An intervention for enhancing the mathematics teaching practices of grade four teachers in the Nelson Mandela Metropolitan area
- Authors: Botha, Adele
- Date: 2011
- Subjects: Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:9499 , http://hdl.handle.net/10948/d1008176 , Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
- Description: Mathematics is regarded as a driving force in economies worldwide. The performance of South African learners in mathematics over the past decade has highlighted that problems are being experienced across all grades. This situation needs to be addressed with urgency. The South African Department of Education stated that quality learning must be the objective for all grades. The implementation of good teaching practices plays a crucial role in improving the quality of education and in guiding learners towards quality learning. To achieve quality mathematics teaching and learning it is imperative to determine what good mathematics teaching practices are. The identification of good mathematic teaching practices will provide a yard stick to measure the mathematics teaching competency of teachers. This study identifies a set of good mathematics teaching practice indicators and evidences applicable to teachers in the Intermediate phase as a first contribution. These indicators and evidences frame the second research contribution: an assessment instrument entitled “A Classroom Observation Tool for Observing Mathematics Teaching Practices in Primary Schools”. As a third research contribution a generic profile of a Grade four mathematics teacher has been built. This generic profile has been built through an analysis of data gathered by means of self-assessment questionnaires completed by the research sample, as well as through applying the observation tool. The value of the generic profile lies in the identification of shared strengths and shared improvement opportunities in the mathematics teaching practice of the sample and as such, it forms the basis of a theory on Grade four mathematics teaching practice. The fourth research contribution is the design and application of an intervention that addresses the shared improvement opportunities. The research study concludes by comparing pre-intervention classroom observation data with post-intervention classroom observation data and reporting on the impact of the intervention.
- Full Text:
- Date Issued: 2011
- Authors: Botha, Adele
- Date: 2011
- Subjects: Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:9499 , http://hdl.handle.net/10948/d1008176 , Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
- Description: Mathematics is regarded as a driving force in economies worldwide. The performance of South African learners in mathematics over the past decade has highlighted that problems are being experienced across all grades. This situation needs to be addressed with urgency. The South African Department of Education stated that quality learning must be the objective for all grades. The implementation of good teaching practices plays a crucial role in improving the quality of education and in guiding learners towards quality learning. To achieve quality mathematics teaching and learning it is imperative to determine what good mathematics teaching practices are. The identification of good mathematic teaching practices will provide a yard stick to measure the mathematics teaching competency of teachers. This study identifies a set of good mathematics teaching practice indicators and evidences applicable to teachers in the Intermediate phase as a first contribution. These indicators and evidences frame the second research contribution: an assessment instrument entitled “A Classroom Observation Tool for Observing Mathematics Teaching Practices in Primary Schools”. As a third research contribution a generic profile of a Grade four mathematics teacher has been built. This generic profile has been built through an analysis of data gathered by means of self-assessment questionnaires completed by the research sample, as well as through applying the observation tool. The value of the generic profile lies in the identification of shared strengths and shared improvement opportunities in the mathematics teaching practice of the sample and as such, it forms the basis of a theory on Grade four mathematics teaching practice. The fourth research contribution is the design and application of an intervention that addresses the shared improvement opportunities. The research study concludes by comparing pre-intervention classroom observation data with post-intervention classroom observation data and reporting on the impact of the intervention.
- Full Text:
- Date Issued: 2011
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
Effects of Isixhosa and English versions of GeoGebra on geometry achievement
- Authors: Matsha, Vuyani Hodecius
- Date: 2019
- Subjects: Mathematics -- Study and teaching , Mathematics Multicultural education -- South Africa -- Eastern Cape Academic achievement Language and languages
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: http://hdl.handle.net/10948/41032 , vital:36284
- Description: The purpose of this study was to investigate the effects of using GeoGebra in different linguistic situations, namely isiXhosa and English, in township schools in Port Elizabeth. The objectives were to design an isiXhosa version of GeoGebra and investigate whether or not using it in first and second languages would offer any different results with regard to achievement in, and visuospatial ability of, geometry. Learners and teachers’ perceptions of the GeoGebra software were investigated within the framework of these variables. A pre-post-test, mixed method, concurrent, embedded triangulation research design was used with qualitative aspects playing a more prominent role than the quantitative data. Data collection strategies included baseline assessment to determine teachers’ perceptions of their ability to work with GeoGebra, focus group interviews with learners, semi-structured interviews with teachers, classroom observation and learners’ geometry tests. The study used Vygotsky’s socio-cultural model as a philosophical framework, while the explanatory framework of this study was situated within Baddeley’s revised model of working memory. The translation of GeoGebra from English to isiXhosa proved to be successful in terms of user responses and the fact that it is the first official African language of this dynamic software to be published, offered and made available online. Pre-post geometry testing revealed that for all the groups, the section on riders displayed the largest mean increase. Performance on the riders, which were aligned to the Curriculum Assessment Policy Statement (CAPS) grade 10 examination papers, can be viewed as an indicator of visuospatial ability. Importantly, the mean scores of the learners using the isiXhosa version of GeoGebra improved more in terms of practical significance (effect size = 0,78 for Riders) than the improvement in scores of learners who used the English version (Effect size = 0,61 for Riders). The total effect sizes of the isiXhosa and English groups were 0,69 and 0,36 respectively. This finding seems to resonate with the findings that language proficiency is an indicator of mathematical achievement. This is so in spite of the small size of the sample because the main purpose of the study was to obtain a brief impression (snapshot) of the situation regarding language issues involved when learning mathematics via the software GeoGebra.
- Full Text:
- Date Issued: 2019
- Authors: Matsha, Vuyani Hodecius
- Date: 2019
- Subjects: Mathematics -- Study and teaching , Mathematics Multicultural education -- South Africa -- Eastern Cape Academic achievement Language and languages
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: http://hdl.handle.net/10948/41032 , vital:36284
- Description: The purpose of this study was to investigate the effects of using GeoGebra in different linguistic situations, namely isiXhosa and English, in township schools in Port Elizabeth. The objectives were to design an isiXhosa version of GeoGebra and investigate whether or not using it in first and second languages would offer any different results with regard to achievement in, and visuospatial ability of, geometry. Learners and teachers’ perceptions of the GeoGebra software were investigated within the framework of these variables. A pre-post-test, mixed method, concurrent, embedded triangulation research design was used with qualitative aspects playing a more prominent role than the quantitative data. Data collection strategies included baseline assessment to determine teachers’ perceptions of their ability to work with GeoGebra, focus group interviews with learners, semi-structured interviews with teachers, classroom observation and learners’ geometry tests. The study used Vygotsky’s socio-cultural model as a philosophical framework, while the explanatory framework of this study was situated within Baddeley’s revised model of working memory. The translation of GeoGebra from English to isiXhosa proved to be successful in terms of user responses and the fact that it is the first official African language of this dynamic software to be published, offered and made available online. Pre-post geometry testing revealed that for all the groups, the section on riders displayed the largest mean increase. Performance on the riders, which were aligned to the Curriculum Assessment Policy Statement (CAPS) grade 10 examination papers, can be viewed as an indicator of visuospatial ability. Importantly, the mean scores of the learners using the isiXhosa version of GeoGebra improved more in terms of practical significance (effect size = 0,78 for Riders) than the improvement in scores of learners who used the English version (Effect size = 0,61 for Riders). The total effect sizes of the isiXhosa and English groups were 0,69 and 0,36 respectively. This finding seems to resonate with the findings that language proficiency is an indicator of mathematical achievement. This is so in spite of the small size of the sample because the main purpose of the study was to obtain a brief impression (snapshot) of the situation regarding language issues involved when learning mathematics via the software GeoGebra.
- Full Text:
- Date Issued: 2019
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:
- Date Issued: 2019
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:
- Date Issued: 2019
Grade 9 second-language learners in township schools : issues of language and mathematics when solving word problems
- Authors: Sepeng, Johannes Percy
- Date: 2010
- Subjects: Mathematics -- Language , Mathematics -- Study and teaching , Language and languages -- Mathematics , Second language acquisition -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9498 , http://hdl.handle.net/10948/1455 , Mathematics -- Language , Mathematics -- Study and teaching , Language and languages -- Mathematics , Second language acquisition -- Study and teaching
- Description: Second language (English) learning of mathematics is common in South African mathematics classrooms, including those in the Eastern Cape Province of South Africa where isiXhosa speakers are taught in the language that is not spoken at home by both teachers and learners. The purpose of this research was to investigate issues of language, both home (isiXhosa) and the language of learning and teaching (LoLT), i.e. English, when 9th grade second language learners engage in problem-solving and sense-making of wor(l)d problems in multilingual mathematics classrooms. In addition, the aim of the study was to explore whether the introduction of discussion and argumentation techniques in these classrooms can ameliorate these issues. The study used a pre-test – intervention – post-test mixed method design utilising both quantitative and qualitative data. The data collection strategies for the purpose of this study included interviews (learners [n=24] and teachers [n=4]), classroom observations, and tests (experimental [n=107] and comparison [69]) in four experimental and two comparison schools in townships of Port Elizabeth. This study is framed by socio-cultural perspective which proposes that collective and individual processes are directly related and that students‘ unrealistic responses to real world problems reflect the students‘ socio-cultural relationship to school mathematics and their willingness to employ the approaches emphasised in school. Analysis of the data generated from pre- and post-tests, interviews and classroom observation schedule suggest that the interventional strategy significantly improved the experimental learners‘ problem-solving skills and sense-making abilities in both English and isiXhosa (but more significantly in English). The statistical results illustrate that the experimental group performed statistical significantly (p < .0005) better in the English posttest compared to comparison group. The data also suggests that the interventional strategy in this study (discussion and argumentation techniques) positively influenced the participating learners‘ word problem-solving abilities. The experimental group appeared to show a tendency to consider reality marginally better than the comparison group after the intervention. In particular, learners seemed to make realistic considerations better in the isiXhosa translation post-test compared to the English post-test. A large practical significant (d = 0.86) difference between the experimental group and the comparison group was also noted in the isiXhosa translation compared to a moderate practical significance (d = 0.57) noted in the English tests after the intervention. As such, the results of the study suggest that the introduction of discussion and argumentation techniques in the teaching and learning of mathematics word problems had a positive effect on learners‘ ability to consider reality during word problem-solving in both languages. Analysis of learners‘ interviews suggests that, although English is the preferred LoLT, they would prefer dual-use/parallel-use of English and isiXhosa for teaching and learning mathematics. There was also evidence of the benefits of code-switching throughout most of the lessons observed, coupled with instances of peer translation, and/or re-voicing. Overall results in this study illustrate that number skills displayed and mathematical errors made by learners seem to be directly related to language use in the classroom.
- Full Text:
- Date Issued: 2010
- Authors: Sepeng, Johannes Percy
- Date: 2010
- Subjects: Mathematics -- Language , Mathematics -- Study and teaching , Language and languages -- Mathematics , Second language acquisition -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , DEd
- Identifier: vital:9498 , http://hdl.handle.net/10948/1455 , Mathematics -- Language , Mathematics -- Study and teaching , Language and languages -- Mathematics , Second language acquisition -- Study and teaching
- Description: Second language (English) learning of mathematics is common in South African mathematics classrooms, including those in the Eastern Cape Province of South Africa where isiXhosa speakers are taught in the language that is not spoken at home by both teachers and learners. The purpose of this research was to investigate issues of language, both home (isiXhosa) and the language of learning and teaching (LoLT), i.e. English, when 9th grade second language learners engage in problem-solving and sense-making of wor(l)d problems in multilingual mathematics classrooms. In addition, the aim of the study was to explore whether the introduction of discussion and argumentation techniques in these classrooms can ameliorate these issues. The study used a pre-test – intervention – post-test mixed method design utilising both quantitative and qualitative data. The data collection strategies for the purpose of this study included interviews (learners [n=24] and teachers [n=4]), classroom observations, and tests (experimental [n=107] and comparison [69]) in four experimental and two comparison schools in townships of Port Elizabeth. This study is framed by socio-cultural perspective which proposes that collective and individual processes are directly related and that students‘ unrealistic responses to real world problems reflect the students‘ socio-cultural relationship to school mathematics and their willingness to employ the approaches emphasised in school. Analysis of the data generated from pre- and post-tests, interviews and classroom observation schedule suggest that the interventional strategy significantly improved the experimental learners‘ problem-solving skills and sense-making abilities in both English and isiXhosa (but more significantly in English). The statistical results illustrate that the experimental group performed statistical significantly (p < .0005) better in the English posttest compared to comparison group. The data also suggests that the interventional strategy in this study (discussion and argumentation techniques) positively influenced the participating learners‘ word problem-solving abilities. The experimental group appeared to show a tendency to consider reality marginally better than the comparison group after the intervention. In particular, learners seemed to make realistic considerations better in the isiXhosa translation post-test compared to the English post-test. A large practical significant (d = 0.86) difference between the experimental group and the comparison group was also noted in the isiXhosa translation compared to a moderate practical significance (d = 0.57) noted in the English tests after the intervention. As such, the results of the study suggest that the introduction of discussion and argumentation techniques in the teaching and learning of mathematics word problems had a positive effect on learners‘ ability to consider reality during word problem-solving in both languages. Analysis of learners‘ interviews suggests that, although English is the preferred LoLT, they would prefer dual-use/parallel-use of English and isiXhosa for teaching and learning mathematics. There was also evidence of the benefits of code-switching throughout most of the lessons observed, coupled with instances of peer translation, and/or re-voicing. Overall results in this study illustrate that number skills displayed and mathematical errors made by learners seem to be directly related to language use in the classroom.
- Full Text:
- Date Issued: 2010
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
Multiple representations and cognitive load: words, arrows, and colours when solving algebraic problems
- Authors: Brey, Amina
- Date: 2013
- Subjects: Algebraic logic , Mathematical analysis , Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9580 , http://hdl.handle.net/10948/d1020392
- Description: This study investigates the possible effects that access to selected multiple representations (words, arrows and colours) have in terms of cognitive load and learner achievement when presented with algebraic problems at grade nine level. The presentation of multiple representations (the intervention) was intended to decrease extraneous cognitive load, manage the intrinsic cognitive load (algebraic problems) and optimise germane cognition (schema acquisition and automation). An explanatory sequential mixed-method design was employed with six hundred and seventy three learners in four secondary schools. Quantitative data were generated via pre-, intervention and post-tests/questionnaires, while qualitative data were obtained from open-ended questions in the pre-, intervention, and post-tests/questionnaires, eight learner focus group interviews (n = 32), and four semi-structured, open-ended teacher interviews. Statistically and practically significant improvement in mean test scores from the pre- to intervention test scores in all schools was noted. No statistically and practically significant improvement was noted in further post-tests except for post-test 2 which employed more challenging problems (statistically significant decrease with a small practical effect). Learners expressed their preference for arrows, followed by colours and then words as effective representations. Teacher generated qualitative data suggests that they realise the importance of using multiple representations as an instructional strategy and implicitly understand the notion of cognitive load. The findings, when considered in the light of literature on cognitive load, suggest that a reduction in extraneous cognitive load by using a more effective instructional design (multiple representations) frees working memory capacity which can then be devoted to the intrinsic cognitive load (algebraic problems) and thereby increase germane cognition (schema acquisition and automation).
- Full Text:
- Date Issued: 2013
- Authors: Brey, Amina
- Date: 2013
- Subjects: Algebraic logic , Mathematical analysis , Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9580 , http://hdl.handle.net/10948/d1020392
- Description: This study investigates the possible effects that access to selected multiple representations (words, arrows and colours) have in terms of cognitive load and learner achievement when presented with algebraic problems at grade nine level. The presentation of multiple representations (the intervention) was intended to decrease extraneous cognitive load, manage the intrinsic cognitive load (algebraic problems) and optimise germane cognition (schema acquisition and automation). An explanatory sequential mixed-method design was employed with six hundred and seventy three learners in four secondary schools. Quantitative data were generated via pre-, intervention and post-tests/questionnaires, while qualitative data were obtained from open-ended questions in the pre-, intervention, and post-tests/questionnaires, eight learner focus group interviews (n = 32), and four semi-structured, open-ended teacher interviews. Statistically and practically significant improvement in mean test scores from the pre- to intervention test scores in all schools was noted. No statistically and practically significant improvement was noted in further post-tests except for post-test 2 which employed more challenging problems (statistically significant decrease with a small practical effect). Learners expressed their preference for arrows, followed by colours and then words as effective representations. Teacher generated qualitative data suggests that they realise the importance of using multiple representations as an instructional strategy and implicitly understand the notion of cognitive load. The findings, when considered in the light of literature on cognitive load, suggest that a reduction in extraneous cognitive load by using a more effective instructional design (multiple representations) frees working memory capacity which can then be devoted to the intrinsic cognitive load (algebraic problems) and thereby increase germane cognition (schema acquisition and automation).
- Full Text:
- Date Issued: 2013
Teachers' and learners' experiences and perceptions concerning the use of English as a language of learning and teaching in bi/multilingual mathematical literarcy classrooms
- Authors: Pillai, Saloshni
- Date: 2013
- Subjects: Education, Bilingual , Mathematics -- Study and teaching , English language -- Usage
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9440 , http://hdl.handle.net/10948/d1021022
- Description: In South Africa, there is concern about the poor achievement by first additional language (FAL) English learners in mathematics, and this is a consequence not solely of the apartheid era but more appropriately, the existing current situation in the classroom. Since 2006, the Department of Basic Education in South Africa introduced mathematical literacy (ML) as another learning area for the Further Education and Training (FET) band. ML, as an alternative choice to mathematics, is envisaged as a key to the understanding of our everyday world filled with numbers. Mathematical literacy FAL English learners and teachers are exposed to a ML curriculum that demands high linguistic skills in English in order to engage with the mathematical concepts through the medium of English which is not their home language. While the Language-in-Education Policy (DoE, 1997) recommends that school language policies promote additive bilingualism and the use of learners’ home languages as languages of learning and teaching (LoLT), there has been little implementation of these recommendations by schools, for the reason that all assessments and learner and teacher support materials (LTSM) are only available in English. Thus it appears that ML creates a language gap when FAL English learners and teachers have to possess a high level of communication and language proficiency of the LoLT English to successfully engage with the mathematical context and content of the ML curriculum since the language itself carries all the meaning. The majority of FAL English learners and teachers struggle with the necessary English language proficiency to successfully interact with the ML curriculum and are often required to use their own home language (code switching) to bring about understanding. In this study, I explore how teachers and learners who are dominantly FAL English speakers, engage in teaching and learning of ML in bi/multilingual classrooms. The main aim of the study is to investigate the FAL English learners’ and teachers’ experiences and perceptions concerning the use of English as the LoLT in bi/multilingual ML classrooms. Qualitative measures were generated through personal interviews (teachers [n=15] and learners [n=25]) from five different secondary schools situated in the rural areas of the Midlands in KwaZulu-Natal. This study is framed by Wenger’s (1991) model of situated learning and Vygotsky’s socio-cultural perspectives, which propose that learning involves a process of engagement in a community of practice and reflects the learners’ sociocultural relationship to school mathematics respectively. The study also describes Cummins’ quadrants and explores the benefits of Cummins’ notion of language use (Cummins, 1984). Analysis of the semi-structured interviews revealed that, despite both teachers’ and learners’ difficulty with the language, English is the more popular language to be used in teaching and learning in bi/multilingual mathematical literacy classrooms since English is accepted as a global language. Worldwide emphasis and dominance of English as a powerful language that gives access to goods and social mobility were also highlighted. However, overall results in this study showed that most participants did express their preference for using their home language isiZulu alongside English through the extensive practice of code switching for the teaching and learning of ML.
- Full Text:
- Date Issued: 2013
- Authors: Pillai, Saloshni
- Date: 2013
- Subjects: Education, Bilingual , Mathematics -- Study and teaching , English language -- Usage
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9440 , http://hdl.handle.net/10948/d1021022
- Description: In South Africa, there is concern about the poor achievement by first additional language (FAL) English learners in mathematics, and this is a consequence not solely of the apartheid era but more appropriately, the existing current situation in the classroom. Since 2006, the Department of Basic Education in South Africa introduced mathematical literacy (ML) as another learning area for the Further Education and Training (FET) band. ML, as an alternative choice to mathematics, is envisaged as a key to the understanding of our everyday world filled with numbers. Mathematical literacy FAL English learners and teachers are exposed to a ML curriculum that demands high linguistic skills in English in order to engage with the mathematical concepts through the medium of English which is not their home language. While the Language-in-Education Policy (DoE, 1997) recommends that school language policies promote additive bilingualism and the use of learners’ home languages as languages of learning and teaching (LoLT), there has been little implementation of these recommendations by schools, for the reason that all assessments and learner and teacher support materials (LTSM) are only available in English. Thus it appears that ML creates a language gap when FAL English learners and teachers have to possess a high level of communication and language proficiency of the LoLT English to successfully engage with the mathematical context and content of the ML curriculum since the language itself carries all the meaning. The majority of FAL English learners and teachers struggle with the necessary English language proficiency to successfully interact with the ML curriculum and are often required to use their own home language (code switching) to bring about understanding. In this study, I explore how teachers and learners who are dominantly FAL English speakers, engage in teaching and learning of ML in bi/multilingual classrooms. The main aim of the study is to investigate the FAL English learners’ and teachers’ experiences and perceptions concerning the use of English as the LoLT in bi/multilingual ML classrooms. Qualitative measures were generated through personal interviews (teachers [n=15] and learners [n=25]) from five different secondary schools situated in the rural areas of the Midlands in KwaZulu-Natal. This study is framed by Wenger’s (1991) model of situated learning and Vygotsky’s socio-cultural perspectives, which propose that learning involves a process of engagement in a community of practice and reflects the learners’ sociocultural relationship to school mathematics respectively. The study also describes Cummins’ quadrants and explores the benefits of Cummins’ notion of language use (Cummins, 1984). Analysis of the semi-structured interviews revealed that, despite both teachers’ and learners’ difficulty with the language, English is the more popular language to be used in teaching and learning in bi/multilingual mathematical literacy classrooms since English is accepted as a global language. Worldwide emphasis and dominance of English as a powerful language that gives access to goods and social mobility were also highlighted. However, overall results in this study showed that most participants did express their preference for using their home language isiZulu alongside English through the extensive practice of code switching for the teaching and learning of ML.
- Full Text:
- Date Issued: 2013
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:
- Date Issued: 2013
- 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:
- Date Issued: 2013
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