This thesis presents an analysis of a learning situation of positive and negative integers. It is considered as a case study within the more general context of the development of school learning analysis tools based on cognitive psychology. An analysis of error patterns obtained from a group of 55 secondary I level students has shown: (1) that the acquisition of the integer concept can imply several levels of integration of the sign and the numerical aspect; (2) that the set of all possible addition and subtraction items can be classified according to their possibility of being related to previous numerical knowledge; (3) that errors in addition and subtraction can be explained by either the utilisation of previous knowledge that was contrary to what was taught, or by systematic transformations of the procedures that were taught, or by problems with the integer concept. The thesis ends with a discussion of the properties of an information processing system that could generate the observed performances, and of the pedagogical implications of that kind of analysis.

The development of numerical skills in children with Down syndrome is an area of research that has been neglected in the literature despite overwhelming evidence of its importance, both pedagogically, and for everyday functioning. The present study examines two important sub-skills of numeracy. Twelve boys with Down syndrome were compared to 24 typically developing boys (matched on verbal mental age and on chronological age) on two novel, computerized tasks designed to measure sequential processing and counting. Boys with Down syndrome performed comparably to both groups of typically matched controls on the sequential task. However, differences emerged when boys with Down syndrome were required to point and attribute meaning to each step on the counting task. These findings offer novel insights into the development of number skills and provide important data that can aid in the creation of syndrome-specific education strategies to maximize the potential of children with Down syndrome.

Thesis (M. Ed.)--University of Hong Kong, 2007. / Also available in print.

Thesis--University of Florida. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 103-105).

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

Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

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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.