An investigation into children's developing mathematical abilities

Master Thesis


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University of Cape Town

This study examines children's developing mathematical abilities during the first three years of their schooling. More particularly, children in grades one, two and three of three different primary schools, in two different regions, had their performances on eleven mathematics tasks monitored over the course of 1996 to examine their developing mathematical abilities. These abilities were investigated in terms of task-particular performances and the assumed competencies (internal mental processes) underlying these performances. The data was generated through the use of a repeated measures design. The theory of the methods used to gather the data and to analyse the results is rooted in Vygotsky's (1978) experimental-developmental approach to the study of higher mental functions. This method of observation proved to be successful to the degree that it allowed for the study of changes in children's performances over a seven month period. The overall findings of the study revealed that the subjects in the sample population had the developmental readiness with which to improve their mathematical abilities. However, when this developmental readiness had to be taken further through formal instruction, their performances were inadequate. The investigation exposed the complexity and importance of language in the successful development of mathematical concepts. The data indicated that the subjects' learning was neither in advance of their development nor was it indicative of the constructivist approach to the task of teaching. Furthermore, there existed a conflict between spontaneous and formal knowledge in engaging with school mathematics tasks.

Bibliography: pages 83-85.