published_or_final_version / Education / Master / Master of Education

published_or_final_version / abstract / toc / Education / Master / Master of Science in Information Technology in Education

The aim of this thesis is to examine the relative importance of working memory, counting ability, and additive reasoning in children's mathematics learning. One hundred and fifteen 6-year-old Chinese children in Hong Kong participated in two waves of assessments. At the first time point (T1 - first grade), they were assessed using non-verbal intelligence, working memory (central executive, phonological loop, and visuospatial sketchpad), counting ability (procedural counting and conceptual knowledge of counting), additive reasoning (knowledge of the commutativity and complement principles), and mathematical achievement (calculation and story problem solving). Approximately 10 months later (T2 - second grade), children's mathematical achievement in calculation and story problem solving were evaluated once again. The extent to which various cognitive factors longitudinally predicted children's mathematical achievement was evaluated in this study. Several key findings were identified through two sets of analyses - multiple regression models and latent profile analysis. The multiple regression analyses showed that counting ability accounted for a significant amount of variance in T1 and T2 calculation beyond the effects of age, IQ, and working memory, in which conceptual knowledge of counting, but not procedural counting, was a unique predictor. However, counting ability did not contribute significantly to story problem solving at both time points. When additive reasoning was also included in the regression model, counting ability made a unique contribution to T1 calculation only, but not T2 calculation. By contrast, additive reasoning and working memory appeared to be more stable and stronger predictors of children's performance in calculation and story problem solving at both time points than counting ability. Additive reasoning explained a substantial and significant amount of variance in calculation and story problem solving at both time points after the effects of age, IQ, working memory, and counting ability were controlled for - Both knowledge of the commutativity and complement principles were unique predictors. Similarly, working memory also accounted for a significant amount of variance in calculation and story problem solving at both time points beyond the influence of age, IQ, counting ability, and additive reasoning. Among the three components of working memory, only the central executive was a unique predictor for all measures of mathematical achievement. Autoregressive analyses provided strong evidence for the longitudinal predictive powers of additive reasoning and working memory. The analyses showed that both additive reasoning and working memory remained significant predictors of T2 mathematical achievement (calculation and story problem solving) even after the effects of children's previous performance were taken into account (i.e. T1 mathematical achievement). Overall, additive reasoning accounted for the greatest amount of variance in mathematical achievement both concurrently and longitudinally among all the other factors. This finding underscores the importance of additive reasoning in the teaching and learning of mathematics in young children. Because additive reasoning (as indicated by the knowledge of the commutativity and complement principles) is a critical variable in this thesis and relatively scarce research has examined this construct, particular concern was paid to the measurement of additive reasoning. It was measured in two ways in the present study: with the support of concrete materials (the concrete condition) and without the support of concrete materials (the abstract condition). Latent profile analysis showed that all children who performed well in the abstract conditions also did well in the concrete conditions, whereas it did not reveal a group of children who performed well in the abstract conitions, but not in the concrete conditions as well. Another interesting finding was that all children who obtained high scores on tasks that assessed their knowledge of the complement principle also obtained high scores in tasks that assessed their understanding of the commutativity principle. The overall pattern of profiles provides initial evidence suggesting that additive reasoning may develop from thinking in the context of specific quantities to thinking about more abstract symbols, and children acquire the knowledge of the commutativity principle in abstract tasks before they start to acquire the knowledge of the complement principle. This finding demonstrated that patterns of individual differences are present in the development of different aspects of additive reasoning. If teachers possess some knowledge about the particular strengths and weaknesses of each child, it would be easier for them to devise teaching strategies that are tailored to the needs of different children, which may relate to the developmental order of the commutativity and complement principles, and the role of concrete materials in this development. Thus, this study contributes to the literature by showing that assessing additive reasoning in different ways and identifying profiles with classification analyses may be useful for educators to understand more about the developmental stage where each child is placed. It appears that a more fine-grained assessment of additive reasoning can be achieved by incorporating both concrete materials and relatively abstract symbols in the assessment.

published_or_final_version / Education / Doctoral / Doctor of Philosophy

何偉傑. / 呈交日期: 2000年9月. / 論文(哲學博士)--香港中文大學, 2001. / 參考文獻 (p. 335-360) / 中英文摘要. / Cheng jiao ri qi: 2000 nian 9 yue. / Available also through the Internet via Dissertations & theses @ Chinese University of Hong Kong. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / He Weijie. / Lun wen (Zhe xue bo shi)--Xianggang Zhong wen da xue, 2001. / Can kao wen xian (p. 335-360) / Zhong Ying wen zhai yao.

published_or_final_version / Education / Doctoral / Doctor of Philosophy

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Science in Information Technology in Education

本文希望探討弱勢小學如何在教育市場化趨勢下，因為收生不足而被教統局宣佈殺校，然而經過學校持分者的奮鬥，一年後竟能取錄足夠學生，成功逆轉重生。研究對象學校近年取錄的學生人數一直上升，甚至成為社區上受歡迎的學校。弱勢學校在汰弱留強的市場定律下竟能逆轉重生，這個香港教育界的特殊現象，箇中原因及意義便是本文著意的地方。 / 本文採用質性研究方法，邀請兩所位於不同貧窮社區的小學接受研究。兩所小學同樣經歷逆轉重生，其中一所小學甚至兩次殺校。在具體田野操作方面，本文採用民族誌研究方法，筆者透過長時間參與觀察、深度訪談、比較閱讀，整理兩所學校由殺校至今的逆轉發展脈絡。 / 研究結果發現，兩所能夠成功逆轉重生的學校從：宏觀層面、中介層面和微觀層面，均能啟動和累積社會資本，並轉化為不同類型的資本，包括：文化資本，經濟資本等，以支援學校的非常態運作，避過殺校宿命。此外，研究發現兩所學校的教師團隊同樣呈現一條由社會資本轉化為教學專業資本的脈絡，並在校本課程的編訂和教學法的探索得到成效，讓學生學習蒙受其利，這是學校逆轉的背後策劃能量。 / 本文期望教育領導人士能重新理解類教育市場脈絡的多端力量，並希望教育領導者了解學校在類教育市場的定位。另外，本文希望讓所有學校持分者重新理解社會資本在教育場域的正面能量。當中尤以校長為核心，啟動和轉化學校社會資本，他的信念和力量將是領導學校逆轉重生，以至持續發展的關鍵。 / 最後，本文無意為弱勢學校逆轉重生的現象下定論，限於資料收集的局限、類教育市場脈絡、社會資本概念的複雜性，本文主要通過現有的材料和論據，為香港弱勢社群教育這個領域作為開拓研究的鋪墊。 / This thesis attempts to answer the question about how a disadvantaged primary school experienced turnaround in a Quasi-education market. / This is an ethnographic study, employing qualitative methods. Two primary schools from two low-income districts were invited to participate. They both suffered from "school closure"(殺校). One of them even went through it twice. Ethnographic research was conducted with Participant Observation, In-depth Interview and Comparative Reading throughout the research duration. / The results of the research showed that two turnaround schools mobilized and accumulated social capital and transformed it into other forms of capital, such as cultural capital and economic capital, in order to support the schools’ contingency plans on macro, meso and micro levels. / Another finding is that the teaching teams of the two turnaround schools also showed a path of transforming social capital into teaching professional capital, including school-based curriculum designs and research into teaching methods. These efforts of the schools succeeded in creating a favorable condition for them not only to survive, but to flourish. / This thesis hopes to call attention to two important facts: / 1. Education leaders can benefit greatly from alerting themselves to the Quasi-education market and its related concepts, and also assessing the position of their own schools in it. / 2. Stake-holders, especially school principals, are shown to be capable of mobilizing and transforming school social capital. His or Her faith and strength are the foundation power of turnaround schools and also their sustainability. / My goal is not to draw a conclusion about turnaround schools in general. Instead, my humble task is to launch an exploratory study of these schools in order to highlight the possibilities open to such schools. Lastly, this research paves a way for future development of studies of the education of disadvantaged groups in Hong Kong. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / 吳偉強. / Parallel title from added title page. / Thesis (Ed.D.) Chinese University of Hong Kong, 2015. / Includes bibliographical references (leaves 321-331). / Abstracts also in English. / Wu Weiqiang.