Implementing mathematics intervention strategies to enhance understanding of number sense: an informative framework for the Ekurhuleni North District, Gauteng province, South Africa
- Authors: Hove, Netsai
- Date: 2022-11
- Subjects: Number concept , Mathematics -- Study and teaching
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/26085 , vital:64835
- Description: This study was prompted by the observation that learners’ performance in mathematics is low in South Africa. Several factors such as teachers’ qualifications, demotivated learners, and limited school resources have been raised and considered. Although number sense forms the foundation blocks for mathematics understanding, limited academic work has been done to explore implementable mathematics instructional interventions for the enhancement of understanding number sense. The purpose of this study was to contribute an implementable mathematics intervention framework for understanding number sense. Since the study focused on exploring intervention activities, it was guided by the pragmatism research philosophy. Data were captured from purposive samples of teachers and stratified samples of 1050 learners from schools in the Ekurhuleni North district in South Africa. The research design comprises the following sequence: survey, pre-test, intervention, post-test, and evaluation by teachers’ focus group discussion. These activities were carried out parallel to document analysis, which provided bench marks. The main data-capturing instruments were the questionnaires, learners’ test, interview, and document analysis guides. Factors analysis to establish associations, differences, and regression was carried out using SPSS and Excel. The study found that: almost all teachers implemented some form of mathematics interventions. Continuous assessment was the main intervention, followed by problem-solving, and the use of games (which was least preferred). Teachers shunned games because they require more time and management skills. Challenges that teachers experienced when implementing mathematics interventions include their limited knowledge and the lack of resources and support from education authorities who expect and emphasise high pass rates in mathematics. The teachers’ focus group discussions evaluated the intervention and proposed the following sequence for instructional intervention on number sense: Stage 1: parroting of number names, for example, six, two, nine and seven Stage 2: symbolic identification, for example, the symbol 6, 2, 9 and 7 Stage 3: association where a learner group six stones, shows two fingers, etc. Stage 4: seriating or ordering done through oral counting and use of inequality symbols: () to compare and estimate values in problems Stage 5: the four operations for addition (+), subtraction (-), multiplication (x) and division (÷) emphasizing estimation and application. The study recommends the adoption, modification and implementation of mathematics intervention framework to enhance number sense. , Thesis (MEd) -- Faculty of Education, 2022
- Full Text:
- Authors: Hove, Netsai
- Date: 2022-11
- Subjects: Number concept , Mathematics -- Study and teaching
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/26085 , vital:64835
- Description: This study was prompted by the observation that learners’ performance in mathematics is low in South Africa. Several factors such as teachers’ qualifications, demotivated learners, and limited school resources have been raised and considered. Although number sense forms the foundation blocks for mathematics understanding, limited academic work has been done to explore implementable mathematics instructional interventions for the enhancement of understanding number sense. The purpose of this study was to contribute an implementable mathematics intervention framework for understanding number sense. Since the study focused on exploring intervention activities, it was guided by the pragmatism research philosophy. Data were captured from purposive samples of teachers and stratified samples of 1050 learners from schools in the Ekurhuleni North district in South Africa. The research design comprises the following sequence: survey, pre-test, intervention, post-test, and evaluation by teachers’ focus group discussion. These activities were carried out parallel to document analysis, which provided bench marks. The main data-capturing instruments were the questionnaires, learners’ test, interview, and document analysis guides. Factors analysis to establish associations, differences, and regression was carried out using SPSS and Excel. The study found that: almost all teachers implemented some form of mathematics interventions. Continuous assessment was the main intervention, followed by problem-solving, and the use of games (which was least preferred). Teachers shunned games because they require more time and management skills. Challenges that teachers experienced when implementing mathematics interventions include their limited knowledge and the lack of resources and support from education authorities who expect and emphasise high pass rates in mathematics. The teachers’ focus group discussions evaluated the intervention and proposed the following sequence for instructional intervention on number sense: Stage 1: parroting of number names, for example, six, two, nine and seven Stage 2: symbolic identification, for example, the symbol 6, 2, 9 and 7 Stage 3: association where a learner group six stones, shows two fingers, etc. Stage 4: seriating or ordering done through oral counting and use of inequality symbols: () to compare and estimate values in problems Stage 5: the four operations for addition (+), subtraction (-), multiplication (x) and division (÷) emphasizing estimation and application. The study recommends the adoption, modification and implementation of mathematics intervention framework to enhance number sense. , Thesis (MEd) -- Faculty of Education, 2022
- Full Text:
Democratic citizenship in mathematics teachers’ preparation in South African Universities
- Olawale, Babawande Emmanuel https://orcid.org/ 0000-0001-5265-1583
- Authors: Olawale, Babawande Emmanuel https://orcid.org/ 0000-0001-5265-1583
- Date: 2021-02
- Subjects: Citizenship -- Study and teaching , Authoritarianism , Mathematics -- Study and teaching
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/20079 , vital:45107
- Description: Promoting a clearer understanding of the role of schools in developing democratic dispositions among young citizens is a matter of importance across the world. This is because school is believed to be the best place where future free and democratic citizens can be prepared. Similarly, it is a place where young people are equipped with the necessary skills and knowledge that will assist them in deliberating democratically, developing a better understanding of political structures and economic and world history, and learning the relevant numeracy, literacy and critical thinking skills. Unfortunately, current teacher education programmes appear to represent potential stumbling blocks to schooling playing a greater role in educating the youth for democracy and democratic citizenship. This study explored two contradictory theoretical roles for mathematics teacher education programmes, in relation to power and control in education and society. The first is that, in reality, mathematics teacher education is essentially re-productive, in that its authoritarian relationship does not encourage confrontational discussion or critique, or challenge existing and dominant practices. The second is that, in a world where democracy is increasingly becoming a global phenomenon central to development, teacher education is (or should be) essentially democratic in nature. Thus, underpinned by the interpretivist paradigm, this study employed a qualitative research approach. It also utilised a case study design as a strategy for data collection, in order to explore how the mathematics teacher education programmes in South African universities prepare learners for democratic citizenship. As such, three universities in two provinces in South Africa participated in the study, and data were collected through interviews, observation and document reviews. At each institution, interviews were carried out with mathematics teacher educators and pre-service mathematics student teachers in their second to fourth year of study. Similarly, observations took place in different teaching sessions at each institution, and in different formats. Relevant documents were also reviewed for the study. The research findings revealed that the concepts of democracy and democratic citizenship are multifaceted. The participants’ understanding of these concepts was influenced by their individual expectations, as well as their social, political and economic environments, among many other factors. In addition, it was evident that mathematics teacher education programmes play a significant role in developing socially active citizens and democratic mathematics teachers. The research findings revealed, however, that contradictions exist between pedagogical approaches that are capable of developing democratic citizens, mathematics teacher educators’ ideal image of their practices within the classroom, and the participants’ conception of mathematics. As a result, no engagement occurs in social and critical pedagogy within mathematics education classrooms, to allow learners to view mathematics as a tool for confronting issues of justice and inequality in their community and the world at large. The research findings also revealed that the practices of the main structures which are tasked with the responsibility of promoting democratic practices within higher education institutions seem ineffective, as a result of favouritism and an autocratic approach to decision making. Based on the research findings, a recommendation is made that mathematics educators democratise their classrooms, in order to develop democratic citizens who are committed to democratic principles. Another recommendation is that, in their mathematics classrooms, educators use a problem-posing pedagogical approach which is capable of challenging power structures, thereby empowering learners as users of mathematics. This will not be possible without a professional development programme guiding mathematics teacher educators in establishing and managing their democratic classrooms. Similarly, it is recommended that student representative councils, as the structures that are best known for supporting democratic citizenship at universities, strive to follow the basic principles of democratic governance. Finally, the researcher concluded that mathematics education and the task of preparing mathematics student teachers for democratic citizenship are of the utmost importance, if South Africans are to cultivate and maintain a democracy that contributes to a culture which fundamentally supports democratic principles. , Thesis (PhD) -- Faculty of Education, 2021
- Full Text:
- Authors: Olawale, Babawande Emmanuel https://orcid.org/ 0000-0001-5265-1583
- Date: 2021-02
- Subjects: Citizenship -- Study and teaching , Authoritarianism , Mathematics -- Study and teaching
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10353/20079 , vital:45107
- Description: Promoting a clearer understanding of the role of schools in developing democratic dispositions among young citizens is a matter of importance across the world. This is because school is believed to be the best place where future free and democratic citizens can be prepared. Similarly, it is a place where young people are equipped with the necessary skills and knowledge that will assist them in deliberating democratically, developing a better understanding of political structures and economic and world history, and learning the relevant numeracy, literacy and critical thinking skills. Unfortunately, current teacher education programmes appear to represent potential stumbling blocks to schooling playing a greater role in educating the youth for democracy and democratic citizenship. This study explored two contradictory theoretical roles for mathematics teacher education programmes, in relation to power and control in education and society. The first is that, in reality, mathematics teacher education is essentially re-productive, in that its authoritarian relationship does not encourage confrontational discussion or critique, or challenge existing and dominant practices. The second is that, in a world where democracy is increasingly becoming a global phenomenon central to development, teacher education is (or should be) essentially democratic in nature. Thus, underpinned by the interpretivist paradigm, this study employed a qualitative research approach. It also utilised a case study design as a strategy for data collection, in order to explore how the mathematics teacher education programmes in South African universities prepare learners for democratic citizenship. As such, three universities in two provinces in South Africa participated in the study, and data were collected through interviews, observation and document reviews. At each institution, interviews were carried out with mathematics teacher educators and pre-service mathematics student teachers in their second to fourth year of study. Similarly, observations took place in different teaching sessions at each institution, and in different formats. Relevant documents were also reviewed for the study. The research findings revealed that the concepts of democracy and democratic citizenship are multifaceted. The participants’ understanding of these concepts was influenced by their individual expectations, as well as their social, political and economic environments, among many other factors. In addition, it was evident that mathematics teacher education programmes play a significant role in developing socially active citizens and democratic mathematics teachers. The research findings revealed, however, that contradictions exist between pedagogical approaches that are capable of developing democratic citizens, mathematics teacher educators’ ideal image of their practices within the classroom, and the participants’ conception of mathematics. As a result, no engagement occurs in social and critical pedagogy within mathematics education classrooms, to allow learners to view mathematics as a tool for confronting issues of justice and inequality in their community and the world at large. The research findings also revealed that the practices of the main structures which are tasked with the responsibility of promoting democratic practices within higher education institutions seem ineffective, as a result of favouritism and an autocratic approach to decision making. Based on the research findings, a recommendation is made that mathematics educators democratise their classrooms, in order to develop democratic citizens who are committed to democratic principles. Another recommendation is that, in their mathematics classrooms, educators use a problem-posing pedagogical approach which is capable of challenging power structures, thereby empowering learners as users of mathematics. This will not be possible without a professional development programme guiding mathematics teacher educators in establishing and managing their democratic classrooms. Similarly, it is recommended that student representative councils, as the structures that are best known for supporting democratic citizenship at universities, strive to follow the basic principles of democratic governance. Finally, the researcher concluded that mathematics education and the task of preparing mathematics student teachers for democratic citizenship are of the utmost importance, if South Africans are to cultivate and maintain a democracy that contributes to a culture which fundamentally supports democratic principles. , Thesis (PhD) -- Faculty of Education, 2021
- Full Text:
Factors affecting grade 6 learners’ performance in Mathematics in the East London Education District
- Authors: Kwateng, Jesse
- Date: 2019
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10353/15935 , vital:40565
- Description: Mathematics is one of the most important subjects rooted in many fields of study but has also been one of the greatest challenges for learners in every country, most especially in the Republic of South Africa. There have been attempts to curb the challenges that have bedeviled the success of mathematics education by governments, the Department of Education and many other stakeholders who have not enjoyed positive results in mathematics in the district of East London. Therefore, this study examines factors affecting grade 6 learners’ performance in mathematics in selected schools within the East London education district. There were three hundred and forty-five (345) grade 6 learners and 12 teachers drawn through a parallel mixed methods sampling. Stratified random sampling was used to select participants for the quantitative strand while purposive sampling was used for selecting 60 learners and 12 teachers for the qualitative strand. The researcher used the mixed method research approach. The instruments used in collecting data were structured questionnaire and semi-structured interviews to elicit information from grade 6 learners and teachers. Information gathered from the learners and teachers included: biographical information, factors affecting teaching and learning of mathematics and suggestions. The quantitative data were analyzed by using descriptive statistics of percentage from the responses of learners. The quantitative analysis was done by using excel 2010 to formulate data into percentages and qualitatively, voice recordings from the respondents semi-structured interviews were reduced through thematic analysis. The findings of the study revealed that some of the qualified mathematics educators preferred to work in another profession. Quality of teaching and learning were less effective due to overcrowded classrooms, inadequate teaching and learning resources, poor monitoring of educators, some of the learners were not adequately motivated and many others. For performance in mathematics to improve in the primary schools in East London Education District, the study made some recommendations from the findings to the stakeholders in education such as the Department of Education, principals, the government, educators and learners. These recommendations might virtually assist in finding lasting solutions to grade 6 learners with mathematics challenges.
- Full Text:
Factors affecting grade 6 learners’ performance in Mathematics in the East London Education District
- Authors: Kwateng, Jesse
- Date: 2019
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10353/15935 , vital:40565
- Description: Mathematics is one of the most important subjects rooted in many fields of study but has also been one of the greatest challenges for learners in every country, most especially in the Republic of South Africa. There have been attempts to curb the challenges that have bedeviled the success of mathematics education by governments, the Department of Education and many other stakeholders who have not enjoyed positive results in mathematics in the district of East London. Therefore, this study examines factors affecting grade 6 learners’ performance in mathematics in selected schools within the East London education district. There were three hundred and forty-five (345) grade 6 learners and 12 teachers drawn through a parallel mixed methods sampling. Stratified random sampling was used to select participants for the quantitative strand while purposive sampling was used for selecting 60 learners and 12 teachers for the qualitative strand. The researcher used the mixed method research approach. The instruments used in collecting data were structured questionnaire and semi-structured interviews to elicit information from grade 6 learners and teachers. Information gathered from the learners and teachers included: biographical information, factors affecting teaching and learning of mathematics and suggestions. The quantitative data were analyzed by using descriptive statistics of percentage from the responses of learners. The quantitative analysis was done by using excel 2010 to formulate data into percentages and qualitatively, voice recordings from the respondents semi-structured interviews were reduced through thematic analysis. The findings of the study revealed that some of the qualified mathematics educators preferred to work in another profession. Quality of teaching and learning were less effective due to overcrowded classrooms, inadequate teaching and learning resources, poor monitoring of educators, some of the learners were not adequately motivated and many others. For performance in mathematics to improve in the primary schools in East London Education District, the study made some recommendations from the findings to the stakeholders in education such as the Department of Education, principals, the government, educators and learners. These recommendations might virtually assist in finding lasting solutions to grade 6 learners with mathematics challenges.
- Full Text:
Pre-service education students’ application of visualisation strategies to solve mathematical word-problems
- Authors: Shaw , Peter
- Date: 2018
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: http://hdl.handle.net/10353/12941 , vital:39406
- Description: This classroom-based action research dissertation examined visualisation strategies used by pre-service Intermediate Phase PGCE education students to solve mathematical word-problems. The setting was an Eastern Cape university. Previous literature indicated a positive correlation between the use of visual scaffolds and success in solving word problems. However, a gap was found insofar as little research had been published on the application of visualisation to word-problems by student teachers in South Africa. This thesis advances our understanding of the role visualisation may play in assisting student teachers to solve word-problems. The theoretic framework was informed by Bruner’s theory of learning. The research was grounded in the hermeneutic tradition. An interpretivist research paradigm was expedited by using an inductive, naturalistic perspective and relativist ontology. Thirtyeight student-teachers participated in the study. Parallel and convergent qualitative and quantitative data gathering instruments were used, thereby facilitating triangulation and examination for microgenesis. It was found that vestiges of past teaching practices initially limited the participants’ knowledge to a deeply-flawed, banking model of routines and an instrumental perception of mathematics. Disruptive calls for social justice impeded progress. Albeit visualisation strategies liberated understanding, many foundational concepts and skills had to be reconstructed. The confluence of time and rehearsal culminated in some measure of expertise. Sustained effort enabled new knowledge to be compressed and consigned to long-term memory. Salient visual representations assisted participants to conceptualise relational mathematical metaconcepts and reduced the cognitive demands imposed by word-problems but that achievement was a hard-won prize.
- Full Text:
- Authors: Shaw , Peter
- Date: 2018
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: http://hdl.handle.net/10353/12941 , vital:39406
- Description: This classroom-based action research dissertation examined visualisation strategies used by pre-service Intermediate Phase PGCE education students to solve mathematical word-problems. The setting was an Eastern Cape university. Previous literature indicated a positive correlation between the use of visual scaffolds and success in solving word problems. However, a gap was found insofar as little research had been published on the application of visualisation to word-problems by student teachers in South Africa. This thesis advances our understanding of the role visualisation may play in assisting student teachers to solve word-problems. The theoretic framework was informed by Bruner’s theory of learning. The research was grounded in the hermeneutic tradition. An interpretivist research paradigm was expedited by using an inductive, naturalistic perspective and relativist ontology. Thirtyeight student-teachers participated in the study. Parallel and convergent qualitative and quantitative data gathering instruments were used, thereby facilitating triangulation and examination for microgenesis. It was found that vestiges of past teaching practices initially limited the participants’ knowledge to a deeply-flawed, banking model of routines and an instrumental perception of mathematics. Disruptive calls for social justice impeded progress. Albeit visualisation strategies liberated understanding, many foundational concepts and skills had to be reconstructed. The confluence of time and rehearsal culminated in some measure of expertise. Sustained effort enabled new knowledge to be compressed and consigned to long-term memory. Salient visual representations assisted participants to conceptualise relational mathematical metaconcepts and reduced the cognitive demands imposed by word-problems but that achievement was a hard-won prize.
- Full Text:
The use of Blackboard as a tool for the teaching and assessment of large classes in mathematics education: a case study of second year level Bachelor of Education students in one university in South Africa
- Authors: Riley, Alanna
- Date: 2013
- Subjects: Blackboards , Blackboard drawing , Mathematics -- Study and teaching , College students , Educational change , Information technology , Teaching -- Aids and devices , College teaching , Assessment , Blended learning
- Language: English
- Type: Thesis , Masters , M Ed
- Identifier: vital:16182 , http://hdl.handle.net/10353/d1006237 , Blackboards , Blackboard drawing , Mathematics -- Study and teaching , College students , Educational change , Information technology , Teaching -- Aids and devices , College teaching , Assessment , Blended learning
- Description: This study locates the Blackboard Learning Management System as a Technology Enhanced Learning tool within the bounds of the discipline of eLearning and aimed to interrogate the use of Blackboard for the purposes of teaching, learning and assessment in large classes. It is evident from the literature reviewed that changes in both Higher Education in the South Africa with regards to policy and legislation in addition to international shifts towards increased access and participation in a fast paced, ever-evolving knowledge-based economy, providing the context for this work. The theoretical framework for this study is not unidimensional due to the fact that the educational field of eLearning as an area of specialisation draws on a multitude of theories in terms of their utility value for instructional design of courses utilising Information and Communications Technology as a mode of delivery. This study was conducted within the bounds of an interpretivist paradigm as the researcher sought to focus on the use of Blackboard and the experiences of the lecturers and students involved in the implementation thereof. The research design for this study took the form of a case study and a multiple case method was employed. The researcher collected data through personal interviews conducted with participating lecturers, while student data was collected by means of a qualitative survey which was conducted through the Blackboard Learning Management System. The data was analyzed by means of a thematic analysis, consistent with the interpretive paradigm chosen for this study. The findings of this study revealed that Blackboard was utilised effectively in order to facilitate communication, access to course resources and promoted more efficient assessment processes. The implementation was however not without challenges many of which were systemic and focused on the lack of resources available to the students. The implications of using Blackboard for teaching and assessment of large classes include the use of the Learning Management System as part of a multimodal method of course delivery in an effort to reach the multitude of registered students both conceptually as well as electronically. The recommendations arising from this study include consideration on the part of the faculty for a unified approach in the use of Blackboard for communication as well as deployment of resources. Additionally, this study may form the foundation of further studies in this field, with a focus on the active engagement and training of lecturers in order to integrate traditional teaching methods with blended learning opportunities.
- Full Text:
- Authors: Riley, Alanna
- Date: 2013
- Subjects: Blackboards , Blackboard drawing , Mathematics -- Study and teaching , College students , Educational change , Information technology , Teaching -- Aids and devices , College teaching , Assessment , Blended learning
- Language: English
- Type: Thesis , Masters , M Ed
- Identifier: vital:16182 , http://hdl.handle.net/10353/d1006237 , Blackboards , Blackboard drawing , Mathematics -- Study and teaching , College students , Educational change , Information technology , Teaching -- Aids and devices , College teaching , Assessment , Blended learning
- Description: This study locates the Blackboard Learning Management System as a Technology Enhanced Learning tool within the bounds of the discipline of eLearning and aimed to interrogate the use of Blackboard for the purposes of teaching, learning and assessment in large classes. It is evident from the literature reviewed that changes in both Higher Education in the South Africa with regards to policy and legislation in addition to international shifts towards increased access and participation in a fast paced, ever-evolving knowledge-based economy, providing the context for this work. The theoretical framework for this study is not unidimensional due to the fact that the educational field of eLearning as an area of specialisation draws on a multitude of theories in terms of their utility value for instructional design of courses utilising Information and Communications Technology as a mode of delivery. This study was conducted within the bounds of an interpretivist paradigm as the researcher sought to focus on the use of Blackboard and the experiences of the lecturers and students involved in the implementation thereof. The research design for this study took the form of a case study and a multiple case method was employed. The researcher collected data through personal interviews conducted with participating lecturers, while student data was collected by means of a qualitative survey which was conducted through the Blackboard Learning Management System. The data was analyzed by means of a thematic analysis, consistent with the interpretive paradigm chosen for this study. The findings of this study revealed that Blackboard was utilised effectively in order to facilitate communication, access to course resources and promoted more efficient assessment processes. The implementation was however not without challenges many of which were systemic and focused on the lack of resources available to the students. The implications of using Blackboard for teaching and assessment of large classes include the use of the Learning Management System as part of a multimodal method of course delivery in an effort to reach the multitude of registered students both conceptually as well as electronically. The recommendations arising from this study include consideration on the part of the faculty for a unified approach in the use of Blackboard for communication as well as deployment of resources. Additionally, this study may form the foundation of further studies in this field, with a focus on the active engagement and training of lecturers in order to integrate traditional teaching methods with blended learning opportunities.
- Full Text:
- «
- ‹
- 1
- ›
- »