Investigating teachers’ experiences of using multiple representations to teach fractions for conceptual understanding in 'Grades 5-7': a Namibian case study
- Authors: Iiyambo,Julia
- Date: 2016
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/1296 , vital:20044
- Description: This study investigated teachers’ experiences of using multiple representations to teach fractions for conceptual understanding in ‘grades 5 – 7’. Three teachers were involved in the study and the main goal was to explore how teachers might work with the additional tools of multiple representations to improve the teaching of fractions for conceptual understanding. Different types of multiple representations such as written mathematical symbols, descriptive written words, pictorial representations, manipulations, concrete reality, oral representations, and experience-based representations and videos or power point presentations were examined. This investigation was carried out through a focus group workshop developed by the researcher and though observations of fraction teaching which took place in schools. The research focused on the teachers working to develop their use of multiple representations to teach fractions and how they implemented what they learned in the workshop into their own classroom teaching. This study was conducted using a qualitative case study design and was oriented in the interpretive paradigm. The three participating teachers in the focus group workshop were observed and interviewed individually. The purpose of observing teaching before the workshop was to observe how the selected teachers taught fractions and in particular to observe which types of representations they used and how these were used to enhance the conceptual understanding of the learners. Post teaching took place after the focus group workshop and the different multiple representations which were used in different lessons were observed and analyzed. The purpose of the interview was to gain an understanding of the teachers’ views of using multiple representations when teaching fractions for conceptual understanding. The data showed that teachers who participated in the focus group workshop worked positively to develop their use of multiple representations to teach fractions. They made sense of fractions and were able to look at representations in different ways to develop the meaning and concepts of fractions. Teachers developed an understanding of working with multiple representations and were able to make connections among concepts and the use of concrete representations. Teachers also developed their lesson plans effectively to involve a variety of teaching methods and multiple representations, despite the limited time available to them. Moreover, teachers used different modes of representation to improve learner engagement in learning activities. Lastly, teachers used multiple representations to teach in ways that improved the learners’ conception of fractions. On the basis of this research, it can be concluded that in-service workshops for teachers on the integration of multiple representative tools in the teaching of ‘Grades 5 – 7’ fractions could provide a valuable contribution to further developing the teaching of fractions in schools.
- Full Text:
- Date Issued: 2016
- Authors: Iiyambo,Julia
- Date: 2016
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/1296 , vital:20044
- Description: This study investigated teachers’ experiences of using multiple representations to teach fractions for conceptual understanding in ‘grades 5 – 7’. Three teachers were involved in the study and the main goal was to explore how teachers might work with the additional tools of multiple representations to improve the teaching of fractions for conceptual understanding. Different types of multiple representations such as written mathematical symbols, descriptive written words, pictorial representations, manipulations, concrete reality, oral representations, and experience-based representations and videos or power point presentations were examined. This investigation was carried out through a focus group workshop developed by the researcher and though observations of fraction teaching which took place in schools. The research focused on the teachers working to develop their use of multiple representations to teach fractions and how they implemented what they learned in the workshop into their own classroom teaching. This study was conducted using a qualitative case study design and was oriented in the interpretive paradigm. The three participating teachers in the focus group workshop were observed and interviewed individually. The purpose of observing teaching before the workshop was to observe how the selected teachers taught fractions and in particular to observe which types of representations they used and how these were used to enhance the conceptual understanding of the learners. Post teaching took place after the focus group workshop and the different multiple representations which were used in different lessons were observed and analyzed. The purpose of the interview was to gain an understanding of the teachers’ views of using multiple representations when teaching fractions for conceptual understanding. The data showed that teachers who participated in the focus group workshop worked positively to develop their use of multiple representations to teach fractions. They made sense of fractions and were able to look at representations in different ways to develop the meaning and concepts of fractions. Teachers developed an understanding of working with multiple representations and were able to make connections among concepts and the use of concrete representations. Teachers also developed their lesson plans effectively to involve a variety of teaching methods and multiple representations, despite the limited time available to them. Moreover, teachers used different modes of representation to improve learner engagement in learning activities. Lastly, teachers used multiple representations to teach in ways that improved the learners’ conception of fractions. On the basis of this research, it can be concluded that in-service workshops for teachers on the integration of multiple representative tools in the teaching of ‘Grades 5 – 7’ fractions could provide a valuable contribution to further developing the teaching of fractions in schools.
- Full Text:
- Date Issued: 2016
The potential economic implications of black locust (Robinia pseudoacacia l.) on agricultural production in South Africa
- Authors: Humphrey, Luke
- Date: 2016
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: http://hdl.handle.net/10962/4069 , vital:20599
- Description: Black Locust (Robinia pseudoacacia L.) is an invasive deciduous, strongly suckering, broad- leaved tree that has the potential to be widely distributed across a large portion of South Africa. Robinia pseudoacacia has invaded all nine of South African provinces, with large infestations found in the Eastern Cape, Kwa Zulu-Natal, Free State and Gauteng provinces. The invasive tree has the potential to spread into livestock grazing lands in South Africa. Because R. pseudoacacia has the ability to spread and thrive in a variety of habitats and resists control, the distribution of the invasive tree into grazing land poses a problem for landowners. The potential economic impacts of R. pseudoacacia on agricultural production stem from the trees ability to reduce the carrying capacity of livestock. This study estimated the potential economic implications of R. pseudoacacia on agricultural production in South Africa, specifically looking at the livestock sector. The prevalence of R. pseudoacacia potential distribution was calculated by using a maximum-entropy predictive habitat model, MAXENT. The distribution of livestock, based on grazing capacity (ha/LSU), in South Africa was then determined. The potential direct economic impacts were estimated by assessing the impact of the potential distribution of R. pseudoacacia on the carrying capacity of livestock. The results showed that an infestation of R. pseudoacacia has the potential to reduce the gross margin in the livestock sector by between approximately R130 million and R961 million, dependent on the probability of invasion. Therefore, the potential invasion of R. pseudoacacia can have detrimental effects on the livestock sector in South Africa. The potential high levels of foregone income and business activity found in this study reaffirm the need to devote resources to develop a viable, economical and effective control method, such as biological control.
- Full Text:
- Date Issued: 2016
- Authors: Humphrey, Luke
- Date: 2016
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: http://hdl.handle.net/10962/4069 , vital:20599
- Description: Black Locust (Robinia pseudoacacia L.) is an invasive deciduous, strongly suckering, broad- leaved tree that has the potential to be widely distributed across a large portion of South Africa. Robinia pseudoacacia has invaded all nine of South African provinces, with large infestations found in the Eastern Cape, Kwa Zulu-Natal, Free State and Gauteng provinces. The invasive tree has the potential to spread into livestock grazing lands in South Africa. Because R. pseudoacacia has the ability to spread and thrive in a variety of habitats and resists control, the distribution of the invasive tree into grazing land poses a problem for landowners. The potential economic impacts of R. pseudoacacia on agricultural production stem from the trees ability to reduce the carrying capacity of livestock. This study estimated the potential economic implications of R. pseudoacacia on agricultural production in South Africa, specifically looking at the livestock sector. The prevalence of R. pseudoacacia potential distribution was calculated by using a maximum-entropy predictive habitat model, MAXENT. The distribution of livestock, based on grazing capacity (ha/LSU), in South Africa was then determined. The potential direct economic impacts were estimated by assessing the impact of the potential distribution of R. pseudoacacia on the carrying capacity of livestock. The results showed that an infestation of R. pseudoacacia has the potential to reduce the gross margin in the livestock sector by between approximately R130 million and R961 million, dependent on the probability of invasion. Therefore, the potential invasion of R. pseudoacacia can have detrimental effects on the livestock sector in South Africa. The potential high levels of foregone income and business activity found in this study reaffirm the need to devote resources to develop a viable, economical and effective control method, such as biological control.
- Full Text:
- Date Issued: 2016
Vocational curriculum report 191(NATED) as a curriculum: a case study of three Eastern Cape TVET Colleges
- Authors: Sixabayi, Siyabonga Prince
- Date: 2016
- Subjects: Vocational education -- Curricula -- South Africa -- Eastern Cape Curriculum planning -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , Degree
- Identifier: http://hdl.handle.net/10353/5126 , vital:29089
- Description: This study aimed to investigate if there are any possible gaps in the offering Vocational Curriculum Report 191, in terms of knowledge, skills and link to the world of work. This study was a case study of three Technical and Vocational Education and Training Colleges that offer Vocational Curriculum Report 191, and it was geographically limited to the province of the Eastern Cape. The five main findings from this study were that firstly, the curriculum offers theory without practice. Secondly, there is a mismatch between what is offered as curriculum at Technical and Vocational Education and Training Colleges and what the labour market wants. Thirdly, lecturers do not have the practical exposure that relates to their fields of study. Fourthly, Vocational Curriculum Report 191 does not promote self-employment of its students and lastly, the curriculum is outdated and does not comply with the criteria of current employment opportunities. The study recommends that the curriculum be reviewed and revised. Technical and Vocational Education and Training colleges need to have in site practice facilities to cater for the practical application of theoretical knowledge of students. Partnerships between Technical and Vocational Education and Training Colleges, the labour market and Sector Education and Training Authorities are strongly recommended in this study.
- Full Text:
- Date Issued: 2016
- Authors: Sixabayi, Siyabonga Prince
- Date: 2016
- Subjects: Vocational education -- Curricula -- South Africa -- Eastern Cape Curriculum planning -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , Degree
- Identifier: http://hdl.handle.net/10353/5126 , vital:29089
- Description: This study aimed to investigate if there are any possible gaps in the offering Vocational Curriculum Report 191, in terms of knowledge, skills and link to the world of work. This study was a case study of three Technical and Vocational Education and Training Colleges that offer Vocational Curriculum Report 191, and it was geographically limited to the province of the Eastern Cape. The five main findings from this study were that firstly, the curriculum offers theory without practice. Secondly, there is a mismatch between what is offered as curriculum at Technical and Vocational Education and Training Colleges and what the labour market wants. Thirdly, lecturers do not have the practical exposure that relates to their fields of study. Fourthly, Vocational Curriculum Report 191 does not promote self-employment of its students and lastly, the curriculum is outdated and does not comply with the criteria of current employment opportunities. The study recommends that the curriculum be reviewed and revised. Technical and Vocational Education and Training colleges need to have in site practice facilities to cater for the practical application of theoretical knowledge of students. Partnerships between Technical and Vocational Education and Training Colleges, the labour market and Sector Education and Training Authorities are strongly recommended in this study.
- Full Text:
- Date Issued: 2016
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