Examining mathematical reasoning through enacted visualisation
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
Investigating mathematical proficiency testing in Namibian school high stakes mathematics examinations: an exploratory study
- Authors: Ndjendja, Elizabeth
- Date: 2019
- Subjects: Education and state -- Namibia , Educational tests and measurements -- Namibia , Mathematics -- Curricula -- Namibia , Mathematics -- Study and teaching -- Namibia , Namibia. Ministry of Education -- Examinations
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/92887 , vital:30759
- Description: The Namibian government has put processes in place to continuously improve its education system in line with educational development in the world. The education reform efforts are administered and coordinated by the Ministry of Education, Arts and Culture. At the centre of these reform efforts are curriculum policy documents and subject syllabuses with the intention of improving the teaching and learning process in the classrooms. These reform efforts appears to overlook the positive influence high stakes assessment has on the teaching and learning process. The study reported in this thesis was designed to investigate the feasibility of assessing separate elements of mathematical proficiency in the high stakes Mathematics assessment in Namibia. The study was designed as a developmental, exploratory research that collected and analysed both qualitative and quantitative data in order to respond to issues raised by five specific research objectives. The data collected enabled the adaptation of some assessment tools in order to distinctly assess selected mathematical proficiency categories. The results further indicated that the envisaged proficiency assessment system could be used to characterise the examination question papers and revealed insights into the conceptualisation of the current assessment system. The results further indicated the visible distinguishability of different elements of proficiency through the developed tools and the learners’ responses to the NSSCO examination. Finally, constrains and affordance which the original assessment system has in relation to the developed system were revealed and addressed. In closing, the research suggested changes and possible adaptation of assessment tools to ensure the proper assessment of mathematical proficiency aspects through high stakes assessment. Immerging issues that needed further research were also highlighted.
- Full Text:
- Date Issued: 2019
- Authors: Ndjendja, Elizabeth
- Date: 2019
- Subjects: Education and state -- Namibia , Educational tests and measurements -- Namibia , Mathematics -- Curricula -- Namibia , Mathematics -- Study and teaching -- Namibia , Namibia. Ministry of Education -- Examinations
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/92887 , vital:30759
- Description: The Namibian government has put processes in place to continuously improve its education system in line with educational development in the world. The education reform efforts are administered and coordinated by the Ministry of Education, Arts and Culture. At the centre of these reform efforts are curriculum policy documents and subject syllabuses with the intention of improving the teaching and learning process in the classrooms. These reform efforts appears to overlook the positive influence high stakes assessment has on the teaching and learning process. The study reported in this thesis was designed to investigate the feasibility of assessing separate elements of mathematical proficiency in the high stakes Mathematics assessment in Namibia. The study was designed as a developmental, exploratory research that collected and analysed both qualitative and quantitative data in order to respond to issues raised by five specific research objectives. The data collected enabled the adaptation of some assessment tools in order to distinctly assess selected mathematical proficiency categories. The results further indicated that the envisaged proficiency assessment system could be used to characterise the examination question papers and revealed insights into the conceptualisation of the current assessment system. The results further indicated the visible distinguishability of different elements of proficiency through the developed tools and the learners’ responses to the NSSCO examination. Finally, constrains and affordance which the original assessment system has in relation to the developed system were revealed and addressed. In closing, the research suggested changes and possible adaptation of assessment tools to ensure the proper assessment of mathematical proficiency aspects through high stakes assessment. Immerging issues that needed further research were also highlighted.
- Full Text:
- Date Issued: 2019
An investigation into the nature of mathematical connections selected grade 7 teachers make when teaching fractions : a Namibian case study.
- Authors: Amupolo, Loide M
- Date: 2015
- Subjects: Mathematics -- Study and teaching -- Namibia , Fractions -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2016 , http://hdl.handle.net/10962/d1016374
- Description: The general understanding of mathematics as a subject and its implications is, in reality alarmingly low. Evidence of this is evident in learners’ performance and their reaction towards the subject. Fractions as a domain of Mathematics are no exception. The majority of the learners do not learn Fractions comfortably. The causes of this may be varied. However, it is believed that one way of ensuring meaningful teaching and learning is to make use of appropriate connections. The significance and the important role of the teacher in making mathematical connections in learning for understanding are well documented in the literature. This study focuses on the nature of mathematical connections selected Grade 7 teachers make when teaching Fractions, as well as their perceptions of the importance of making such connections. This qualitative case study was conducted in three schools in the Oshana region. The purpose was to investigate how mathematics teachers make connections in fractions. Underpinned by an interpretive paradigm, the study made use of observations and interviews to generate data. The framework borrowed from Businkas’ (2008) study was used in analysing and coding the nature of connections used in the lessons observed. An individual conversation on the nature and perceptions of the connections made in the observed lessons was undertaken with each teacher followed by a focus group discussion that aimed at analysing deeper perceptions on connections. The main findings of the study revealed that teachers made use of all the different types of connections as per Businkas’s framework. The frequency of occurrence showed that Instruction-Oriented Connection and Multiple Representation connections topped the list of connections used. Teachers pointed out that connections to prior knowledge and making multiple representations were most significant, as they related to learners’ existing knowledge and pointed to different ways of solving a problem. The teachers were, however, not familiar with the other connections identified as this was their first experience of interrogating connections. They, however, agreed on the importance of making those connections. The teachers agreed that meaningful connections indeed helped with their conceptual understanding of Mathematics. They believed that connections can increase learners’ interest in school and help reduce negative views of fractions, in particular, and mathematics in general. However, they felt that the limited number of resources, poor teaching approaches and the inability of creating fraction sense may hinder them from making appropriate connections.
- Full Text:
- Date Issued: 2015
- Authors: Amupolo, Loide M
- Date: 2015
- Subjects: Mathematics -- Study and teaching -- Namibia , Fractions -- Study and teaching -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2016 , http://hdl.handle.net/10962/d1016374
- Description: The general understanding of mathematics as a subject and its implications is, in reality alarmingly low. Evidence of this is evident in learners’ performance and their reaction towards the subject. Fractions as a domain of Mathematics are no exception. The majority of the learners do not learn Fractions comfortably. The causes of this may be varied. However, it is believed that one way of ensuring meaningful teaching and learning is to make use of appropriate connections. The significance and the important role of the teacher in making mathematical connections in learning for understanding are well documented in the literature. This study focuses on the nature of mathematical connections selected Grade 7 teachers make when teaching Fractions, as well as their perceptions of the importance of making such connections. This qualitative case study was conducted in three schools in the Oshana region. The purpose was to investigate how mathematics teachers make connections in fractions. Underpinned by an interpretive paradigm, the study made use of observations and interviews to generate data. The framework borrowed from Businkas’ (2008) study was used in analysing and coding the nature of connections used in the lessons observed. An individual conversation on the nature and perceptions of the connections made in the observed lessons was undertaken with each teacher followed by a focus group discussion that aimed at analysing deeper perceptions on connections. The main findings of the study revealed that teachers made use of all the different types of connections as per Businkas’s framework. The frequency of occurrence showed that Instruction-Oriented Connection and Multiple Representation connections topped the list of connections used. Teachers pointed out that connections to prior knowledge and making multiple representations were most significant, as they related to learners’ existing knowledge and pointed to different ways of solving a problem. The teachers were, however, not familiar with the other connections identified as this was their first experience of interrogating connections. They, however, agreed on the importance of making those connections. The teachers agreed that meaningful connections indeed helped with their conceptual understanding of Mathematics. They believed that connections can increase learners’ interest in school and help reduce negative views of fractions, in particular, and mathematics in general. However, they felt that the limited number of resources, poor teaching approaches and the inability of creating fraction sense may hinder them from making appropriate connections.
- Full Text:
- Date Issued: 2015
- «
- ‹
- 1
- ›
- »