The purpose of this study is to focus on constructing a modelling-based learning environment to improve learner performance in grade 6 mathematics classrooms. The purpose emanates from the continued poor performance of learners in mathematics at different school levels, especially grade 6. The teaching and learning of mathematics is explained from an ontological point of departure, focussing on constructivist paradigms. Different types of constructivism are discussed with special attention to the school mathematics domain. The learning, problem based learning, problem solving and learning environment are key components in the discussion. A theoretical perspective on the design of modelling as a powerful learning environment in primary schools mathematics classrooms is provided. Focus is placed on the applicability of the modelling-based learning environment on the South African mathematics curriculum and on study orientation as a key component to help develop an understanding of why learners perform or do not perform in mathematics. A mixed method research design, in which quantitative and qualitative are combined to achieve the outcomes of the research problem, is chosen for this research study project to provide a purposeful research framework. The findings of the research include not only learners’ improvement in dealing with non-routine, mathematical word problems but also in general-routine, mathematical word problems. A second finding shows that the overall SOM pre/post/retention showed good reliability, acceptable construct validity, good practical significance, and large effect but had low to medium effect in individual fields. The univariate analysis for the Crossover design used indicated that the problem solving field had statistical significance and practical significance, and the study milieu and mathematical confidence field might have statistical significance and practical significance. The third finding provided evidence concerning teacher administration, teacher and learner interaction, assessment and homework. The findings from the quantitative and qualitative data-analysis and interpretations, and literature review, guided the researcher in proposing a construct for a modelling-based learning environment as a means to improve learners’ mathematics performance in grade 6 mathematics classes in the John Toalo Gaetswe (JTG) District. The contribution that this study makes is to propose a construct for a modelling-based learning environment to improve learner performance in grade 6 mathematics. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

The purpose of this study is to focus on constructing a modelling-based learning environment to improve learner performance in grade 6 mathematics classrooms. The purpose emanates from the continued poor performance of learners in mathematics at different school levels, especially grade 6. The teaching and learning of mathematics is explained from an ontological point of departure, focussing on constructivist paradigms. Different types of constructivism are discussed with special attention to the school mathematics domain. The learning, problem based learning, problem solving and learning environment are key components in the discussion. A theoretical perspective on the design of modelling as a powerful learning environment in primary schools mathematics classrooms is provided. Focus is placed on the applicability of the modelling-based learning environment on the South African mathematics curriculum and on study orientation as a key component to help develop an understanding of why learners perform or do not perform in mathematics. A mixed method research design, in which quantitative and qualitative are combined to achieve the outcomes of the research problem, is chosen for this research study project to provide a purposeful research framework. The findings of the research include not only learners’ improvement in dealing with non-routine, mathematical word problems but also in general-routine, mathematical word problems. A second finding shows that the overall SOM pre/post/retention showed good reliability, acceptable construct validity, good practical significance, and large effect but had low to medium effect in individual fields. The univariate analysis for the Crossover design used indicated that the problem solving field had statistical significance and practical significance, and the study milieu and mathematical confidence field might have statistical significance and practical significance. The third finding provided evidence concerning teacher administration, teacher and learner interaction, assessment and homework. The findings from the quantitative and qualitative data-analysis and interpretations, and literature review, guided the researcher in proposing a construct for a modelling-based learning environment as a means to improve learners’ mathematics performance in grade 6 mathematics classes in the John Toalo Gaetswe (JTG) District. The contribution that this study makes is to propose a construct for a modelling-based learning environment to improve learner performance in grade 6 mathematics. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014