This longitudinal study tracks how 5- to 7-year-olds perform with early number skills. The aim of this study is to diagnose at-risk mathematics students by distinguishing the skills that, if not mastered by the end of Kindergarten, lead to greater difficulty in mathematics in 1st grade. This study’s methodology is mixed as it follows an exploratory and inductive path in light of its use of a hypothesis, an interpretive path in light of its interest in the individual student, and a positivist path in light of its focus on developing rules from analyzed data. An oral diagnostic test based on a comprehensive collection of early number skills was used to test students as Kindergarteners and again as 1st graders. The test results created benchmarks, revealing how the majority of the students performed with early number skills. The test results also revealed that each early number skill is highly, moderately, or minimally predictive in terms of student placement by the end of 1st grade. When comparing the individual skill scores of each Kindergarten student to his/her total test results of 1st grade, the predictive power of each skill emerged. Performing poorly with skills that are minimally predictive did not seem to have an impact on how the Kindergarten student finished in 1st grade; performing poorly with moderately predictive skills had a greater impact on 1st grade placement; performing poorly with highly predictive skills in Kindergarten increased the likelihood that the student would finish in the lower attaining group in 1st grade. A third result of the test showed that certain skills serve as preconditions for other skills; success with certain skills usually meant success with other skills. These connections between skills point to a learning model called in this study “simultaneous pathways,” indicating that there are connections between certain skills, and that students can be learning on several pathways simultaneously. The impact of the predictive power of early number skills is that diagnosis becomes more effective. Early diagnosis means early remediation which may prevent at-risk students from falling further behind their peers. The benchmarks developed by this research will help teachers assess their students because they will know the general skill level of Kindergarteners and 1st graders. This oral diagnostic test informs curriculum development. If test results show that students are missing the skills that are highly predictive, teachers can address those gaps in order to insure mastery.

Text in Afrikaans / Die doel van hierdie navorsing is, om te bepaal of gesyferdheid by kleuters binne `n speelgroepsituasie ontwikkel kan word deur middel van `n program wat wiskundige konsepte aan kleuters oordra. Ten einde hierdie doel te bereik is `n wiskunde program waarin verskillende hulpmiddels gebruik word, vir die kleuters aangebied. Die wiskunde program wat gebruik is, is saamgestel aan die hand van Charner, Murphy en Clark (2007) se “The Giant Encyclopedia of Math Activities for Children 3 to 6”. Die aktiwiteite wat tydens die voortoets en natoets gebruik is, is uit verskillende bronne op die internet verkry. Die aktiwiteite is uit gemelde bronne geneem en aangepas om by kleuters se ontwikkelingsvermoë te pas. Aan die einde van die wiskunde program kon daar `n verbetering in al die leerders se wiskunde vaardighede waargeneem word. Die resultate van die studie dui dus daarop dat kleuters se begrip en vaardigheid met wiskundige konsepte op `n vroeë ouderdom in `n speelgroep ontwikkel kan word. / The aim of this study was to determine whether numeracy can be developed among preschoolers in `n playgroup situation by means of a numeracy programme which introduces them to mathematical concepts. To achieve this aim a numeracy programme was used to introduce the mathematical concepts. The numeracy programme that was used is a programme compiled from “The Giant Encyclopedia of Math Activities for Children 3 to 6” by Charner, Murphy and Clark (2007). The activities which were used during the pre-test and post-test were taken from different sources on the internet. The activities taken from these different sources were adapted to the appropriate developmental phase of the preschoolers. At the end of the programme the post-test indicated an improvement in the mathematical competence of all the learners. The results of the study prove that preschoolers in a playgroup can improve their numeracy skills in the early years. / Teacher Education / M. Ed. (Didaktiek)

Text in Afrikaans / Die doel van hierdie navorsing is, om te bepaal of gesyferdheid by kleuters binne `n speelgroepsituasie ontwikkel kan word deur middel van `n program wat wiskundige konsepte aan kleuters oordra. Ten einde hierdie doel te bereik is `n wiskunde program waarin verskillende hulpmiddels gebruik word, vir die kleuters aangebied. Die wiskunde program wat gebruik is, is saamgestel aan die hand van Charner, Murphy en Clark (2007) se “The Giant Encyclopedia of Math Activities for Children 3 to 6”. Die aktiwiteite wat tydens die voortoets en natoets gebruik is, is uit verskillende bronne op die internet verkry. Die aktiwiteite is uit gemelde bronne geneem en aangepas om by kleuters se ontwikkelingsvermoë te pas. Aan die einde van die wiskunde program kon daar `n verbetering in al die leerders se wiskunde vaardighede waargeneem word. Die resultate van die studie dui dus daarop dat kleuters se begrip en vaardigheid met wiskundige konsepte op `n vroeë ouderdom in `n speelgroep ontwikkel kan word. / The aim of this study was to determine whether numeracy can be developed among preschoolers in `n playgroup situation by means of a numeracy programme which introduces them to mathematical concepts. To achieve this aim a numeracy programme was used to introduce the mathematical concepts. The numeracy programme that was used is a programme compiled from “The Giant Encyclopedia of Math Activities for Children 3 to 6” by Charner, Murphy and Clark (2007). The activities which were used during the pre-test and post-test were taken from different sources on the internet. The activities taken from these different sources were adapted to the appropriate developmental phase of the preschoolers. At the end of the programme the post-test indicated an improvement in the mathematical competence of all the learners. The results of the study prove that preschoolers in a playgroup can improve their numeracy skills in the early years. / Teacher Education / M. Ed. (Didaktiek)

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)