At-risk student teachers’ attitudes and aspirations as learners and teachers of mathematics

This study explored foundation phase first year student teachers’ perceptions about mathematics. The focus on their attitudes towards mathematics in two roles – (1) as learners of mathematics, based on their prior experiences at school and (2) as aspirant teachers of mathematics for children in the early grades. Data sources were students’ drawings/collages as well as written interpretations and elaborations of the drawings/collages. The findings indicated that participants had generally negative attitudes towards the learning of mathematics. Factors such as the transition from primary to high school, teacher qualities and mathematics-related anxiety contributed to the shaping of their attitudes. It was encouraging to note that over half the participants expressed positive attitudes in their roles as future teachers, with all expressing the desire to provide better mathematics experiences to their future learners.IBS

Teaching and learning about whole numbers in primary school

This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.</p