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 evaluation of the impact of the Rhodes University Master of Education in Mathematics Education Programme in Namibia from the perspectives of its graduates
- Authors: David, Johannes
- Date: 2021-10-29
- Subjects: Master of education degree Namibia , Rhodes University. Department of Education , Mathematics Study and teaching , Critical thinking , Master of education degree Evaluation , Career development Namibia , Educational change Namibia , College students Attitudes
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191942 , vital:45181
- Description: Rhodes University (RU) has been offering a MEdME (Masters in Education, Mathematics Education) degree in Namibia for over 12 years without evaluating its success and impact. This study aimed to evaluate the MEdME programme’s impact on the graduates and on mathematics education in Namibia from the perspectives of its graduates. The study also evaluated the factors that enabled or limited the impact of the programme from the perspective of RU staff members. A three-phased research study was implemented to achieve this. Phase I was a MEdME theses audit to analyze what each graduate researched which then guided the sampling process. Phase II was a distribution of a questionnaire to willing MEdME graduates to elicit their views about the programme's impact. In Phase III, selected graduates were interviewed to follow up on the questionnaire. The RU academic staff members were also interviewed about the programme's design and rationale, as well as their perspectives on its impact on graduates' professional lives. The study found that graduates believed that the programme made them more critical reflexive practitioners (CRPs) who: are now self-introspective, can reflect in context and are competent researchers. This is a sign of the programme attaining its objectives of developing and growing CRPs and graduates, who have advanced in their fields, including their ability to do research. The programme also created opportunities for graduates to study further and/or publish papers. The programme further opened up opportunities for graduates’ promotion into positions of influence in the Ministry of Education where they can positively impact on mathematics education transformation in Namibia (METN). The graduates consequently noticed improvements in some areas but they also noticed room for improvement in other areas of mathematics education in Namibia. This study therefore suggests that more mathematics teachers study further, improve their research capacity and contribute more to METN. The study also suggests a national campaign to increase mathematics teachers' content knowledge. Furthermore, the programme should reintroduce coursework to address students’ subject content knowledge. RU is also advised to explore offering a Professional MEd in Namibia for students who want to focus more on improving their mathematics content knowledge. It is also proposed that Namibia establish a research bank where researchers can upload their theses for wider dissemination. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: David, Johannes
- Date: 2021-10-29
- Subjects: Master of education degree Namibia , Rhodes University. Department of Education , Mathematics Study and teaching , Critical thinking , Master of education degree Evaluation , Career development Namibia , Educational change Namibia , College students Attitudes
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191942 , vital:45181
- Description: Rhodes University (RU) has been offering a MEdME (Masters in Education, Mathematics Education) degree in Namibia for over 12 years without evaluating its success and impact. This study aimed to evaluate the MEdME programme’s impact on the graduates and on mathematics education in Namibia from the perspectives of its graduates. The study also evaluated the factors that enabled or limited the impact of the programme from the perspective of RU staff members. A three-phased research study was implemented to achieve this. Phase I was a MEdME theses audit to analyze what each graduate researched which then guided the sampling process. Phase II was a distribution of a questionnaire to willing MEdME graduates to elicit their views about the programme's impact. In Phase III, selected graduates were interviewed to follow up on the questionnaire. The RU academic staff members were also interviewed about the programme's design and rationale, as well as their perspectives on its impact on graduates' professional lives. The study found that graduates believed that the programme made them more critical reflexive practitioners (CRPs) who: are now self-introspective, can reflect in context and are competent researchers. This is a sign of the programme attaining its objectives of developing and growing CRPs and graduates, who have advanced in their fields, including their ability to do research. The programme also created opportunities for graduates to study further and/or publish papers. The programme further opened up opportunities for graduates’ promotion into positions of influence in the Ministry of Education where they can positively impact on mathematics education transformation in Namibia (METN). The graduates consequently noticed improvements in some areas but they also noticed room for improvement in other areas of mathematics education in Namibia. This study therefore suggests that more mathematics teachers study further, improve their research capacity and contribute more to METN. The study also suggests a national campaign to increase mathematics teachers' content knowledge. Furthermore, the programme should reintroduce coursework to address students’ subject content knowledge. RU is also advised to explore offering a Professional MEd in Namibia for students who want to focus more on improving their mathematics content knowledge. It is also proposed that Namibia establish a research bank where researchers can upload their theses for wider dissemination. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
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