Die doel van hierdie verhandeling is om 'n algoritme vir kleinstekwadrate-benaderings te vind en om met behulp van die algoritme 'n rekenaarprogram te ontwikkel vir die minimering van die kleinstekwadrate- benadering en die passings van krommes deur gegewe eksperimentele data. Eerstens word die norm en die pseudo-inverse van matrikse sowel as Householder-transformasies bespreek, aangesien ons daarvan gebruik maak in die oplossing van ons probleem. In die lineere kleinstekwadrate-probleem word die koeffisiente matriks A ontbind in 'n produk van 'n ortogonale en 'n bo-driehoeksmatriks. Hierdie produk word dan gebruik om die pseudo-inverse van A te verkry. Die algoritme wat ontwikkel is vir die nie-lineere kleinstekwadrate- probleem is gebaseer op die Gauss-Newton-Marquardt-metode, waar met elke stap 'n lineere kleinstekwadrate-probleem opgelos word. Resultate wat met behulp van die algoritme verkry is, word ook vergelyk met die resultate van ander algoritmes. / Dissertation (MSc)--University of Pretoria, 1977. / gm2014 / Mathematics and Applied Mathematics / Unrestricted

The reading skill is the most important skills for the 21st century. The Progress in International Reading Literacy Study (PIRLS) found that nearly 80% of South African students haven’t mastered the basic reading skills at Grade 5 level. If the learner hasn’t mastered the skill of reading, his/her progression at school will be severely inhibited and learning problems will result. Reading consists of certain basic skills, namely receiving messages, perceptual skills, decoding the message and learning. A reading programme that stimulates the learner visually, auditory and tactually promotes learning and memory, is the key to reading success. There are a variety of reading methods, but in the scope of this study the multisensory reading approach is regarded as the most suitable reading approach for the Foundation Phase. The literacy study found that the human being is a multisensory creature that uses all senses to explore his/her environment. Multisensory approaches to learning have been applied with success to learners for longer than a century and are supported by the latest neuro images scientific research. During a multisensory approach, the emphasis is on phonological awareness, decoding, spelling and comprehension. In this study, the Orton-Gillingham approach is used where sounds are linked with the written symbol through visual, auditory and tactile stimuli. A quantitative pre-experimental two group pre-test, post-test research design was followed. 42 Grade 2 Afrikaans-speaking students participated in the intervention programme. The degree to which the students reading improved in the five week period determined to which extent the intervention programme influenced the reading abilities of the learners. The data analysis of pre-and post-reading revealed that after application of the multisensory reading programme a significant improvement regarding reading speed, word recognition and reading comprehension occurred. / Thesis (M.Ed.)--North-West University, Vaal Triangle Campus, 2011

The reading skill is the most important skills for the 21st century. The Progress in International Reading Literacy Study (PIRLS) found that nearly 80% of South African students haven’t mastered the basic reading skills at Grade 5 level. If the learner hasn’t mastered the skill of reading, his/her progression at school will be severely inhibited and learning problems will result. Reading consists of certain basic skills, namely receiving messages, perceptual skills, decoding the message and learning. A reading programme that stimulates the learner visually, auditory and tactually promotes learning and memory, is the key to reading success. There are a variety of reading methods, but in the scope of this study the multisensory reading approach is regarded as the most suitable reading approach for the Foundation Phase. The literacy study found that the human being is a multisensory creature that uses all senses to explore his/her environment. Multisensory approaches to learning have been applied with success to learners for longer than a century and are supported by the latest neuro images scientific research. During a multisensory approach, the emphasis is on phonological awareness, decoding, spelling and comprehension. In this study, the Orton-Gillingham approach is used where sounds are linked with the written symbol through visual, auditory and tactile stimuli. A quantitative pre-experimental two group pre-test, post-test research design was followed. 42 Grade 2 Afrikaans-speaking students participated in the intervention programme. The degree to which the students reading improved in the five week period determined to which extent the intervention programme influenced the reading abilities of the learners. The data analysis of pre-and post-reading revealed that after application of the multisensory reading programme a significant improvement regarding reading speed, word recognition and reading comprehension occurred. / Thesis (M.Ed.)--North-West University, Vaal Triangle Campus, 2011

The aim of the study was to investigate and describe how the mother in the home school fulfils her role as a teacher for her child in the foundation phase. The literature review confirmed that mothers choose to home school their children for various reasons, and use different approaches in home schooling. The home school teacher as well as the home school learner have certain responsibilities to fulfil, which bring about certain challenges that they have to face. An evaluation of home schooling showed various concerns regarding these learners’ performance and development, especially scholastically and socially. Unstructured interviews were conducted with selected mothers to explore their perceptions of their role as a teacher, the degree of differentiation between their mother and teacher roles, and the execution of their roles. An analysis of the home school learners’ schoolbooks was done, focusing on the input and feedback of the mother teacher. The researcher’s observations and reflections were included in the analysis. Findings: · The mothers do not differentiate between their mother and teacher role. · Their teaching was influenced by their own experiences, their views on teaching and learning and their views on the roles they fulfil in the home school. · Each home school situation is unique and the mothers’ perceptions of the roles they fulfil and the execution thereof differ greatly and are influenced by the context in which the home schooling takes place. / Dissertation (MEd (Educational Psychology))--University of Pretoria, 2006. / Educational Psychology / unrestricted