In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.

In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.

Text in Afrikaans / Die doel van hierdie navorsing was om vas te stel of leerders in Graad R die nodige wiskundige vaardighede deur gestruktureerde spel bemeester het wat as grondslag vir verdere wiskunde-onderrig kan dien. In die literatuurstudie is die verskillende wiskunde konsepte in diepte ondersoek. Daar is ook gefokus op die oordra van wiskunde konsepte aan jong leerders. Verder is daar in die literatuurstudie ondersoek ingestel na die doel, waardes, tipes, ontwikkeling van spel asook spel in die moderne era. Vir die empiriese ondersoek is 103 Graad R-leerders van ses verskillende skole betrek. Daar is gebruik gemaak van ʼn ewekansige steekproef by die skole wat bereid was om aan die studie deel te neem. Die ondersoek het plaasgevind deur die gebruik van die positivistiese kwantitatiewe navorsingsmetode. Daar is gebruik gemaak van vraelyste om te bepaal wat die bemeestering van wiskundige vaardighede by Graad R-leerders is. Gestruktureerde spel is as hulpmiddel gebruik vir die insameling van die navorsingsmateriaal. Die resultate is bekom deur die vraelyste statisties te verwerk. Daar is ook vraelyste aan die onderwysers gegee om meer agtergrond oor hulle onderrigmetodes asook die onderwysers se eie gevoel teenoor en kennis van wiskunde te bekom. Die navorsingsresultate bevestig dat die meerderheid van die Graad R-leerders oor ʼn goeie wiskundige grondslag beskik. Dus is daar deur die studie gevind dat dit belangrik is dat jong kinders baie moet speel om nuwe vaardighede aan te leer, maar ook die geleentheid moet hê om die vaardighede te beoefen. / The purpose of this research was to determine whether learners in Grade R mastered the necessary math skills through structured play that could serve as a basis for further mathematics training. In the literature various math concepts were studied in depth. The main focus was on the transfer of math concepts to young learners. The literature study further focussed on the purpose, values, and types of play, development of play and play in the modern era. An empirical study using random sampling was done using 103 Grade R learners from six different schools who were willing to participate in the study. The study was done using the positivism quantitative research methodology. Questionnaires were used to determine the mastery of mathematical skills by Grade R learners. Structured play was used as a tool to collect the research material. The results were obtained by processing the questionnaires statistically. Questionnaires were also completed by the teachers to confirm their background knowledge, teaching methods as well as to determine the teachers‟ own feelings towards and their knowledge of mathematics. The research results confirm that the majority of Grade R learners have obtained a good math foundation. The study also confirmed that it is important that young children need to play to learn new skills and must have the opportunity to practise the new skills. / Psychology of Education / D. Ed. (Sielkundige Opvoedkunde)

Text in Afrikaans / Die doel van hierdie navorsing was om vas te stel of leerders in Graad R die nodige wiskundige vaardighede deur gestruktureerde spel bemeester het wat as grondslag vir verdere wiskunde-onderrig kan dien. In die literatuurstudie is die verskillende wiskunde konsepte in diepte ondersoek. Daar is ook gefokus op die oordra van wiskunde konsepte aan jong leerders. Verder is daar in die literatuurstudie ondersoek ingestel na die doel, waardes, tipes, ontwikkeling van spel asook spel in die moderne era. Vir die empiriese ondersoek is 103 Graad R-leerders van ses verskillende skole betrek. Daar is gebruik gemaak van ʼn ewekansige steekproef by die skole wat bereid was om aan die studie deel te neem. Die ondersoek het plaasgevind deur die gebruik van die positivistiese kwantitatiewe navorsingsmetode. Daar is gebruik gemaak van vraelyste om te bepaal wat die bemeestering van wiskundige vaardighede by Graad R-leerders is. Gestruktureerde spel is as hulpmiddel gebruik vir die insameling van die navorsingsmateriaal. Die resultate is bekom deur die vraelyste statisties te verwerk. Daar is ook vraelyste aan die onderwysers gegee om meer agtergrond oor hulle onderrigmetodes asook die onderwysers se eie gevoel teenoor en kennis van wiskunde te bekom. Die navorsingsresultate bevestig dat die meerderheid van die Graad R-leerders oor ʼn goeie wiskundige grondslag beskik. Dus is daar deur die studie gevind dat dit belangrik is dat jong kinders baie moet speel om nuwe vaardighede aan te leer, maar ook die geleentheid moet hê om die vaardighede te beoefen. / The purpose of this research was to determine whether learners in Grade R mastered the necessary math skills through structured play that could serve as a basis for further mathematics training. In the literature various math concepts were studied in depth. The main focus was on the transfer of math concepts to young learners. The literature study further focussed on the purpose, values, and types of play, development of play and play in the modern era. An empirical study using random sampling was done using 103 Grade R learners from six different schools who were willing to participate in the study. The study was done using the positivism quantitative research methodology. Questionnaires were used to determine the mastery of mathematical skills by Grade R learners. Structured play was used as a tool to collect the research material. The results were obtained by processing the questionnaires statistically. Questionnaires were also completed by the teachers to confirm their background knowledge, teaching methods as well as to determine the teachers‟ own feelings towards and their knowledge of mathematics. The research results confirm that the majority of Grade R learners have obtained a good math foundation. The study also confirmed that it is important that young children need to play to learn new skills and must have the opportunity to practise the new skills. / Psychology of Education / D. Ed. (Sielkundige Opvoedkunde)