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:
- Date Issued: 2022-11
- 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:
- Date Issued: 2022-11
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:
- Date Issued: 2021-02
- 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:
- Date Issued: 2021-02
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