An investigation of teachers' mathematical task selection in the Zambia context
- Authors: Kangwa, Evaristo
- Date: 2013
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1384 , http://hdl.handle.net/10962/d1001512
- Description: This research sought to investigate the sources and type of tasks used in the teaching of trigonometry in Zambia’s secondary schools, and to investigate the criteria used and decisions made by teachers in their selection and implementation of tasks. The study was conducted in three different school types located in high cost, medium cost and low cost respectively. One participant was chosen from each of the different categories of schools. The research was located within an interpretive paradigm. Data were collected through semi-structured interviews, lesson observations and document analysis which include: lesson plans for five consecutive days, pupils’ activity books and three textbooks predominantly used by the teachers. Document analysis was informed by the task analysis guide and essential themes which were used to tease out teachers’ task practice with regard to criteria used and decisions made in the selection and implementation of tasks. Essential themes that were qualitatively established were validated and explicated by the qualitative analysis. The findings of the study indicate that teachers picked tasks from prescribed textbooks. The study further suggests that teachers selected a mix of low and high level tasks, procedures without connections and procedures with connections tasks to be specific. There were no memorisations and doing mathematics tasks. Their choice of tasks was based on the purpose for which the task was intended. Some tasks were selected for the purpose of practicing the procedures and skills, other tasks for the promotion conceptual development. Most of high level tasks decline to low level tasks during implementation. The findings also indicate that teachers selected and implemented a variety of tasks and concepts. Furthermore, teachers presented tasks in various forms of representations and in a variety of ways. However, the results of this study could not be generalized because of the small sample involved. The results presented reflect the views and task practices of the target group. A possibility for future study would be to consider a large population, drawn across the country.
- Full Text:
- Date Issued: 2013
- Authors: Kangwa, Evaristo
- Date: 2013
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1384 , http://hdl.handle.net/10962/d1001512
- Description: This research sought to investigate the sources and type of tasks used in the teaching of trigonometry in Zambia’s secondary schools, and to investigate the criteria used and decisions made by teachers in their selection and implementation of tasks. The study was conducted in three different school types located in high cost, medium cost and low cost respectively. One participant was chosen from each of the different categories of schools. The research was located within an interpretive paradigm. Data were collected through semi-structured interviews, lesson observations and document analysis which include: lesson plans for five consecutive days, pupils’ activity books and three textbooks predominantly used by the teachers. Document analysis was informed by the task analysis guide and essential themes which were used to tease out teachers’ task practice with regard to criteria used and decisions made in the selection and implementation of tasks. Essential themes that were qualitatively established were validated and explicated by the qualitative analysis. The findings of the study indicate that teachers picked tasks from prescribed textbooks. The study further suggests that teachers selected a mix of low and high level tasks, procedures without connections and procedures with connections tasks to be specific. There were no memorisations and doing mathematics tasks. Their choice of tasks was based on the purpose for which the task was intended. Some tasks were selected for the purpose of practicing the procedures and skills, other tasks for the promotion conceptual development. Most of high level tasks decline to low level tasks during implementation. The findings also indicate that teachers selected and implemented a variety of tasks and concepts. Furthermore, teachers presented tasks in various forms of representations and in a variety of ways. However, the results of this study could not be generalized because of the small sample involved. The results presented reflect the views and task practices of the target group. A possibility for future study would be to consider a large population, drawn across the country.
- Full Text:
- Date Issued: 2013
Case study : using visual representations to enhance conceptual knowledge of division in mathematics
- Authors: Joel, Linea Beautty
- Date: 2013
- Subjects: Mathematics -- Study and teaching , Visual learning , Division -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1992 , http://hdl.handle.net/10962/d1013356
- Description: Literature emphasizes how important it is that procedural and conceptual knowledge of mathematics should be learned in integration. Yet, generally, the learning and teaching in mathematics classrooms relies heavily on isolated procedures. This study aims to improve teaching and learning of partitive and quotitive division, moving away from isolated procedural knowledge to that of procedures with their underlying concepts through the use of manipulatives, visual representation and questioning. Learning and teaching lessons were designed to teach partitive and quotitive division both procedurally and conceptually. The study explored the roles these manipulatives, visual representations and questioning played toward the conceptual learning of partitive and quotitive division. It was found that manipulatives and iconic visualization enhanced learning, and this could be achieved through scaffolding using a questioning approach. It was concluded that manipulatives and iconic visualization need to be properly planned and used, and integrated with questioning to achieve success in the learning of procedural and conceptual knowledge.
- Full Text:
- Date Issued: 2013
Case study : using visual representations to enhance conceptual knowledge of division in mathematics
- Authors: Joel, Linea Beautty
- Date: 2013
- Subjects: Mathematics -- Study and teaching , Visual learning , Division -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1992 , http://hdl.handle.net/10962/d1013356
- Description: Literature emphasizes how important it is that procedural and conceptual knowledge of mathematics should be learned in integration. Yet, generally, the learning and teaching in mathematics classrooms relies heavily on isolated procedures. This study aims to improve teaching and learning of partitive and quotitive division, moving away from isolated procedural knowledge to that of procedures with their underlying concepts through the use of manipulatives, visual representation and questioning. Learning and teaching lessons were designed to teach partitive and quotitive division both procedurally and conceptually. The study explored the roles these manipulatives, visual representations and questioning played toward the conceptual learning of partitive and quotitive division. It was found that manipulatives and iconic visualization enhanced learning, and this could be achieved through scaffolding using a questioning approach. It was concluded that manipulatives and iconic visualization need to be properly planned and used, and integrated with questioning to achieve success in the learning of procedural and conceptual knowledge.
- Full Text:
- Date Issued: 2013
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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