Thesis (M.Ed.)--University of Hong Kong, 1987. / Includes bibliographical references (leaf 111-117). Also available in print.

Thesis (Ed. D.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Oregon, 2001. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 114-117). Also available for download via the World Wide Web; free to University of Oregon users.

Title from title page of PDF (University of Missouri--St. Louis, viewed February 9, 2010). Includes bibliographical references (p.174-195).

Published also as Thesis--Catholic University of America. / Bibliography: p. 54-55.

Humans are born with a basic sense of number. This number sense, which is now called the Approximate Number System (ANS), allows us to represent numerosity without the use of symbols. There has been a debate on whether this nonsymbolic ANS contributes to our symbolic mathematics skills, and the recent findings are inclined to support the link between the two. However, what remains unclear is the mechanism underlying the relationship between the ANS and our mathematics skills, and whether children with Mathematics Learning Disabilities (MLD) suffer from a defective ANS. The present thesis aimed at addressing the above issues in two studies. Study 1 aimed at identifying the mechanism of how the ANS contributes to children’s mathematics skills. A group of 210 kindergarteners were tested on their ANS acuity, number-numerosity mapping skills (measured by counting and estimation tasks), and their arithmetic skills. They were then re-tested twice when they were in Grade 1.Using Structural Equation Modeling, it was found that children’s ANS acuity in kindergarten predicted their arithmetic skills one year later, and the relationship was mediated by their number-numerosity mapping skills. This suggested that ANS may contribute to mathematics learning by enabling more precise mapping between number symbols and the corresponding numerosity representation, hence making numbers meaningful. Studies 2A and 2B aimed at verifying whether children with MLD suffered from deficits in their ANS as well as their number-numerosity mapping skills. The same group of participants was followed one more time in Grade 2. Using the standard low-achievement method (Study 2A) and a more data-driven method known as the latent class growth analysis(Study 2B), two groups of children with MLD were identified. Both groups of children had deficits in both the ANS and their number-numerosity mapping skills as compared with their normally-achieving peers. Other groups of low-achieving children were also identified, and their difficulties seemed to be contributed by factors other than their ANS. While one of the low-achieving groups seemed to have deficit lying mainly on the number-numerosity mapping skills, the other low-achieving group did not show any cognitive deficits but had much lower SES compared to other groups. The relationship between the ANS and children’s mathematics achievement was supported and elaborated in the present study. The findings not only articulated a potential mechanism of how children learned about mathematics, but they also allowed educators to have better understanding of the cognitive profiles of children with MLD, thus facilitating early identification and intervention. The different profiles of the low-achieving groups also highlighted the need for differential intervention for different groups of low-achieving children. / published_or_final_version / Psychology / Doctoral / Doctor of Philosophy

No description available.

No description available.

The twenty-first century society demands a high level of mathematical literacy. This drove Korean educators to evaluate their students using international mathematics tests such as TIMSS, PISA and IMO. In these tests, Korean students ranked highly among the participating countries. Korean students, however, had done poorly in the application of mathematics in daily life situations as well as in their interest in mathematics in comparison to those of other countries. Based on these observations, the present study was an investigation on the contexts which Korean grade 8 to 10 students would prefer to deal with mathematics, in order to improve these weak points and thus increase their mathematical power. The aim of the study was to investigate mathematical literacy in connection with the relevance of mathematics and mathematical modelling. The study paid more attention to mathematics education in real life situations.

This thesis reports data gathered through case studies of ten of the students who took part in a survey of secondary school students who had been invited to camps at which the New Zealand teams were chosen for the International Mathematical Olympiad (IMO) in the first five years of this country�s participation in the IMO. The case studies data gave individuals� narratives that were captivating yet complex, unique yet universal, clear yet not easily described all of apiece. I read widely in response to the information they offered and found that reflection and a narrative style of presentation assisted the grasping of nuances and implications of the students� narratives. Few of the parents of the students were particularly competent in mathematics or able to account for their child�s curiosity, concentration and skills in pursuing a fascination with number. In most of the families, all members were encouraged to follow their own inclinations and interests, to respect the maintenance of a balance of cultural and physical activities, to regard books and play as normal life supports, and to believe that discovery, enchantment and pleasure were both goals and accomplishments of everyday life. Most of the students experienced less encouragement at school than they might have expected, and unpleasant experiences could be linked with a teacher�s apparent lack of appreciation of a student�s mathematical ability. Both the case studies and the initial survey suggested that most teachers, at any level of formal education, were doing all they were capable of doing in mathematics, and that the students responded to opportunities to self-select subjects and topics that interested them and to the help and company offered by mentors and peers who had flair and competence in appropriate subject areas. Few of the case studies students were motivated by strategies dependent on a high level of competition or a 'sorting' of that offered in formal education (through attitudes and practical organisation such as timetabling) into either Arts or Science subjects. Most were attracted to the study of languages and/or philosophy and some to that of computer science. Most showed interest and some prowess in individual cultural and physical activities requiring perseverance. Largely, they were motivated by finding fresh or novel ways of integrating diverse knowledge, and by associating with peers. They enjoyed and valued self-awareness, intellectual independence, chances to empathise with ideas and people, and tasks that were in harmony with the dictates of their own volition. Evidence of differences among the case studies students - even though they had all been identified as very able in mathematics - led me to Vadim Krutetskii�s theories of the components of mathematical ability and their functioning and thus to new views, first, of the interplay between aptitude and languages of perception, inner comprehension and outer expression and, second, of the relationships between giftedness and other attributes of human abilities and endeavours. These appreciations suggested that the models of education and support commonly exhibited in the case studies students� families and in the environments of their extra-school activities had been more encouraging of their gifts, talents and personal growth than those often exhibited in the schools they attended.