Thesis (Ph. D.)--University of Chicago, Department of Education. / A Dissertation, submitted to the Faculty of the Graduate School of Arts and Literature, in candidacy for the Degree of Doctor of Philosophy, Department of Education. Includes bibliographical references.

Thesis (Ph. D.)--Columbia University, 1940. / "Lithoprinted." Bibliography: p. 195-199.

Thesis (M. Phil.)--University of Hong Kong, 2009. / Includes bibliographical references (p. 112-117). Also available in print.

This dissertation sought to explore dimensions of preschooler conceptual awareness of the principles of counting. The study derived its focus from the research of Rochel Gelman and, in particular, the principles of counting she purports are implicitly understood by young children. Their frequent inability to manifest this awareness in their counting performances is explained as resulting from their susceptibility to task demands. This study explores this position by seeking to facilitate performance in order that conceptual understanding might be more apparent. The sample for this study consisted of 40 children (20 aged 3 years 3 months-3 years 9 months; 20 aged 4 years 3 months-4 years 9 months) selected randomly from a cross section of preschool and day-care centers in Adelaide, South Australia. Phase 1 of the study explored the impact of a procedure which allowed for children to receive both visual and tactile feedback on their counting behavior on array sizes ranging from 2 to 19. The results show conclusively that this self-monitoring technique significantly improved counting performances for both age groups. In doing so it lends support to the Gelman hypothesis that conceptual awareness of the 'how-to' count principles can be masked by task demands. Phase 2 of the study looked at the complex 'order-irrelevance' principle. The results suggest that preschoolers understand that items can be counted in any order before they appreciate that this has no impact on cardinal value. The extreme susceptibility of preschoolers to variations in task demands necessitates further exploration of design and analysis parameters.

"Number is one of man's schemes for adapting himself to his environment. Development of the concept of number in man is intricately bound up with growth in him of language. Man is a social being and almost from birth, language activity becomes a part of his reactions to stimuli. He is therefore apt to use a partial language response even when the stimulus does not come from a strictly social setting"--Introduction. / Typescript. / "June, 1920." / Includes bibliographical references (leaves 89-91).

Thesis (Ph. D.)--Columbia University. / "Being vol. XIII, no. 1, of Columbia university contributions of philosophy, psychology and education. The results, of this research were presented before the Section of anthropology and psychology of the New York academy of sciences, and the monograph is published under the auspices of the Academy."

This study investigated domains within the tasks of ordination, cardination and natural number. In addition, it examined the sequencing of the development of established domains between ordination, cardination and natural number. One hundred and forty-eight children were individually given a test designed to ascertain the presence of arithmetic related skills. The task of cardination was designed to detect the ability to associate numbers with sets containing a group of elements ranging from one to five. The task of ordination was designed to detect the ability to associate a number with a relative position within a group of ordered objects. The task of natural number assessed children's ability to add numbers with a sum equal to five or less. Latent structure analysis was used to analyze the results. Four different models were used in order to establish domains within each task. The four models that were used tested independence, equiprobability, ordered relations and asymmetrical equivalence. The results showed two domains for cardination. One item in a set constituted one domain while three and five items in a set constituted a second domain. The domain for ordination included relative positions one, three and five. In regards to natural number, the results showed a permeable domain. There was some indication of ordering but it was not strong enough to yield separate domains. The same models were then used to compare across the different tasks. The results showed that the easiest cardination domain developed before ordination and natural number. The results also showed that the ordination task was equivalent to one of the natural number tasks. All of the other comparisons between cardination, ordination and natural number yielded asymmetrically equivalent relations. That is, there was an ordering but the ordering was not strong enough to establish separate domains.

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Thesis (Ph. D.)--Columbia University. / "Being vol. XIII, no. 1, of Columbia university contributions of philosophy, psychology and education. The results, of this research were presented before the Section of anthropology and psychology of the New York academy of sciences, and the monograph is published under the auspices of the Academy."