Investigating a way of teaching transformation geometry in grade 9 applying van Hiele’s theory and Kilpatrick’s model : a case study
- Authors: Geja, Nokuzola Hlaleleni
- Date: 2015
- Subjects: Hiele, Pierre M. van , Kilpatrick, Jeremy , Transformations (Mathematics) , Geometry -- Study and teaching (Secondary) , Geometry -- Mathematical models , Educational tests and measurements
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2066 , http://hdl.handle.net/10962/d1020601
- Description: Transformation geometry has been neglected in our schools because teachers are often not proficient enough to teach it, as it was not part of the syllabus during their training. The study investigates effective ways of teaching transformation geometry in grade 9, applying van Hiele’s theory (1986) of geometry teaching and learning and Kilpatrick’s model of mathematical proficiency. The teaching programme activities require consistent use of physical manipulatives by the teacher for effective teaching, learning and understanding of geometric concepts. The type of study is a case study. Data collection tools are: - baseline evaluation, teacher & learner interviews (pre & post programme intervention) and observation (pre & post) during the implementation of the teaching programme. Results were analysed both qualitatively and quantitatively. My research findings show some improvement of learner performance after the application of the programme. Baseline evaluation shows that some learners attained below and above 30%. Interviews showed that some learners had problems before the implementation of the programme and some problems were eliminated by the use of the programme activities and learning progression was evident. Learner performance showed that learners had acquired some knowledge and critical thinking and reasoning skills, reflection skills, communication through LOLT improved, commitment to activities of the programme and teaching practice had improved. Learner performance showed that a learner can be in two different levels at the same time. Consistent use of manipulatives resulted in effective teaching and learning of geometry in grade 9. The results of this research support other researchers’ views of teaching geometry using van Hiele’s theory (1986) and Kilpatrick et al. (2001). Shaw (2002) argues that teaching geometry with manipulatives enhances conceptual understanding by the learner. In my opinion, it also promotes immediate intervention by the teacher as soon as the learner picks an incorrect object. The project enhanced and improved levels of communication between the learner, teacher and others in the classroom.
- Full Text:
- Date Issued: 2015
- Authors: Geja, Nokuzola Hlaleleni
- Date: 2015
- Subjects: Hiele, Pierre M. van , Kilpatrick, Jeremy , Transformations (Mathematics) , Geometry -- Study and teaching (Secondary) , Geometry -- Mathematical models , Educational tests and measurements
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2066 , http://hdl.handle.net/10962/d1020601
- Description: Transformation geometry has been neglected in our schools because teachers are often not proficient enough to teach it, as it was not part of the syllabus during their training. The study investigates effective ways of teaching transformation geometry in grade 9, applying van Hiele’s theory (1986) of geometry teaching and learning and Kilpatrick’s model of mathematical proficiency. The teaching programme activities require consistent use of physical manipulatives by the teacher for effective teaching, learning and understanding of geometric concepts. The type of study is a case study. Data collection tools are: - baseline evaluation, teacher & learner interviews (pre & post programme intervention) and observation (pre & post) during the implementation of the teaching programme. Results were analysed both qualitatively and quantitatively. My research findings show some improvement of learner performance after the application of the programme. Baseline evaluation shows that some learners attained below and above 30%. Interviews showed that some learners had problems before the implementation of the programme and some problems were eliminated by the use of the programme activities and learning progression was evident. Learner performance showed that learners had acquired some knowledge and critical thinking and reasoning skills, reflection skills, communication through LOLT improved, commitment to activities of the programme and teaching practice had improved. Learner performance showed that a learner can be in two different levels at the same time. Consistent use of manipulatives resulted in effective teaching and learning of geometry in grade 9. The results of this research support other researchers’ views of teaching geometry using van Hiele’s theory (1986) and Kilpatrick et al. (2001). Shaw (2002) argues that teaching geometry with manipulatives enhances conceptual understanding by the learner. In my opinion, it also promotes immediate intervention by the teacher as soon as the learner picks an incorrect object. The project enhanced and improved levels of communication between the learner, teacher and others in the classroom.
- Full Text:
- Date Issued: 2015
The diversity of aquatic insects in the Tsitsikamma region, with implications for aquatic ecosystem conservation
- Authors: Bellingan, Terence Andrew
- Date: 2011
- Subjects: Aquatic insects -- South Africa -- Tsitsikamma , Aquatic insects -- Classification -- South Africa -- Tsitsikamma , Aquatic ecology -- South Africa -- Tsitsikamma , Ecosystem management -- South Africa -- Tsitsikamma , Stream conservation -- South Africa -- Tsitsikamma
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5664 , http://hdl.handle.net/10962/d1005348 , Aquatic insects -- South Africa -- Tsitsikamma , Aquatic insects -- Classification -- South Africa -- Tsitsikamma , Aquatic ecology -- South Africa -- Tsitsikamma , Ecosystem management -- South Africa -- Tsitsikamma , Stream conservation -- South Africa -- Tsitsikamma
- Description: As a result of research carried out within the last decade to assess the diversity of macroinvertebrates of the Salt River in the Western Cape Province, South Africa, surveys of macroinvertebrates of 20 sites on 11 selected rivers from the same mountain range source were undertaken. This was done to make a preliminary assessment of the conservation status of the rivers of this region. Aquatic insects from the orders Ephemeroptera, Odonata, Plecoptera, Megaloptera, Trichoptera and the dipteran family Simuliidae were collected using techniques to maximize the number of taxa found. The insects collected were identified to species level where possible. Water physicochemical parameters were recorded at all sites for each sampling trip to characterize these rivers and to establish a set of baseline data for future comparisons. These parameters included measurements made on site and analysis of the concentrations of all the major ions in water samples in the laboratory. Multivariate analyses including Principle Components Analysis and Canonical Correspondence Analysis were used to reveal patterns within the water physicochemistry and species distributional data. Results include the identification of 123 species from 70 genera and 30 families. A total of 31 species were found to be undescribed, of which 17 were not previously collected and are thus completely new to science. In addition, four of these species could not be placed into any known genus. The analysis of water physicochemistry showed a clear distinction between rivers of Table Mountain sandstone and Bokkeveld shale origin. Downstream effects of anthropogenic influences were discernable too. Distinct macroinvertebrate assemblages were found based upon stream order and water chemistry composition. pH proved to be the most important driver of invertebrate assemblage composition. The high levels of endemism of the macroinvertebrates found within the upper reaches of these rivers and their degree of ecological specialization make these systems a priority for the conservation of aquatic biodiversity on a national and global scale.
- Full Text:
- Date Issued: 2011
- Authors: Bellingan, Terence Andrew
- Date: 2011
- Subjects: Aquatic insects -- South Africa -- Tsitsikamma , Aquatic insects -- Classification -- South Africa -- Tsitsikamma , Aquatic ecology -- South Africa -- Tsitsikamma , Ecosystem management -- South Africa -- Tsitsikamma , Stream conservation -- South Africa -- Tsitsikamma
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5664 , http://hdl.handle.net/10962/d1005348 , Aquatic insects -- South Africa -- Tsitsikamma , Aquatic insects -- Classification -- South Africa -- Tsitsikamma , Aquatic ecology -- South Africa -- Tsitsikamma , Ecosystem management -- South Africa -- Tsitsikamma , Stream conservation -- South Africa -- Tsitsikamma
- Description: As a result of research carried out within the last decade to assess the diversity of macroinvertebrates of the Salt River in the Western Cape Province, South Africa, surveys of macroinvertebrates of 20 sites on 11 selected rivers from the same mountain range source were undertaken. This was done to make a preliminary assessment of the conservation status of the rivers of this region. Aquatic insects from the orders Ephemeroptera, Odonata, Plecoptera, Megaloptera, Trichoptera and the dipteran family Simuliidae were collected using techniques to maximize the number of taxa found. The insects collected were identified to species level where possible. Water physicochemical parameters were recorded at all sites for each sampling trip to characterize these rivers and to establish a set of baseline data for future comparisons. These parameters included measurements made on site and analysis of the concentrations of all the major ions in water samples in the laboratory. Multivariate analyses including Principle Components Analysis and Canonical Correspondence Analysis were used to reveal patterns within the water physicochemistry and species distributional data. Results include the identification of 123 species from 70 genera and 30 families. A total of 31 species were found to be undescribed, of which 17 were not previously collected and are thus completely new to science. In addition, four of these species could not be placed into any known genus. The analysis of water physicochemistry showed a clear distinction between rivers of Table Mountain sandstone and Bokkeveld shale origin. Downstream effects of anthropogenic influences were discernable too. Distinct macroinvertebrate assemblages were found based upon stream order and water chemistry composition. pH proved to be the most important driver of invertebrate assemblage composition. The high levels of endemism of the macroinvertebrates found within the upper reaches of these rivers and their degree of ecological specialization make these systems a priority for the conservation of aquatic biodiversity on a national and global scale.
- Full Text:
- Date Issued: 2011
The zoogeography of the cetaceans in Algoa Bay
- Authors: Melly, Brigitte Leigh
- Date: 2011
- Subjects: Cetacea -- South Africa -- Algoa Bay , Cetacea -- Behavior -- South Africa -- Algoa Bay , Cetacea -- South Africa -- Algoa Bay -- Geographical distribution , Cetacea -- Counting -- South Africa -- Algoa Bay
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4858 , http://hdl.handle.net/10962/d1005534 , Cetacea -- South Africa -- Algoa Bay , Cetacea -- Behavior -- South Africa -- Algoa Bay , Cetacea -- South Africa -- Algoa Bay -- Geographical distribution , Cetacea -- Counting -- South Africa -- Algoa Bay
- Description: The most recent study on cetaceans in Algoa Bay, South Africa, was conducted over 14 years ago. Consequently, knowledge of the cetacean species visiting this bay is currently based on incidental observations and stranding data. A number of developments in recent years: a deepwater port, proposed oil refinery, increased boating and fishing (commercial and recreational), a proposed Marine Protected Area, and the release of a whale-watching permit, all of which may impact these animals in some way, highlight the need for a baseline study on cetaceans. Therefore, the aim of this study was to determine the spatial and temporal distribution, and habitat preference of cetaceans in Algoa Bay. Boat-based surveys were conducted monthly between March 2009 and July 2010. At each sighting the GPS location, species, group size and composition, and behaviour were recorded. Using GIS, the sighting data was related to data layers of geographical variables such as sea surface temperature, depth and sea-floor substrate. Approximately 365 hours of search effort were completed over 57 surveys, with a total of 346 sightings. Species observed were: southern right whales (Eubalaena australis), humpback whales (Megaptera novaeangliae), Bryde’s whales (Balaenoptera brydei), Indian Ocean bottlenose dolphins (Tursiops aduncus), Indo-Pacific humpback dolphins (Sousa chinensis), and longbeaked common dolphins (Delphinus capensis). Southern right whales were observed during austral winter, utilising the shallow, protected areas of the bay as a mating and nursery ground. Humpback whales were also recorded extensively during winter, in more offshore waters, with a significant number of mother-calf pairs sighted. Bryde’s whales were recorded in offshore waters during summer and autumn, where they were primarily observed travelling and foraging. Bottlenose dolphins were the most prolific species sighted. They were recorded year-round throughout the inshore waters of the bay, with large group sizes (up to 500 animals), and displayed a wide variety of behaviours. Humpback dolphins were observed in extremely shallow and inshore waters (mean bottom depth of 6.6 m) along the south-west corner of the bay, in small groups of approximately three individuals. Common dolphins were the least observed species, and were mainly observed foraging in large groups of up to 800 individuals. The results of this study indicate how cetaceans utilise the bay in significantly different ways. Geographical and anthropogenic factors have influenced the spatial and temporal distribution of these animals and have resulted in habitat preferences, as well as potential key habitats, in the bay. Thus, this study has provided baseline information for future research and for better informed conservation and management strategies in Algoa Bay.
- Full Text:
- Date Issued: 2011
- Authors: Melly, Brigitte Leigh
- Date: 2011
- Subjects: Cetacea -- South Africa -- Algoa Bay , Cetacea -- Behavior -- South Africa -- Algoa Bay , Cetacea -- South Africa -- Algoa Bay -- Geographical distribution , Cetacea -- Counting -- South Africa -- Algoa Bay
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4858 , http://hdl.handle.net/10962/d1005534 , Cetacea -- South Africa -- Algoa Bay , Cetacea -- Behavior -- South Africa -- Algoa Bay , Cetacea -- South Africa -- Algoa Bay -- Geographical distribution , Cetacea -- Counting -- South Africa -- Algoa Bay
- Description: The most recent study on cetaceans in Algoa Bay, South Africa, was conducted over 14 years ago. Consequently, knowledge of the cetacean species visiting this bay is currently based on incidental observations and stranding data. A number of developments in recent years: a deepwater port, proposed oil refinery, increased boating and fishing (commercial and recreational), a proposed Marine Protected Area, and the release of a whale-watching permit, all of which may impact these animals in some way, highlight the need for a baseline study on cetaceans. Therefore, the aim of this study was to determine the spatial and temporal distribution, and habitat preference of cetaceans in Algoa Bay. Boat-based surveys were conducted monthly between March 2009 and July 2010. At each sighting the GPS location, species, group size and composition, and behaviour were recorded. Using GIS, the sighting data was related to data layers of geographical variables such as sea surface temperature, depth and sea-floor substrate. Approximately 365 hours of search effort were completed over 57 surveys, with a total of 346 sightings. Species observed were: southern right whales (Eubalaena australis), humpback whales (Megaptera novaeangliae), Bryde’s whales (Balaenoptera brydei), Indian Ocean bottlenose dolphins (Tursiops aduncus), Indo-Pacific humpback dolphins (Sousa chinensis), and longbeaked common dolphins (Delphinus capensis). Southern right whales were observed during austral winter, utilising the shallow, protected areas of the bay as a mating and nursery ground. Humpback whales were also recorded extensively during winter, in more offshore waters, with a significant number of mother-calf pairs sighted. Bryde’s whales were recorded in offshore waters during summer and autumn, where they were primarily observed travelling and foraging. Bottlenose dolphins were the most prolific species sighted. They were recorded year-round throughout the inshore waters of the bay, with large group sizes (up to 500 animals), and displayed a wide variety of behaviours. Humpback dolphins were observed in extremely shallow and inshore waters (mean bottom depth of 6.6 m) along the south-west corner of the bay, in small groups of approximately three individuals. Common dolphins were the least observed species, and were mainly observed foraging in large groups of up to 800 individuals. The results of this study indicate how cetaceans utilise the bay in significantly different ways. Geographical and anthropogenic factors have influenced the spatial and temporal distribution of these animals and have resulted in habitat preferences, as well as potential key habitats, in the bay. Thus, this study has provided baseline information for future research and for better informed conservation and management strategies in Algoa Bay.
- Full Text:
- Date Issued: 2011
Limiting vulnerability exposure through effective patch management: threat mitigation through vulnerability remediation
- Authors: White, Dominic Stjohn Dolin
- Date: 2007 , 2007-02-08
- Subjects: Computer networks -- Security measures , Computer viruses , Computer security
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4629 , http://hdl.handle.net/10962/d1006510 , Computer networks -- Security measures , Computer viruses , Computer security
- Description: This document aims to provide a complete discussion on vulnerability and patch management. The first chapters look at the trends relating to vulnerabilities, exploits, attacks and patches. These trends describe the drivers of patch and vulnerability management and situate the discussion in the current security climate. The following chapters then aim to present both policy and technical solutions to the problem. The policies described lay out a comprehensive set of steps that can be followed by any organisation to implement their own patch management policy, including practical advice on integration with other policies, managing risk, identifying vulnerability, strategies for reducing downtime and generating metrics to measure progress. Having covered the steps that can be taken by users, a strategy describing how best a vendor should implement a related patch release policy is provided. An argument is made that current monthly patch release schedules are inadequate to allow users to most effectively and timeously mitigate vulnerabilities. The final chapters discuss the technical aspect of automating parts of the policies described. In particular the concept of 'defense in depth' is used to discuss additional strategies for 'buying time' during the patch process. The document then goes on to conclude that in the face of increasing malicious activity and more complex patching, solid frameworks such as those provided in this document are required to ensure an organisation can fully manage the patching process. However, more research is required to fully understand vulnerabilities and exploits. In particular more attention must be paid to threats, as little work as been done to fully understand threat-agent capabilities and activities from a day to day basis. , TeX output 2007.02.08:2212 , Adobe Acrobat 9.51 Paper Capture Plug-in
- Full Text:
- Date Issued: 2007
- Authors: White, Dominic Stjohn Dolin
- Date: 2007 , 2007-02-08
- Subjects: Computer networks -- Security measures , Computer viruses , Computer security
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4629 , http://hdl.handle.net/10962/d1006510 , Computer networks -- Security measures , Computer viruses , Computer security
- Description: This document aims to provide a complete discussion on vulnerability and patch management. The first chapters look at the trends relating to vulnerabilities, exploits, attacks and patches. These trends describe the drivers of patch and vulnerability management and situate the discussion in the current security climate. The following chapters then aim to present both policy and technical solutions to the problem. The policies described lay out a comprehensive set of steps that can be followed by any organisation to implement their own patch management policy, including practical advice on integration with other policies, managing risk, identifying vulnerability, strategies for reducing downtime and generating metrics to measure progress. Having covered the steps that can be taken by users, a strategy describing how best a vendor should implement a related patch release policy is provided. An argument is made that current monthly patch release schedules are inadequate to allow users to most effectively and timeously mitigate vulnerabilities. The final chapters discuss the technical aspect of automating parts of the policies described. In particular the concept of 'defense in depth' is used to discuss additional strategies for 'buying time' during the patch process. The document then goes on to conclude that in the face of increasing malicious activity and more complex patching, solid frameworks such as those provided in this document are required to ensure an organisation can fully manage the patching process. However, more research is required to fully understand vulnerabilities and exploits. In particular more attention must be paid to threats, as little work as been done to fully understand threat-agent capabilities and activities from a day to day basis. , TeX output 2007.02.08:2212 , Adobe Acrobat 9.51 Paper Capture Plug-in
- Full Text:
- Date Issued: 2007
The effects of the invasive mussel mytilus galloprovincialis and human exploitation on the indigenous mussel Perna perna on the South Coast of South Africa
- Authors: Rius Viladomiu, Marc
- Date: 2005
- Subjects: Mussels -- South Africa , Perna -- South Africa , Mytilus galloprovincialis -- South Africa , Mytilidae -- South Africa , Biological invasions , Marine resources conservation -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5684 , http://hdl.handle.net/10962/d1005370 , Mussels -- South Africa , Perna -- South Africa , Mytilus galloprovincialis -- South Africa , Mytilidae -- South Africa , Biological invasions , Marine resources conservation -- South Africa
- Description: In South Africa, the indigenous mussel Perna perna is threatened by both an invasive species and excessive human exploitation. The Mediterranean mussel Mytilus galloprovincialis is an invasive species that has been introduced to many parts of the world. In South Africa, this species arrived in the 1970s and spread rapidly along the west coast where today it is the dominant mussel species. Along the west coast, M. galloprovincialis is competitively superior in all aspects to the indigenous mussel species, and, as a result, has displaced some of them. On the south coast, M. galloprovincialis found more oligotrophic waters, higher species richness, and a stronger competitor in the indigenous mussel P. perna. The rate of spread of M. galloprovincialis along the south coast has decreased over the last 10 years and the present eastern limit of its distribution in South African is East London. On the south coast, M. galloprovincialis has not yet completely replaced P. perna; instead, the two exhibit spatial segregation, with P. perna dominating the low shore, M. galloprovincialis the high shore and an overlap zone between the two. An experiment on competition was carried out at one site on the south coast. The results showed that, on the low shore, P. perna is a more dominant competitor for space than M. galloprovincialis. Also byssus attachment of the two species differs, P. perna being much stronger than M. galloprovincialis, which suffers high mortality due to wave action on the low shore, especially in monospecific beds. As a result, mortality of M. galloprovincialis through wave action is reduced by the presence of P. perna, which seems to confer protection against dislodgement. However, in the absence of strong wave action, P. perna competitively excludes M. galloprovincialis. Human exploitation along 160 km of coast was examined by sampling mussel populations and using aerial surveys to determine where harvesters were distributed. Collectors did not seem to discriminate between species. The study has shown that higher abundances of mussels were found in protected or inaccessible sites, while in unprotected sites mussels were scarce. Coastal nature reserves are being proven to be effective in protecting mussel populations.
- Full Text:
- Date Issued: 2005
- Authors: Rius Viladomiu, Marc
- Date: 2005
- Subjects: Mussels -- South Africa , Perna -- South Africa , Mytilus galloprovincialis -- South Africa , Mytilidae -- South Africa , Biological invasions , Marine resources conservation -- South Africa
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5684 , http://hdl.handle.net/10962/d1005370 , Mussels -- South Africa , Perna -- South Africa , Mytilus galloprovincialis -- South Africa , Mytilidae -- South Africa , Biological invasions , Marine resources conservation -- South Africa
- Description: In South Africa, the indigenous mussel Perna perna is threatened by both an invasive species and excessive human exploitation. The Mediterranean mussel Mytilus galloprovincialis is an invasive species that has been introduced to many parts of the world. In South Africa, this species arrived in the 1970s and spread rapidly along the west coast where today it is the dominant mussel species. Along the west coast, M. galloprovincialis is competitively superior in all aspects to the indigenous mussel species, and, as a result, has displaced some of them. On the south coast, M. galloprovincialis found more oligotrophic waters, higher species richness, and a stronger competitor in the indigenous mussel P. perna. The rate of spread of M. galloprovincialis along the south coast has decreased over the last 10 years and the present eastern limit of its distribution in South African is East London. On the south coast, M. galloprovincialis has not yet completely replaced P. perna; instead, the two exhibit spatial segregation, with P. perna dominating the low shore, M. galloprovincialis the high shore and an overlap zone between the two. An experiment on competition was carried out at one site on the south coast. The results showed that, on the low shore, P. perna is a more dominant competitor for space than M. galloprovincialis. Also byssus attachment of the two species differs, P. perna being much stronger than M. galloprovincialis, which suffers high mortality due to wave action on the low shore, especially in monospecific beds. As a result, mortality of M. galloprovincialis through wave action is reduced by the presence of P. perna, which seems to confer protection against dislodgement. However, in the absence of strong wave action, P. perna competitively excludes M. galloprovincialis. Human exploitation along 160 km of coast was examined by sampling mussel populations and using aerial surveys to determine where harvesters were distributed. Collectors did not seem to discriminate between species. The study has shown that higher abundances of mussels were found in protected or inaccessible sites, while in unprotected sites mussels were scarce. Coastal nature reserves are being proven to be effective in protecting mussel populations.
- Full Text:
- Date Issued: 2005
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