Visual representations of linear algebraic expressions: a case study in a Grade 9 after-school mathematics club
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Herbert, Sindisiwe
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/424019 , vital:72116
- Description: Visualisation is commonly used as a tool in introducing algebra through visual or kinaesthetic sequences designed to prompt learners' development of a general rule for moving from a term's position to its output value. Fluency in both the concepts and the conventions of elementary algebra are essential to learners, as algebra forms the language in which many advanced mathematical ideas are encoded. Moreover, algebraic fluency is often associated with an ability to think abstractly about arithmetic processes. In many classrooms, however, research has shown that learners often focus on fluency in algebraic conventions rather than concepts, learning how to manipulate expressions without understanding the algorithms they are taught to follow. This trend can be linked to several causes, including teacher-centred mathematics classrooms in which learners are – whether implicitly or explicitly – encouraged to copy formulae and methods in order to ‘get it right in a test’ without necessarily grasping the underlying logical relationships. This case study, therefore, aimed to determine whether there was value in using visual, kinaesthetic models to broaden and deepen learners' use of algebra. To that end, in the context of an extra-curricular mathematics club that aimed to decentre the teachers and demand innovative ideas of the participants, six pairs of Grade 9 learners were tasked with creating visual representations of a linear algebraic expression using coloured building cubes. The responses to this task over the course of five assignments were many and varied and almost universally displayed a sustained internal logic that the learners were able to explain and develop. Most pairs began with a visual list of terms arranged in sets of towers, pyramids or, in one case, a spiral. At the end of the study, all but one of the pairs had settled on a Visual Expression, in which various colours were used to represent elements of the algebra such as the values of the coefficient, the variable and the constant term. The participants' representations grew in complexity over the course of the study and the conformity of the final responses showed that the club was a collaborative space in which learners shared ideas. However, the structure of the Visual Expressions and their own confessions of nerves about ‘getting it wrong’ in the interviews suggest that the participants were stuck in a mindset that led them to seek out and idealise the representation closest to the original algebra, even though that representation revealed little about the structural relationship underlying the expression. , Thesis (MEd) -- Faculty of Education, Secondary and Post-School Education, 2023
- Full Text:
- Date Issued: 2023-10-13
Year-end oversight in Local Government: a case study of water and sanitation service delivery at Amathole District Municipality
- Authors: Seoke, Duncan
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/425206 , vital:72219
- Description: Poor service delivery is a challenge that has continued to plague the constitutional democracy of South Africa. Legislation has, in response, been passed to ensure efficient service delivery. Despite this legislation, municipal service delivery has been alarmingly poor, and reports on municipal performance and newspaper articles have corroborated this. On the causes of poor service delivery, the existing literature appears to have focused on financial mismanagement, corruption, and the incapacity of officials. Absent from existing literature are discussions on how municipal service delivery is affected by the lack of interrelatedness between municipal public resource management processes (such as revenue collection, expenditure management and oversight). This dissertation addresses this gap by examining the municipal public resource management processes from an oversight perspective. The study sought to analyse the effectiveness of year-end oversight at Amathole District Municipality (ADM) over water and sanitation services. This research aimed to study the year-end oversight over service delivery with reference to the Municipal Public Resource Management (MPRM) model. According to the model, effective service delivery includes inter alia effective oversight, as oversight forms part of the entire system of the municipal resource management cycle. Thus, for the MPRM model, oversight should be exercised on all these processes. The research was a desktop analysis that used both a qualitative and quantitative research methodology. The primary document analysed was the ADM Oversight Report (OR). This report is produced by the Municipal Public Accounts Committee (MPAC) and reflects the year-end oversight conducted by the MPAC on the municipality's activities. In the analysis of the OR, it was concluded that the ADM MPAC had failed to conduct effective year-end oversight of W&S services. The efficacy of the ADM MPAC's year-end oversight was measured against guidelines for effective year-end oversight from the National Treasury and the MPRM model. The findings suggested that there were inefficiencies in the manner that the ADM MPAC exercised its year-end oversight. , Thesis (MA) -- Faculty of Humanities, Sociology, 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Seoke, Duncan
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/425206 , vital:72219
- Description: Poor service delivery is a challenge that has continued to plague the constitutional democracy of South Africa. Legislation has, in response, been passed to ensure efficient service delivery. Despite this legislation, municipal service delivery has been alarmingly poor, and reports on municipal performance and newspaper articles have corroborated this. On the causes of poor service delivery, the existing literature appears to have focused on financial mismanagement, corruption, and the incapacity of officials. Absent from existing literature are discussions on how municipal service delivery is affected by the lack of interrelatedness between municipal public resource management processes (such as revenue collection, expenditure management and oversight). This dissertation addresses this gap by examining the municipal public resource management processes from an oversight perspective. The study sought to analyse the effectiveness of year-end oversight at Amathole District Municipality (ADM) over water and sanitation services. This research aimed to study the year-end oversight over service delivery with reference to the Municipal Public Resource Management (MPRM) model. According to the model, effective service delivery includes inter alia effective oversight, as oversight forms part of the entire system of the municipal resource management cycle. Thus, for the MPRM model, oversight should be exercised on all these processes. The research was a desktop analysis that used both a qualitative and quantitative research methodology. The primary document analysed was the ADM Oversight Report (OR). This report is produced by the Municipal Public Accounts Committee (MPAC) and reflects the year-end oversight conducted by the MPAC on the municipality's activities. In the analysis of the OR, it was concluded that the ADM MPAC had failed to conduct effective year-end oversight of W&S services. The efficacy of the ADM MPAC's year-end oversight was measured against guidelines for effective year-end oversight from the National Treasury and the MPRM model. The findings suggested that there were inefficiencies in the manner that the ADM MPAC exercised its year-end oversight. , Thesis (MA) -- Faculty of Humanities, Sociology, 2023
- Full Text:
- Date Issued: 2023-10-13
“Rwanda cannot be exorcised”: representations of the trauma of the Rwandan Genocide in selected films and novels
- Authors: Jennings, Kathleen
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/425067 , vital:72206
- Description: Although the Rwandan genocide (itsembabwoko in Kinyarwanda) has often been compared with the Holocaust, in terms of literary and cinematic narratives it has been largely underrepresented, with the notable exception of the release of the films Hotel Rwanda (2004) and Sometimes in April (2005), as well as novels such as Gil Courtemanche’s A Sunday at the Pool in Kigali (2003). However, although there is now a larger oeuvre of works on the subject, they are often not widely known or disseminated beyond their countries of origin. Of even greater concern is the fact that most cinematic narratives on itsembabwoko rely on Western narrative structures in their approach to storytelling. As a result, trauma in these narratives largely tends to focus on the experiences of Western protagonists or on Rwandan protagonists from a Western point of view. This tendency can be tied to the use of Western trauma theory in exploring the effects of the genocide on its witnesses and survivors, at the expense of arguably more relevant postcolonial trauma theory. This presents a problem in theorising the trauma of itsembabwoko, which occurred in a highly specific historical context involving the processes of colonization and decolonization, and in which the difficulties in unifying a population which had been split along socio-economic lines since pre-colonial times remained unresolved. Despite its shortcomings in the postcolonial African context, it would be a mistake to dismiss Yale trauma theory entirely, however, since theorists such as Cathy Caruth still provide valuable insights into the effects of trauma on both the individual and the collective. As a result, I have sought to find commonalities between the two schools of thought, so as to create a more nuanced view of itsembabwoko, its repercussions and the violence preceding it. In writing this thesis, I have selected mostly Rwandan authors, often survivors of the genocide, whose works provide an alternative view of Rwanda’s violent history to that presented in the works mentioned above. Given that the majority of the texts I focus on have been released more recently – mostly the mid-2010s – and are less well-known than their Western counterparts, they provide the opportunity to compare first-hand accounts with those that can only partially recreate the terror of anti-Tutsi violence in Rwanda. My analysis hopefully provides a new perspective on the dominant narratives which have shaped the way in which non-Rwandan (predominantly Western) audiences understand the genocide. The overall aim of this thesis, then, is to demonstrate the importance of placing the genocide and its resultant trauma in a broader historical context, with a view to establishing that it is shortsighted to ignore the impact of pre- and post-genocide trauma on the Rwandan people when discussing itsembabwoko. Though this has been achieved in socio-historical studies, such as Mahmood Mamdani’s When Victims Become Killers: Colonialism, Nativism, and the Genocide in Rwanda, very little has been produced on literary and cinematic representations of the genocide. , Thesis (MA) -- Faculty of Humanities, Literary Studies in English 2023
- Full Text:
- Date Issued: 2023-10-13
- Authors: Jennings, Kathleen
- Date: 2023-10-13
- Subjects: Uncatalogued
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/425067 , vital:72206
- Description: Although the Rwandan genocide (itsembabwoko in Kinyarwanda) has often been compared with the Holocaust, in terms of literary and cinematic narratives it has been largely underrepresented, with the notable exception of the release of the films Hotel Rwanda (2004) and Sometimes in April (2005), as well as novels such as Gil Courtemanche’s A Sunday at the Pool in Kigali (2003). However, although there is now a larger oeuvre of works on the subject, they are often not widely known or disseminated beyond their countries of origin. Of even greater concern is the fact that most cinematic narratives on itsembabwoko rely on Western narrative structures in their approach to storytelling. As a result, trauma in these narratives largely tends to focus on the experiences of Western protagonists or on Rwandan protagonists from a Western point of view. This tendency can be tied to the use of Western trauma theory in exploring the effects of the genocide on its witnesses and survivors, at the expense of arguably more relevant postcolonial trauma theory. This presents a problem in theorising the trauma of itsembabwoko, which occurred in a highly specific historical context involving the processes of colonization and decolonization, and in which the difficulties in unifying a population which had been split along socio-economic lines since pre-colonial times remained unresolved. Despite its shortcomings in the postcolonial African context, it would be a mistake to dismiss Yale trauma theory entirely, however, since theorists such as Cathy Caruth still provide valuable insights into the effects of trauma on both the individual and the collective. As a result, I have sought to find commonalities between the two schools of thought, so as to create a more nuanced view of itsembabwoko, its repercussions and the violence preceding it. In writing this thesis, I have selected mostly Rwandan authors, often survivors of the genocide, whose works provide an alternative view of Rwanda’s violent history to that presented in the works mentioned above. Given that the majority of the texts I focus on have been released more recently – mostly the mid-2010s – and are less well-known than their Western counterparts, they provide the opportunity to compare first-hand accounts with those that can only partially recreate the terror of anti-Tutsi violence in Rwanda. My analysis hopefully provides a new perspective on the dominant narratives which have shaped the way in which non-Rwandan (predominantly Western) audiences understand the genocide. The overall aim of this thesis, then, is to demonstrate the importance of placing the genocide and its resultant trauma in a broader historical context, with a view to establishing that it is shortsighted to ignore the impact of pre- and post-genocide trauma on the Rwandan people when discussing itsembabwoko. Though this has been achieved in socio-historical studies, such as Mahmood Mamdani’s When Victims Become Killers: Colonialism, Nativism, and the Genocide in Rwanda, very little has been produced on literary and cinematic representations of the genocide. , Thesis (MA) -- Faculty of Humanities, Literary Studies in English 2023
- Full Text:
- Date Issued: 2023-10-13