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:
- Date Issued: 2023-03-29
- 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:
- Date Issued: 2023-03-29
An investigation into the use of traditional Xhosa dance to teach mathematics: a case study in a Grade 7 class
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
- Full Text:
- Date Issued: 2012
- Authors: Mbusi, Nokwanda Princess
- Date: 2012
- Subjects: Mathematics -- Study and teaching (Primary) Teaching -- Aids and devices -- Research Xhosa (African people) -- Music Education, Primary -- South Africa -- Eastern Cape , Music in mathematics education
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1617 , http://hdl.handle.net/10962/d1003499
- Description: This study seeks to explore mathematical concepts embedded in traditional Xhosa dance and how these concepts can be incorporated into a learning programme for the teaching and learning of mathematics. The study seeks to gain insight into whether learners could benefit from the implementation of such a learning programme. Learners from a Grade 7 class in a rural school performed traditional Xhosa dances and their performances were captured through video recording. The video recordings were then observed and analysed to determine the mathematical concepts embedded in the dances. These concepts were then linked to those found in the Grade 7 mathematics curriculum. A learning programme integrating mathematical concepts from the dance activities with mathematical concepts from the Grade 7 curriculum was then designed. The learning programme contained mathematical problem solving activities that required learners to re-enact the dance performances in order to find the required solutions. The learning programme was then implemented with the learners over a period of three weeks. During the implementation, learners’ behaviour towards the learning experience was observed, their engagement with the problem solving activities as well as their strategies for solving the problems, were carefully observed. Also, their interactions with each other were noted. After the implementation of the learning programme, focus group interviews were held with learners to determine their opinions, attitudes and feelings about their experience of learning mathematics through traditional Xhosa dance. Key findings indicated that traditional Xhosa dance can be used as a medium for learning many concepts in the mathematics curriculum; the use of the dance gave learners an opportunity to learn mathematics from a familiar context and to participate actively and collaboratively in their learning. Also, it emerged that the use of dance to teach mathematics had potential to help improve learners’ attitudes towards mathematics. Conclusions were reached that the dance had potential for use as a means for the meaningful learning of mathematics. However, limitations and challenges with the study were identified, such as its limited replicability in other mathematics classrooms.
- Full Text:
- Date Issued: 2012
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