Young children's ideas about number words and scripts and the connection with their progress in arithmetic

Abstract

This thesis is concerned with the learning of the conventional system of decimal numeration by children in the earliest years of school. Conforming to a constructivist view of learning it has the premise that young children elaborate early ideas on how conventional number words and numerals are organised. A basic tenet of this thesis is that external systems of spoken and written numeration have to be acted upon to be known by a child.

More than one decade ago Sinclair and Sinclair (1984) set forth the question about the possible links between the knowledge that pre-school children develop about written numerals in their environment and the development of number concepts. The findings and conclusions of this thesis advance some answers to the above question. Following a longitudinal investigation with two lines of study this research set out to explore children's theories on written and spoken numeration and how these theories might affect their progress in arithmetical knowledge. The first line of study interpreted children's progress in arithmetic according to an established constructivist model of stages of conceptualisation. The second line of study explored children's ideas upon number words and numerals and their possible transformation during the investigation. Nine case studies were selected from a reception class of a school in the South of England - 4 to 5 year-old children. The fieldwork was conducted in two stages during a one-year-long investigation. Findings revealed that children's conjectures on written and spoken numeration are established and reorganised towards increasing compatibility with conventional numeration. Second, findings of this study suggest that children's reasoning in arithmetic becomes increasingly sophisticated due to two systems of constructions that they start establishing from an early age. One system concerns their reflections on their actions of counting and the other concerns their abstractions of a system of spoken and written signs in social use. Although these two systems of constructions are initially separate, they integrate to empower children's growing sophistication in mathematics.

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