Software design patterns provide a solution space of tried and tested best practices for a specified problem within a given context. The solution space is non-prescriptive and is described in terms of relationships between roles that can be assigned to software components. Architectural patterns are used to specify high level designs of complete systems, as opposed to domain or tactical level patterns that address specific lower level problem areas. Pattern Languages comprise multiple software patterns combining in multiple possible sequences to form a language with the individual patterns forming the language vocabulary while the valid sequences through the patterns define the grammar. Pattern Languages provide flexible generalised solutions within a particular domain that can be customised to solve problems of differing characteristics and levels of iii complexity within the domain. The specification of one or more Pattern Languages tailored to the Mobile Augmented Reality domain can therefore provide a generalised guide for the design and architecture of Mobile Augmented Reality applications from an architectural level down to the ”nuts-and-bolts” implementation level. While there is a large body of research into the technical specialisations pertaining to Mobile Augmented Reality, there is a dearth of up-to-date literature covering Mobile Augmented Reality design. This thesis fills this vacuum by: 1. Providing architectural patterns that provide the spine on which the design of Mobile Augmented Reality artefacts can be based; 2. Documenting existing patterns within the context of Mobile Augmented Reality; 3. Identifying new patterns specific to Mobile Augmented Reality; and 4. Combining the patterns into Pattern Languages for Detection & Tracking, Rendering & Interaction and Data Access for Mobile Augmented Reality. The resulting Pattern Languages support design at multiple levels of complexity from an object-oriented framework down to specific one-off Augmented Reality applications. The practical contribution of this thesis is the specification of architectural patterns and Pattern Language that provide a unified design approach for both the overall architecture and the detailed design of Mobile Augmented Reality artefacts. The theoretical contribution is a design theory for Mobile Augmented Reality gleaned from the extraction of patterns and creation of a pattern language or languages.
- Full Text:
- Date Issued: 2020
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