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).

"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"-- / Typescript / "June, 1920" / M.A. Florida State College for Women / Includes bibliographical references (leaves 89-91)

Thesis (M.Ed.)--University of Hong Kong, 1984. / Includes bibliographical references (leaf 81-85). Also available in print.

Thesis (M.A.)--University of California, Santa Cruz, 1992. / Typescript. Includes bibliographical references (leaves 77-80).

No description available.

MSc Research Project. July 2013. / This study focuses on understanding the strategies used by a sample of high ability and low ability Grade 2 learners drawn from two government primary schools in Gauteng, with emphasis on more concrete or more abstract strategies learners use to solve early number problems. This study takes place against the backdrop of poor performance in South African schools more especially across the foundation phase and also amidst claims that learners remain largely dependent on concrete strategies for solving problems. The theoretical background for this study is drawn from Sfard’s (1992) “Dual Nature of Mathematical Conceptions” and also Sfard’s (1992) theory of reification. I used on a wide range of literature on strategies for counting, addition, subtraction within my analysis of nine videos of high ability learners and 9 videos of low ability learners with the aim of examining the strategies these learners use when dealing with early number concepts. My findings pointed to the limited use of higher levels of abstraction in solving early number problems. Whilst there is progression from the concrete to the abstract levels of conception this is not happening at a pace and depth that is required for Foundation Phase learners in order for them to effectively engage with more challenging and complicated arithmetic in the Intermediate Phase.

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

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

No description available.