Why do learners and teachers experience problems with the concept of zero?
- Authors: Jooste, Zonia
- Date: 2012
- Subjects: Numbers, Divisibility of -- Study and teaching (Primary) -- South Africa Numbers, Divisibility of -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa -- Eastern Cape Mathematics teachers -- Training of -- South Africa -- Western Cape Education, Primary -- Curricula -- South Africa Education, Secondary -- Curricula -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1906 , http://hdl.handle.net/10962/d1006764
- Description: The controversy around the inclusion of zero in the number system has been widely documented. Influential mathematicians in various ancient cultures did not accept zero as a number. The idea of the empty set was too abstract and they could not conceptualise division by zero. Surprisingly, understanding of the concept is still a matter of concern today. In spite of expansive reports on and recommendations for developing conceptualisation of the concept, learners and teachers still experience problems similar to those that ancient mathematicians struggled with. The study was initiated by an observation of Grade 7 learners' inability to solve the problems 4 × 0 and 0 ÷ 7 effectively or at all. I investigated why Grade 3 to 6 learners and mathematics teachers on a BEd (in-service) course and an accredited ACE course experience problems with the concept of zero. I was especially interested in the understanding of multiplication and division by zero. I investigated teachers' knowledge of zero's characteristics as a number, the history of zero and how they teach the concept, in order to support my assumptions. The data production process was performed over a period of two years. It involved a multi-case opportunity sample approach embedded in the empirical field that formed the backdrop of my involvement as mathematics education specialist in schools in the Western and Eastern Cape. The interpretative orientation of the study allowed me to conduct inquiries that served to confirm or challenge my assumptions and enabled me to construct generalisations that depict learners' and teachers' knowledge construction. The qualitative data analysis informed the presentation and discussion of the findings. The single most important message conveyed to readers of this study is that the value of zero as a number, its importance in the number system, its properties and its behaviour in calculations, should not be underrated. Teaching of this abstract concept requires competent teachers who are able to mediate understanding in the most effective and innovative manner. Professional development programmes should orchestrate this competence and curriculum developers and textbook authors should acknowledge the significance of learning and teaching the concept of zero.
- Full Text:
- Date Issued: 2012
- Authors: Jooste, Zonia
- Date: 2012
- Subjects: Numbers, Divisibility of -- Study and teaching (Primary) -- South Africa Numbers, Divisibility of -- Study and teaching (Secondary) -- South Africa Mathematics teachers -- Training of -- South Africa -- Eastern Cape Mathematics teachers -- Training of -- South Africa -- Western Cape Education, Primary -- Curricula -- South Africa Education, Secondary -- Curricula -- South Africa
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1906 , http://hdl.handle.net/10962/d1006764
- Description: The controversy around the inclusion of zero in the number system has been widely documented. Influential mathematicians in various ancient cultures did not accept zero as a number. The idea of the empty set was too abstract and they could not conceptualise division by zero. Surprisingly, understanding of the concept is still a matter of concern today. In spite of expansive reports on and recommendations for developing conceptualisation of the concept, learners and teachers still experience problems similar to those that ancient mathematicians struggled with. The study was initiated by an observation of Grade 7 learners' inability to solve the problems 4 × 0 and 0 ÷ 7 effectively or at all. I investigated why Grade 3 to 6 learners and mathematics teachers on a BEd (in-service) course and an accredited ACE course experience problems with the concept of zero. I was especially interested in the understanding of multiplication and division by zero. I investigated teachers' knowledge of zero's characteristics as a number, the history of zero and how they teach the concept, in order to support my assumptions. The data production process was performed over a period of two years. It involved a multi-case opportunity sample approach embedded in the empirical field that formed the backdrop of my involvement as mathematics education specialist in schools in the Western and Eastern Cape. The interpretative orientation of the study allowed me to conduct inquiries that served to confirm or challenge my assumptions and enabled me to construct generalisations that depict learners' and teachers' knowledge construction. The qualitative data analysis informed the presentation and discussion of the findings. The single most important message conveyed to readers of this study is that the value of zero as a number, its importance in the number system, its properties and its behaviour in calculations, should not be underrated. Teaching of this abstract concept requires competent teachers who are able to mediate understanding in the most effective and innovative manner. Professional development programmes should orchestrate this competence and curriculum developers and textbook authors should acknowledge the significance of learning and teaching the concept of zero.
- Full Text:
- Date Issued: 2012
Woman vulnerability to HIV/AIDS : an investigation into women's conceptions and experiences in negotiating sex and safe sex in Okalongo constituency, Omusati Region, Namibia
- Authors: Haipinge, Rauha
- Date: 2013
- Subjects: AIDS (Disease) in women -- Namibia -- Omusati AIDS (Disease) -- Social aspects -- Namibia -- Omusati HIV infections -- Social aspects -- Namibia -- Omusati Women -- Namibia -- Omusati -- Social conditions Women -- Sexual behavior -- Namibia -- Omusati Man-woman relationships -- Namibia -- Omusati Sex instruction -- Namibia -- Omusati Safe sex in AIDS prevention -- Namibia -- Omusati Sex role -- Namibia -- Omusati HIV-positive persons -- Sex differences -- Namibia -- Omusati Male domination (Social structure) -- Namibia -- Omusati Sex discrimination against women -- Namibia -- Omusati
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1839 , http://hdl.handle.net/10962/d1004337
- Description: This study emerged from the high prevalence rate of HIV and AIDS infection among women in Sub-Saharan Africa, which has no exception to Namibia. Women have been vulnerable to HIV and AIDS let alone on sex related issues since the epidemic emerged, but not research has been done specifically to Okalongo women. The way in which women vulnerable to HIV and AIDS infection were explored by examined social and cultural identities that affect women’s sexual relations in negotiating sex and safe sex. Qualitative study on a sample of fifteen women was conducted in Okalongo. The purpose of this study was to investigate the conceptions and experiences of women in negotiating sex and safe sex with their husband and partners. Feminist theory guided the methodology and analysis of data. I assumed that gender roles andsexuality are socially constructed, shaped by religion, social, political, and economic influences and modified throughout life. Feminist theory assisted in documentary the ways in which the female’s gender and sexuality in Okalongo is shaped by cultural influences and by institutions that disadvantage female and other oppressed groups by silencing their voices. The feminist further guided the discussion of the contradicting messages about women’s sexuality and their experiences, as women complied, conformed and even colluded with their oppression. To address the issue under study, the primary analysis of data from the focus group discussion and individual interview were utilised. The following themes were the heart of analysis: Women Positionality, Normalisation and Compliance, Women Agency and Male Dominance Power, Women Perceptions of Risk, Sex Education in and out of school among Women.In this study the data suggested that women in Okalongo are more vulnerable to their lack of assertiveness, as they have difficult in developing an authoritative voice, they tend to be humble about their achievements and knowledge and to only assertively when concerned about others. The findings supported the literature that women’s vulnerability is strongly influenced and tied by broader forces present in the society. Women’s vulnerability is real and needs to be tackled for any progress to occur in the fight against AIDS. Until factors that constraints and enabling women agency to negotiate sex and safe sex acknowledged and addressed, women will continue to succumb to the HIV pandemic.
- Full Text:
- Date Issued: 2013
- Authors: Haipinge, Rauha
- Date: 2013
- Subjects: AIDS (Disease) in women -- Namibia -- Omusati AIDS (Disease) -- Social aspects -- Namibia -- Omusati HIV infections -- Social aspects -- Namibia -- Omusati Women -- Namibia -- Omusati -- Social conditions Women -- Sexual behavior -- Namibia -- Omusati Man-woman relationships -- Namibia -- Omusati Sex instruction -- Namibia -- Omusati Safe sex in AIDS prevention -- Namibia -- Omusati Sex role -- Namibia -- Omusati HIV-positive persons -- Sex differences -- Namibia -- Omusati Male domination (Social structure) -- Namibia -- Omusati Sex discrimination against women -- Namibia -- Omusati
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1839 , http://hdl.handle.net/10962/d1004337
- Description: This study emerged from the high prevalence rate of HIV and AIDS infection among women in Sub-Saharan Africa, which has no exception to Namibia. Women have been vulnerable to HIV and AIDS let alone on sex related issues since the epidemic emerged, but not research has been done specifically to Okalongo women. The way in which women vulnerable to HIV and AIDS infection were explored by examined social and cultural identities that affect women’s sexual relations in negotiating sex and safe sex. Qualitative study on a sample of fifteen women was conducted in Okalongo. The purpose of this study was to investigate the conceptions and experiences of women in negotiating sex and safe sex with their husband and partners. Feminist theory guided the methodology and analysis of data. I assumed that gender roles andsexuality are socially constructed, shaped by religion, social, political, and economic influences and modified throughout life. Feminist theory assisted in documentary the ways in which the female’s gender and sexuality in Okalongo is shaped by cultural influences and by institutions that disadvantage female and other oppressed groups by silencing their voices. The feminist further guided the discussion of the contradicting messages about women’s sexuality and their experiences, as women complied, conformed and even colluded with their oppression. To address the issue under study, the primary analysis of data from the focus group discussion and individual interview were utilised. The following themes were the heart of analysis: Women Positionality, Normalisation and Compliance, Women Agency and Male Dominance Power, Women Perceptions of Risk, Sex Education in and out of school among Women.In this study the data suggested that women in Okalongo are more vulnerable to their lack of assertiveness, as they have difficult in developing an authoritative voice, they tend to be humble about their achievements and knowledge and to only assertively when concerned about others. The findings supported the literature that women’s vulnerability is strongly influenced and tied by broader forces present in the society. Women’s vulnerability is real and needs to be tackled for any progress to occur in the fight against AIDS. Until factors that constraints and enabling women agency to negotiate sex and safe sex acknowledged and addressed, women will continue to succumb to the HIV pandemic.
- Full Text:
- Date Issued: 2013
Women leadership: a case study in the Otjozondjupa Region, Namibia
- Authors: Araes, Cornelia
- Date: 2012
- Subjects: Women -- Education (Primary) -- Namibia Leadership in women -- Education (Primary) -- Namibia Management -- Education (Primary) -- Namibia Educational leadership -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1825 , http://hdl.handle.net/10962/d1003711
- Description: Empowerment of women in leadership and in particular, school leadership has been the focus of the Namibian government and the country since independence in 1990. Different policies and laws, post‐independence, make provision for women empowerment and leadership in a range of organisations and institutions throughout the country. However, reports on gender equity in leadership positions suggest that Namibia is not really moving towards these policy goals at a sufficiently quick pace. A lot still needs to be achieved in terms of transforming the gender stereotyping in Namibia, which still suffers from the legacy of gender discrimination of the apartheid era. Modern‐day academic authors and journalists portray an increasing interest in an awareness of the advantages of women leadership. Women are increasingly perceived to have leadership styles more suitable for contemporary conditions than men. It is against this backdrop that this study sought to investigate women leadership in the Otjiwarongo circuit in the Otjozondjupa educational region in Namibia. The study used a qualitative, interpretive research paradigm. It adopted a case study approach. The primary participants consisted of four women principals in the Otjiwarongo circuit and the secondary participants included four women education officers from the same circuit. Semi‐structured interviews, a focus group interview and observation were applied as methods for collecting data and the data collection period was just over six weeks. Data analysis was done through coding and identification of categories. The findings revealed that women principals possessed the qualities of commitment, good communication and are passionate about their work, which are qualities normally associated with effective leadership. In terms of their role in their schools, they emerged as democratic leaders who involved all stakeholders in the decision making process through consensus. In addition, they demonstrated distributive and servant leadership in their interactions with stakeholders. The main challenge to the leadership position of these women principals seemed to be the stereotypical view held, that as women, they had to work twice as hard as men at leading schools. The study recommended that people oriented leadership styles, such as the ones enacted by the women principals in this study, are highly recommended for effective leadership in the 21st century.
- Full Text:
- Date Issued: 2012
- Authors: Araes, Cornelia
- Date: 2012
- Subjects: Women -- Education (Primary) -- Namibia Leadership in women -- Education (Primary) -- Namibia Management -- Education (Primary) -- Namibia Educational leadership -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1825 , http://hdl.handle.net/10962/d1003711
- Description: Empowerment of women in leadership and in particular, school leadership has been the focus of the Namibian government and the country since independence in 1990. Different policies and laws, post‐independence, make provision for women empowerment and leadership in a range of organisations and institutions throughout the country. However, reports on gender equity in leadership positions suggest that Namibia is not really moving towards these policy goals at a sufficiently quick pace. A lot still needs to be achieved in terms of transforming the gender stereotyping in Namibia, which still suffers from the legacy of gender discrimination of the apartheid era. Modern‐day academic authors and journalists portray an increasing interest in an awareness of the advantages of women leadership. Women are increasingly perceived to have leadership styles more suitable for contemporary conditions than men. It is against this backdrop that this study sought to investigate women leadership in the Otjiwarongo circuit in the Otjozondjupa educational region in Namibia. The study used a qualitative, interpretive research paradigm. It adopted a case study approach. The primary participants consisted of four women principals in the Otjiwarongo circuit and the secondary participants included four women education officers from the same circuit. Semi‐structured interviews, a focus group interview and observation were applied as methods for collecting data and the data collection period was just over six weeks. Data analysis was done through coding and identification of categories. The findings revealed that women principals possessed the qualities of commitment, good communication and are passionate about their work, which are qualities normally associated with effective leadership. In terms of their role in their schools, they emerged as democratic leaders who involved all stakeholders in the decision making process through consensus. In addition, they demonstrated distributive and servant leadership in their interactions with stakeholders. The main challenge to the leadership position of these women principals seemed to be the stereotypical view held, that as women, they had to work twice as hard as men at leading schools. The study recommended that people oriented leadership styles, such as the ones enacted by the women principals in this study, are highly recommended for effective leadership in the 21st century.
- Full Text:
- Date Issued: 2012
Working for ecosystems: an account of how pathways of learning lead to SMME development in a municipal social-ecological programme within a green economy context
- Burger, Margaret Hendrieka Margo
- Authors: Burger, Margaret Hendrieka Margo
- Date: 2017
- Subjects: Working for Ecosystems (South Africa) , Small business -- South Africa , Environmental education -- South Africa -- Durban , Sustainable development -- South Africa -- Durban
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7735 , vital:21291
- Description: Global climate change alters climatic zones to the extent that species invasion and, in particular, invasive alien plant growth, is regarded as one of the biggest threats to ecosystem functioning. Socio-ecological adaptive management practices have emerged from these threats as opportunities in developing countries where the immediacy of poverty relief acts as a political drawcard and potential for job creation. Local workers in the eThekwini Municipality’s ‘Working for Ecosystems’ biodiversity management programme (WFE) are emerging as micro-enterprise contractors (SMMEs). The transition from worker to entrepreneur has been part of the ethos and long-term planning of the Working for Ecosystems programme at a management level with a view to economic inclusion and realising long-term sustainable livelihoods. Evidence from narratives support claims of transformative outcomes. The findings of this study show that transformation is accessed at various levels: at a management level, at a well-established SMME level and from worker-to- SMME level. These show an “articulation of learning pathways and the connections that are made without a formally structured pathway of learning being in place” (Lotz-Sisitka & Ramsarup, 2013, p. 33). The routes followed to knowledge, practice and sustainability competences by participants in Working for Ecosystems are examined within the complex constellation of material- economic, social-political and cultural-discursive structures and are conceptualised as learning pathways. To fully appreciate the evolving and multidimensional nature of the emergence of SMME practice learning in the Working for Ecosystems programme, relational ontology as a perspective was introduced, with the intention of emphasising the relationship between practice, knowledge and context. Narrative enquiry and extensive data analysis was used as the method to examine workplace learning pathways. These workplace learning pathways can be enriched by more explicitly integrating observation of local and indigenous knowledge of biodiversity in everyday work and practice. However, intermittent contractual work causes disruption in learning pathways formation and results in a lack of stability in conflict with the aims of the programme’s objectives of building capacity and robustness. Findings show that skills development in terms of workplace learning with intersecting, diverse levels of participation and knowledge flow, is particularly important for learning pathways development in the field of invasive alien plant control where divergent values, norms and levels of practice are operational. Prior knowledge, of either indigenous plants or business functioning mechanisms, scaffolds SMME skills through relevance and connected learning in the two fields of practice pertaining to the Working for Ecosystems programme. Clarity of management roles and solidarity within management enhances SMME functioning and learning pathway development for all participants. The Expanded Public Works Programmes (such as Working for Ecosystems) are examined as an opportunity for acquisition of knowledge, competence and new skills development. A prime competence for sustainability understanding is interpersonal skills as these form an essential link with most other competences and as such should be foregrounded in training and learning pathway development. Site selection and time in the programme is a critical factor for expansive learning pathways and environmental stewardship development. Ultimately, in examining and reflecting on the Education for Sustainable Development and green economy potential, it is apparent that learning pathway development needs more support to realise the possibility of entrepreneurship and its political and social significance in terms of sustainable livelihoods. There is a need to recognise diversity, multiple ways of knowing and learning, in learning pathways development “to build joint capacity to cope with complex sustainability challenges” (Wiek, Withycombe, & Redman, 2011).
- Full Text:
- Date Issued: 2017
- Authors: Burger, Margaret Hendrieka Margo
- Date: 2017
- Subjects: Working for Ecosystems (South Africa) , Small business -- South Africa , Environmental education -- South Africa -- Durban , Sustainable development -- South Africa -- Durban
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7735 , vital:21291
- Description: Global climate change alters climatic zones to the extent that species invasion and, in particular, invasive alien plant growth, is regarded as one of the biggest threats to ecosystem functioning. Socio-ecological adaptive management practices have emerged from these threats as opportunities in developing countries where the immediacy of poverty relief acts as a political drawcard and potential for job creation. Local workers in the eThekwini Municipality’s ‘Working for Ecosystems’ biodiversity management programme (WFE) are emerging as micro-enterprise contractors (SMMEs). The transition from worker to entrepreneur has been part of the ethos and long-term planning of the Working for Ecosystems programme at a management level with a view to economic inclusion and realising long-term sustainable livelihoods. Evidence from narratives support claims of transformative outcomes. The findings of this study show that transformation is accessed at various levels: at a management level, at a well-established SMME level and from worker-to- SMME level. These show an “articulation of learning pathways and the connections that are made without a formally structured pathway of learning being in place” (Lotz-Sisitka & Ramsarup, 2013, p. 33). The routes followed to knowledge, practice and sustainability competences by participants in Working for Ecosystems are examined within the complex constellation of material- economic, social-political and cultural-discursive structures and are conceptualised as learning pathways. To fully appreciate the evolving and multidimensional nature of the emergence of SMME practice learning in the Working for Ecosystems programme, relational ontology as a perspective was introduced, with the intention of emphasising the relationship between practice, knowledge and context. Narrative enquiry and extensive data analysis was used as the method to examine workplace learning pathways. These workplace learning pathways can be enriched by more explicitly integrating observation of local and indigenous knowledge of biodiversity in everyday work and practice. However, intermittent contractual work causes disruption in learning pathways formation and results in a lack of stability in conflict with the aims of the programme’s objectives of building capacity and robustness. Findings show that skills development in terms of workplace learning with intersecting, diverse levels of participation and knowledge flow, is particularly important for learning pathways development in the field of invasive alien plant control where divergent values, norms and levels of practice are operational. Prior knowledge, of either indigenous plants or business functioning mechanisms, scaffolds SMME skills through relevance and connected learning in the two fields of practice pertaining to the Working for Ecosystems programme. Clarity of management roles and solidarity within management enhances SMME functioning and learning pathway development for all participants. The Expanded Public Works Programmes (such as Working for Ecosystems) are examined as an opportunity for acquisition of knowledge, competence and new skills development. A prime competence for sustainability understanding is interpersonal skills as these form an essential link with most other competences and as such should be foregrounded in training and learning pathway development. Site selection and time in the programme is a critical factor for expansive learning pathways and environmental stewardship development. Ultimately, in examining and reflecting on the Education for Sustainable Development and green economy potential, it is apparent that learning pathway development needs more support to realise the possibility of entrepreneurship and its political and social significance in terms of sustainable livelihoods. There is a need to recognise diversity, multiple ways of knowing and learning, in learning pathways development “to build joint capacity to cope with complex sustainability challenges” (Wiek, Withycombe, & Redman, 2011).
- Full Text:
- Date Issued: 2017
Writing, identity, and change : a narrative case study of the use of journals to promote reflexivity within a Drama Studies curriculum
- Authors: Sutherland, Alexandra
- Date: 2005
- Subjects: Drama -- Study and teaching (Higher) -- South Africa Drama in education Scholarly publishing Academic writing Reflection (Philosophy) Playwriting
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1845 , http://hdl.handle.net/10962/d1004384
- Description: The study adopts a case study examination of three student reflective joumals written about class and field based applied Drama experiences over one year. The journals were written as part of a curriculum outcome to develop reflective practice, for one Drama Honours paper (Educational Drama and Theatre) at Rhodes University Drama Department, South Africa. Based on a narrative inquiry approach, the study documents the changes in identity, discourse, and representation of self and other, which emerge through the journal writing process. The research analyses how identities are constructed through reflective writing practices, and how these identities might relate to the arguments for the development of reflexivity. The development of reflexivity is seen as integral to contemporary educational policies associated with lifelong learning, and the skills required of graduates in South Africa's emerging democracy. These policies centre on means of preparing students for a world characterised by change and instability, or what Barnett (2000) has termed a "supercomplex world". The research findings suggest that journal writing within a Drama Studies curriculum, allows students to construct subjectivities which support Barnett's claim that "the main pedagogical task in a university is not that of the transmission of knowledge but of promoting forms of human being appropriate to the conditions of supercomplexity" (Barnett, 2000b: 164). In addition, the development of different writing genres within a Drama Studies curriculum allows students to develop disciplinarily relevant ways of discussing and researching artistic processes and products. A reflective journal is a potential site for students to interrogate and construct emerging identities which enable them to negotiate diversity, thus preparing them for their lives beyond the university.
- Full Text:
- Date Issued: 2005
- Authors: Sutherland, Alexandra
- Date: 2005
- Subjects: Drama -- Study and teaching (Higher) -- South Africa Drama in education Scholarly publishing Academic writing Reflection (Philosophy) Playwriting
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1845 , http://hdl.handle.net/10962/d1004384
- Description: The study adopts a case study examination of three student reflective joumals written about class and field based applied Drama experiences over one year. The journals were written as part of a curriculum outcome to develop reflective practice, for one Drama Honours paper (Educational Drama and Theatre) at Rhodes University Drama Department, South Africa. Based on a narrative inquiry approach, the study documents the changes in identity, discourse, and representation of self and other, which emerge through the journal writing process. The research analyses how identities are constructed through reflective writing practices, and how these identities might relate to the arguments for the development of reflexivity. The development of reflexivity is seen as integral to contemporary educational policies associated with lifelong learning, and the skills required of graduates in South Africa's emerging democracy. These policies centre on means of preparing students for a world characterised by change and instability, or what Barnett (2000) has termed a "supercomplex world". The research findings suggest that journal writing within a Drama Studies curriculum, allows students to construct subjectivities which support Barnett's claim that "the main pedagogical task in a university is not that of the transmission of knowledge but of promoting forms of human being appropriate to the conditions of supercomplexity" (Barnett, 2000b: 164). In addition, the development of different writing genres within a Drama Studies curriculum allows students to develop disciplinarily relevant ways of discussing and researching artistic processes and products. A reflective journal is a potential site for students to interrogate and construct emerging identities which enable them to negotiate diversity, thus preparing them for their lives beyond the university.
- Full Text:
- Date Issued: 2005