Various researchers have indicated the importance of graphs in physical sciences and the difficulties that learners may experience with graphs. More specifically, learners’ problems with motion graphs have been reported in literature. Learners’ difficulty in the application of basic concepts in graphs to solve kinematics graphs problems leads to underperformance in physical sciences. Their ability to handle problems in kinematics graphs is enhanced if they have an effective knowledge base or conceptual resources on graphs. In South Africa there seems to be a gap between the GET [General Education and Training] and FET [Further Education and Training] band’s requirements on graphs. A smooth learning progression is needed. For this reason this study selected to investigate the conceptual resources acquired by grade 10 learners from grade 9 that can be used productively for the learning of kinematics graphs in grade 10. The primary aim of the study was to determine and analyse grade 10 learners’ conceptual resources for learning kinematics graphs in physical sciences. The use of a mixed method approach was considered appropriate for this study. The mixed method depended on the quantitative method to produce precise and measurable data, while a qualitative method was to enhance the understanding of the data produced by the quantitative method. Data obtained by quantitative methods was drawn into tables and graphs, and the consistency in responses determined. Patterns and trends in learners’ reasoning were probed with the aid of qualitative method. In the study it was reported that the quantitative data in the form of a questionnaire was completed by 201 learners. Qualitative data was also obtained by interviewing three learners with varying abilities. The results showed that many learners could answer mathematics questions, but struggled with similar questions in kinematics. The results further showed that the learners did not answer the questionnaire consistently, but their responses depended on the context of the questions. In the interviews learners used everyday applications to explain scientific concepts, instead of using scientific principles. Still, some of the everyday applications may be used as resources for teaching the science concepts. From the results it can be deduced that learners’ conceptual resources can influence their understanding of kinematics graphs in physics. These resources are gained from everyday experiences and previous learning in mathematics and the natural sciences. A constraint is that many learners do not efficiently integrate their mathematics and physics knowledge. iv In the study some learners did not transfer their mathematics knowledge to physics, while others could not transfer their physics knowledge to mathematics. From the results recommendations can be made for the teaching of graphs in the GET band for easier progress into the FET band. The strategy to improve understanding of kinematics graphs is to progressively integrate mathematics and physics from grade nine. Line graphs should be treated in more detail in grade 9 to form proper conceptual resources for kinematics graphs in grade ten. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

Various researchers have indicated the importance of graphs in physical sciences and the difficulties that learners may experience with graphs. More specifically, learners’ problems with motion graphs have been reported in literature. Learners’ difficulty in the application of basic concepts in graphs to solve kinematics graphs problems leads to underperformance in physical sciences. Their ability to handle problems in kinematics graphs is enhanced if they have an effective knowledge base or conceptual resources on graphs. In South Africa there seems to be a gap between the GET [General Education and Training] and FET [Further Education and Training] band’s requirements on graphs. A smooth learning progression is needed. For this reason this study selected to investigate the conceptual resources acquired by grade 10 learners from grade 9 that can be used productively for the learning of kinematics graphs in grade 10. The primary aim of the study was to determine and analyse grade 10 learners’ conceptual resources for learning kinematics graphs in physical sciences. The use of a mixed method approach was considered appropriate for this study. The mixed method depended on the quantitative method to produce precise and measurable data, while a qualitative method was to enhance the understanding of the data produced by the quantitative method. Data obtained by quantitative methods was drawn into tables and graphs, and the consistency in responses determined. Patterns and trends in learners’ reasoning were probed with the aid of qualitative method. In the study it was reported that the quantitative data in the form of a questionnaire was completed by 201 learners. Qualitative data was also obtained by interviewing three learners with varying abilities. The results showed that many learners could answer mathematics questions, but struggled with similar questions in kinematics. The results further showed that the learners did not answer the questionnaire consistently, but their responses depended on the context of the questions. In the interviews learners used everyday applications to explain scientific concepts, instead of using scientific principles. Still, some of the everyday applications may be used as resources for teaching the science concepts. From the results it can be deduced that learners’ conceptual resources can influence their understanding of kinematics graphs in physics. These resources are gained from everyday experiences and previous learning in mathematics and the natural sciences. A constraint is that many learners do not efficiently integrate their mathematics and physics knowledge. iv In the study some learners did not transfer their mathematics knowledge to physics, while others could not transfer their physics knowledge to mathematics. From the results recommendations can be made for the teaching of graphs in the GET band for easier progress into the FET band. The strategy to improve understanding of kinematics graphs is to progressively integrate mathematics and physics from grade nine. Line graphs should be treated in more detail in grade 9 to form proper conceptual resources for kinematics graphs in grade ten. / MEd (Natural Sciences Education), North-West University, Potchefstroom Campus, 2014

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)