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.
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- Date Issued: 2012
Willingness to pay for pharmacist-provided services directed towards reducing risks of medication-related problems
- Authors: Mushunje, Irvine Tawanda
- Date: 2012
- Subjects: Pharmaceutical industry , Pharmacy -- Practice -- Finance , Pharmacist and patient , Prescription pricing
- Language: English
- Type: Thesis , Masters , MPharm
- Identifier: vital:10133 , http://hdl.handle.net/10948/d1008053 , Pharmaceutical industry , Pharmacy -- Practice -- Finance , Pharmacist and patient , Prescription pricing
- Description: Pharmacists as members of health care teams, have a central role to play with respect to medication. The pharmaceutical care and cognitive services which pharmacists are able to provide can help prevent, ameliorate or correct medication-related problems. There are however many barriers to the provision of these services and one of the barriers commonly cited by pharmacists is the lack of remuneration for their expert services. The aim of this study is to ascertain if patients in South Africa are willing to pay for pharmacist-provided services which may reduce medication related problems, and thereby determine the perceived value of the pharmacist-provided services, by patients. The study will also seek to determine factors that influence willingness to pay (WTP), including financial status, gender, race, age and level of education. In addition the perceived value of the pharmacist‘s role in patient care, by third party payers (SA Medical Aid providers) and their WTP for pharmacist-provided services (such as DSM) on behalf of patients through their monthly premiums will also be investigated. The study was conducted as a two-phase process: the first phase focused on the opinions of patients and the second phase on the medical aid companies. In phase-1 a convenience sample of 500 patients was recruited by fifty community pharmacies distributed throughout the nine South African provinces. Data collection, consisting of telephonic administration of the questionnaires, was conducted and the survey responses were captured on a Microsoft Excel® spreadsheet. All the captured information was analyzed using descriptive statistics, box and whisker plots, analysis of variance (ANOVA) and regression analysis. In phase-2, medical aid schemes that are registered with the Council of Medical Schemes (CMSs) of South Africa were included in this research. A fifteen point questionnaire was completed electronically via e-mail by willing medical aid participants. Data was analyzed using descriptive statistics only. Only 233 or 88.6 percent, of the 263 participating respondents, were willing to pay at least one rand towards pharmacist-provided services. On average respondents were willing to pay R126.76 as out-of-pocket expenses. Respondents‘ WTP increased as the risk associated with medication-related problems was reduced due to pharmaceutical care intervention. Of the 263 respondents who took part in this research, fifty percent were willing to pay at least R100 for a risk reduction of 30 percent, R120 for a 60 percent reduction and approximately R150 for a greater than 90 percent risk reduction. It was also found that the respondents‘ willingness to pay was influenced by their age, earnings, racial grouping, employment status, medical aid status and their level of satisfaction with pharmacist-provided care services. Of the thirty-one open medical aid schemes only eight (25.8 percent) participated in the study. Findings indicate that all the participating medical aid respondents were unwilling to pay for pharmacist-provided care services, although they perceived pharmacists as very influential healthcare providers and as having a significant role to play in reducing medication-related problems. In conclusion it was found that majority of participants were willing to pay for pharmacist-provided services directed towards reducing risks associated with medication-related problems. Until pharmacists are able to prove pharmaceutical care‘s utility and cost-effectiveness to third-party payers, pharmacists must look to the patient for reimbursement.
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- Date Issued: 2012
Winston Leonard Spencer Churchill: a psychobiographical study
- Authors: Moolman, Bilué Anton
- Date: 2012
- Subjects: Churchill, Winston -- 1874-1965 , Psychology -- Biographical methods
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:9903 , http://hdl.handle.net/10948/d1009434 , Churchill, Winston -- 1874-1965 , Psychology -- Biographical methods
- Description: Psychobiography is a qualitative approach to exploring and understanding the life story of an individual through the lens of psychological theory. The application of theory is typically conducted on the finished lives of well-known or enigmatic people. This study explores and describes the psychological development across the lifespan of Winston Leonard Spencer Churchill, by applying the Individual Psychology of Alfred Adler. Winston Churchill voted the greatest Briton of the twentieth century, was an author, painter, adventure, soldier, politician and Prime Minister that led the United Kingdom during World War Two. Extensive data has been examined in this work to ensure an accurate description of Winston Churchill‘s life. Alexander‘s model of identifying salient themes was used to analyse the data within a conceptual framework derived from the theory. Churchill‘s difficult childhood motivated him to succeed, his passion for the nation of Britain and his dislike of the Nazi regime meant that Churchill was always abreast with current affairs, anticipating every possible scenario of attack. When the time came to fight the Nazi‘s Churchill was ready to die for his country. The research findings highlight Churchill‘s ability to rise above his childhood stigmas and surpass all expectations and so cementing his name into the history of a country he loved and a democratic world he hoped for. Alfred Adler‘s Individual Psychology proposes that an individual‘s potential weaknesses can be used as a means to strive and achieve greatness within their sphere of influence.
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- Date Issued: 2012
Winter rotational cover crops effects on soil strength, aggregate stability and water conservation of a hardsetting cambisol in Eastern Cape Province, South Africa
- Authors: Mupambwa, Hupenyu Allan
- Date: 2012
- Subjects: Cover crops -- South Africa -- Eastern Cape , Soil mechanics , Crop rotation , Crops and soils , Soil penetration test
- Language: English
- Type: Thesis , Masters , MSc Agric (Crop Science)
- Identifier: vital:11868 , http://hdl.handle.net/10353/453 , Cover crops -- South Africa -- Eastern Cape , Soil mechanics , Crop rotation , Crops and soils , Soil penetration test
- Description: Winter rotational cover crops (WRCC) are often used to boost soil fertility and plant nutrition. However, selection and use of WRCC for soil physical improvement is usually overlooked. The objective of this study was to determine the effects of WRCC on soil strength, aggregate stability and water conservation of a hardsetting soil. The soil physical properties were determined after four rotations of growing monocultures of vetch (Vicia dasycarpa cv. Max), lupin (Lupinus angustifolius cv. Tanjil) and oats (Avena sativa cv. Sederberg) and after two rotations of growing bicultures of oats (Avena sativa cv. Pallinup) and vetch (Vicia dasycarpa cv. Max) across two soil layers, 0 to 15 cm and 15 to 30 cm. The individual WRCC and a weedy fallow constituted the treatments in the monoculture study whilst in the biculture study the various combinations of WRCC namely; 90% oat plus 10% vetch (O90V10); 70% oat plus 30% vetch (O70V30) and 50% oat plus 50% vetch (O50V50) and a weedy fallow constituted the treatments. After four rotations with cover crop monocultures, oats significantly (P ≤ 0.05) reduced penetration resistance (PR) whilst vetch increased PR in both soil layers compared to the weedy fallow control. The effect of the biculture treatments was only experienced within the 15 to 30 cm depth. The treatments O50V50 and O70V30 increased the PR compared to the control. The WRCC in monoculture significantly increased the soil aggregate stability relative to the control in both soil layers. Vetch, lupin and oats resulted in a 41.7%; 20.4% and 15.7% increase in MWD in the 0 to 15 cm soil layer and 47.2%; 44.2% and 39.7% in the 15 to 30 cm depth, respectively. An increase in aggregate stability was associated with increased macro-aggregation. Under the biculture, WRCC slightly increased, non- significantly, the aggregate stability. Both hot water and dilute acid extractable polysaccharides showed no significant correlation with aggregate stability in the two studies. Oats monoculture resulted in a significant difference (P ≤ 0.05) on cumulative infiltration compared to the control. However, after 2 h vetch and lupin showed no significant difference from the control on cumulative infiltration. Oats resulted in a 7.8% increase in final infiltration rate (FIR) whilst vetch and lupin reduced FIR by 9% and 16.7% respectively, compared to the control. Bicultures of oats and vetch significantly (P ≤ 0.05) increased cumulative infiltration compared to the weedy fallow control. A similar significant increase in FIR was also observed under bicultures. The treatments O50V50; O90V10 and O70V30 resulted in a 163.3%; 113.3% and 105.4% increase in FIR respectively, compared to the control. Cover crop monocultures significantly (P ≤ 0.05) increased plant available water (PAW) compared to the weedy fallow, with vetch, oats and lupin resulting in a 28.3%; 22% and 23.9% increase respectively, in PAW. However, no significant differences were observed on PAW after two rotations with bicultures. Compared with winter weedy fallow, WRCC improved most of the soil physical properties under study, with the most suitable results expected under bicultures compared to monocultures. Under CA, selection of WRCC like oats, vetch and lupin, one should therefore take into consideration their effects on soil physical properties as a selection criterion and not biomass and fertility alone.
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- Date Issued: 2012
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.
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- Date Issued: 2012
μCloud : a P2P cloud platform for computing service provision
- Authors: Fouodji Tasse, Ghislain
- Date: 2012 , 2012-08-22
- Subjects: Cloud computing , Peer-to-peer architecture (Computer networks) , Computer architecture , Computer service industry
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4663 , http://hdl.handle.net/10962/d1006669 , Cloud computing , Peer-to-peer architecture (Computer networks) , Computer architecture , Computer service industry
- Description: The advancements in virtualization technologies have provided a large spectrum of computational approaches. Dedicated computations can be run on private environments (virtual machines), created within the same computer. Through capable APIs, this functionality is leveraged for the service we wish to implement; a computer power service (CPS). We target peer-to-peer systems for this service, to exploit the potential of aggregating computing resources. The concept of a P2P network is mostly known for its expanded usage in distributed networks for sharing resources like content files or real-time data. This study adds computing power to the list of shared resources by describing a suitable service composition. Taking into account the dynamic nature of the platform, this CPS provision is achieved using a self stabilizing clustering algorithm. So, the resulting system of our research is based around a hierarchical P2P architecture and offers end-to-end consideration of resource provisioning and reliability. We named this system μCloud and characterizes it as a self-provisioning cloud service platform. It is designed, implemented and presented in this dissertation. Eventually, we assessed our work by showing that μCloud succeeds in providing user-centric services using a P2P computing unit. With this, we conclude that our system would be highly beneficial in both small and massively deployed environments. , KMBT_223 , Adobe Acrobat 9.51 Paper Capture Plug-in
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- Date Issued: 2012