Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)




Dr. Linda Siegel


This thesis explores various aspects of young children's concepts of number and length. The intentions of the author were: to examine some of the factors which affect young children's choices of quantitative strategies; to explore their understanding of comparative terms such as "longer" and "more"; to consider some questions about the nature of concepts and cognitive development.

The first part of the introduction describes theories of number, both formal and psychological, with particular emphasis on Piaget's theory of number. Six main issues are derived from the theories. The author argues that these issues might all benefit from a research paradigm in which the young child's concept of number is studied in conjunction with his concept of length. For example, most number theorists assign the small numbers in the natural number series a unique status. The author argues that while it is possible that small number of elements will enable numerical operations, they may make length operations more difficult when they are arranged in a linear formation. This can only be determined by asking the child to evaluate both number and length on the same stimulus arrays. The next three sections of the introduction review previous research relevant to: factors influencing children's choice of strategy; the nature of their understanding of quantitative terms; theories of concept acquisition and cognitive development. The final section restates the six main theoretical issues in light of previous research findings.

The second chapter presents six experiments. In all these experiments the author asks young children between three and seven to make judgments of the equivalence of the number and length of two rows of elements. However, in each experiment different aspects of the task are varied, amongst them: the set size; training; the means of presentation of the rows; the nature of the terms used, whether positive, for example "more", or negative, for example "less"; presentation of two or three dimensional arrays.

The major finding of the research is that some children consistently employ a length strategy to judge both number and length; other children consistently employ a number strategy to judge both number and length. These strategy biases can be altered through changes in task variables such as set size and training. For example, small sets produce a number bias, large sets a length bias. Strategy biases also occur in response to negative terms such as "shorter", and on three dimensional as well as two dimensional arrays.

In the final chapter the author discusses the implications of the research findings for the six main issues outlined in the introduction. The author concludes that children's early quantity concepts are multidimensional. Initially the child may begin with a superordinate concept of bigness. In the course of cognitive development the child acquires various plans for discriminating dimensions, estimating quantitatives, and differentiating situations appropriate to the application of these strategies. In the absence of appropriate plans for any of the above, the child may substitute inappropriate plans in some consistent fashion. The inappropriate, consistently applied plans account for systematic strategy errors. In the course of time and experience these plans come to act as referents for the linguistic system. The author also concludes that, while some of Piaget's insights and theoretical arguments have been invaluable in aiding psychologists' understanding of the development of quantity concepts, various aspects of his theories such as the notion of centering and the role of transformation in the development of conservation, require further specification or modification.

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