An analysis of mathematical connections in the presentations of fraction concepts in Namibian grade 7 mathematics textbooks
- Authors: Sibeso, Pumulo Priscah
- Date: 2024-04-05
- Subjects: Mathematics Study and teaching (Primary) Namibia , Fractions , Textbooks Criticism, Textual , Connections (Mathematics) , National Institute for Educational Development (Namibia) , Mathematics teachers In-service training
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436488 , vital:73276
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
- Full Text:
- Authors: Sibeso, Pumulo Priscah
- Date: 2024-04-05
- Subjects: Mathematics Study and teaching (Primary) Namibia , Fractions , Textbooks Criticism, Textual , Connections (Mathematics) , National Institute for Educational Development (Namibia) , Mathematics teachers In-service training
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436488 , vital:73276
- Description: This study investigated how selected grade 11 mathematics learners used smartphones with the MathCityMap application to learn trigonometry outdoors for conceptual understanding. The aim of this research project was to explore outdoor mathematics learning for conceptual understanding using smartphones. This case study of grade 11 mathematics learners in Lejweleputswa District in the Free State Province, was informed by the Realistic Mathematics Education theory. The study is grounded within an interpretive paradigm and used the explanatory sequential mixed-method design. Forty-two grade 11 mathematics learners participated in the survey and from these 12 were purposively selected to participate in walking the mathematics trails and interviews. The findings revealed that, while the grade 11 mathematics learners acknowledged the significance and value of using smartphones for learning mathematics, they were prohibited from carrying or using smartphones on the school premises, as part of the school code of conduct. The preferred use of smartphones for learning mathematics was understandable, as the survey was conducted at a time when the COVID-19 pandemic and associated restrictions were still in place. The survey unearthed that among applications for learning mathematics, the MathCityMap application was not known by the learners who participated in the survey. Mathematics trails observations indicated that outdoor tasks were a source of mathematical concepts or formal mathematical knowledge, and enabled learners to reinvent mathematical ideas and concepts with adult guidance. Learners were able to make use of appropriate mathematical models and connections. The mathematics trails ignited robust discussions among learners, and prompted learners to draw from prior knowledge, and recognise and identify suitable mathematical models and shapes from the real-world objects. Learners were able to use multiple representations, make necessary mathematical links, and use their prior knowledge to enhance their trigonometry conceptual understanding. This study concluded that using smartphones with the MathCityMap application could enhance conceptual understanding of trigonometry. The implications for teachers are that learners should be exposed to outdoor mathematics learning using smartphones with the MathCityMap application to improve their conceptual understanding. It is hoped that the results of this study can be used by various stakeholders, who include, inter alia, mathematics subject advisors and teacher training institutions, to enhance learners’ conceptual understanding of mathematics. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
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Integrating music and mathematics for connecting across multiple constructs of fractional understanding: an RME task design journey
- Authors: Lovemore, Tarryn Shirley
- Date: 2023-03-29
- Subjects: Communities of practice , Interdisciplinary approach in education , Fractions , Mathematics Study and teaching , Music in mathematics education , Number line
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/366200 , vital:65842 , DOI https://doi.org/10.21504/10962/366200
- Description: Two South African curricular aims: appreciating creativity in mathematics and developing conceptual understanding, motivated this study. Negative views towards mathematics and challenges in teaching and learning fractions at primary school level are reported in literature, with the part-whole construct of fractions often the sole teaching focus. Despite challenges in curriculum integration (high demands on teachers and diluting disciplines), benefits, such as motivation and creative thinking, are noted. I recognised music-mathematics integration as an opportune context for designing tasks to support learners in moving flexibly between the fraction as ratio, fraction as measure and part-whole constructs. Guided by Realistic Mathematics Education principles, I embarked on a participatory dual-design experiment in task design, grappling within three micro-Communities of Practice (micro-CoPs) and across two planes: the Design-Theorising Plane and the Grounded-Practice Plane. In the Design-Theorising Plane, I worked with my two doctoral supervisors, grappling with design obstacles and finding resolutions. COVID-19 restrictions shifted our meetings to online platforms, allowing documentation and analysis of the task design process through recording functions. In the Grounded-Practice Plane, I worked within two separate micro-CoPs, both at independent schools (eight and two participating teachers respectively). Data on the teachers’ interrogation and implementation of the designed tasks were obtained via formal and informal interviews. Their reflections informed ongoing adaptations to the task design. Data were analysed in a matrix I designed and via NVivo coding. Findings include both the product of the task design journey (eight music-mathematics lessons, resources, and representations) and the process (ten groupings of Obstacle-Resolution Cycles). Three key questions (relating to music-mathematics fidelity; to task simplification for implementation; and to appropriate music-mathematics representation) were used in addressing each Obstacle-Resolution Cycle. Designing tasks to teach the part-whole construct of fractions was relatively straightforward, but designing tasks to teach the fraction as ratio and fraction as measure constructs was more challenging. These constructs could not be conflated by superimposing the music and mathematical linear representations. Aligning them, however, allowed for moving flexibly between the constructs. The teachers reported that the integrated music-mathematics tasks and supporting resources enhanced their learners’ fractional problem-solving abilities, simultaneously promoting more positive learner dispositions towards mathematics. , Thesis (PhD) -- Faculty of Education, Education, 2023
- Full Text:
- Authors: Lovemore, Tarryn Shirley
- Date: 2023-03-29
- Subjects: Communities of practice , Interdisciplinary approach in education , Fractions , Mathematics Study and teaching , Music in mathematics education , Number line
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/366200 , vital:65842 , DOI https://doi.org/10.21504/10962/366200
- Description: Two South African curricular aims: appreciating creativity in mathematics and developing conceptual understanding, motivated this study. Negative views towards mathematics and challenges in teaching and learning fractions at primary school level are reported in literature, with the part-whole construct of fractions often the sole teaching focus. Despite challenges in curriculum integration (high demands on teachers and diluting disciplines), benefits, such as motivation and creative thinking, are noted. I recognised music-mathematics integration as an opportune context for designing tasks to support learners in moving flexibly between the fraction as ratio, fraction as measure and part-whole constructs. Guided by Realistic Mathematics Education principles, I embarked on a participatory dual-design experiment in task design, grappling within three micro-Communities of Practice (micro-CoPs) and across two planes: the Design-Theorising Plane and the Grounded-Practice Plane. In the Design-Theorising Plane, I worked with my two doctoral supervisors, grappling with design obstacles and finding resolutions. COVID-19 restrictions shifted our meetings to online platforms, allowing documentation and analysis of the task design process through recording functions. In the Grounded-Practice Plane, I worked within two separate micro-CoPs, both at independent schools (eight and two participating teachers respectively). Data on the teachers’ interrogation and implementation of the designed tasks were obtained via formal and informal interviews. Their reflections informed ongoing adaptations to the task design. Data were analysed in a matrix I designed and via NVivo coding. Findings include both the product of the task design journey (eight music-mathematics lessons, resources, and representations) and the process (ten groupings of Obstacle-Resolution Cycles). Three key questions (relating to music-mathematics fidelity; to task simplification for implementation; and to appropriate music-mathematics representation) were used in addressing each Obstacle-Resolution Cycle. Designing tasks to teach the part-whole construct of fractions was relatively straightforward, but designing tasks to teach the fraction as ratio and fraction as measure constructs was more challenging. These constructs could not be conflated by superimposing the music and mathematical linear representations. Aligning them, however, allowed for moving flexibly between the constructs. The teachers reported that the integrated music-mathematics tasks and supporting resources enhanced their learners’ fractional problem-solving abilities, simultaneously promoting more positive learner dispositions towards mathematics. , Thesis (PhD) -- Faculty of Education, Education, 2023
- Full Text:
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