by Cheng Fun Chung. / Bibliography: leaves 48-51 / Thesis (M.A.Ed.)--Chinese University of Hong Kong, 1983

Many people seem to agree that arithmetic is hard. Because of this difficulty, there has been a movement to postphone the beginning to arithmetic teaching from first grade to second or third grade. This movement presents an opposing view in relation to other subject matter areas. The actual teaching of other subjects is moving into the lower grades rather than out of the lower grades as teachers realize more and more the importance of these subjects in relation to younger children. Each first grade teacher should realize the resonsibility involved in developing the number readiness that will affect the child's future understanding of the various extensions of the initial concept of number. / Typescript. / "August, 1958." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Sarah Lou Hammond, Professor Directing Paper. / Includes bibliographical references (leaf 39).

"Since arithmetic is a skill that presents almost insurmountable difficulty for some children there is a need for investigation of the methods and materials of teaching. Assuming that the meaning theory is a desirable way of teaching numbers the writer has endeavored to organize some ideas and objectives for developing quantitative understanding in children at the first and second grade levels. The writer has not attempted an exhaustive study of the problem but has focused her attention on principles that would be of immediate aid during the coming school year"--Introduction. / "August, 1952." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Elizabeth Hamlin, Professor Directing Paper. / Includes bibliographical references (leaf 42).

Bibliography: pages 83-85. / This study examines children's developing mathematical abilities during the first three years of their schooling. More particularly, children in grades one, two and three of three different primary schools, in two different regions, had their performances on eleven mathematics tasks monitored over the course of 1996 to examine their developing mathematical abilities. These abilities were investigated in terms of task-particular performances and the assumed competencies (internal mental processes) underlying these performances. The data was generated through the use of a repeated measures design. The theory of the methods used to gather the data and to analyse the results is rooted in Vygotsky's (1978) experimental-developmental approach to the study of higher mental functions. This method of observation proved to be successful to the degree that it allowed for the study of changes in children's performances over a seven month period. The overall findings of the study revealed that the subjects in the sample population had the developmental readiness with which to improve their mathematical abilities. However, when this developmental readiness had to be taken further through formal instruction, their performances were inadequate. The investigation exposed the complexity and importance of language in the successful development of mathematical concepts. The data indicated that the subjects' learning was neither in advance of their development nor was it indicative of the constructivist approach to the task of teaching. Furthermore, there existed a conflict between spontaneous and formal knowledge in engaging with school mathematics tasks.

Includes Course Papers. / Includes bibliographies. / Very little is known about how young children think and behave when faced by computers and the broad array of mathematical software available. Much of the software has been developed by adults in the way adults see young children reasoning. A class of twenty English-speaking boys of approximately 12 years of age were exposed to carefully selected mathematical software without adult (teacher) interference, to clarify how these pupils would react to that software. Special focus was placed on the interactions of three children throughout the series of twenty lessons, using two video cameras to record their behaviour. The size of the groupings was changed to consider the effect of group size on the pupils' interactions. Various 'themes' evolved out of reviewing the video recordings. These 'themes' were then linked to Research data. It appears that these pupils had great trouble in reading and interpreting instructions accurately. Also, the software made assumptions of what the pupils could do. The interaction and collaboration by the boys seemed at its best when they were in a group of two as 'peer equals'. The class recognised and used the services of those boys they considered 'experts' in the use of computers. The video-recordings showed that the pupils preferred having pencil and paper available to record information and their estimations, rather than having to rely on memory. It seemed to give permanence to their thoughts and make these more explicit and organised. An analysis of the data also showed that the software and the boys' reaction to it was distinctly sexist. The names of the software (SNOOKER, PILOT, MATHS - CARS IN MOTION, etc.) can be seen as male. The boys gave the computer a 'personality' and referred to it as a 'he'. Also, a disturbing tendency among these pupils was the way they interpreted the software and reacted to it in a distinctive military fashion. This can be attributed to the boys having to battle, explode or bomb their way to victory; to shoot something or be shot in much of the software available. My role of being 'non-expert' was an extremely difficult one as the pupils had expectations of me, and the shortcomings in the software obliged some form of interference. My conclusions are that the mathematical software needs to be appropriate and relevant to what is being done in the class rather than to exist on its own outside of it, and that it could aid the pupil to think about his thinking.

A thesis submitted to the Wits school of Education, Faculty of Humanities, University of the Witwatersrand in fulfillment of the requirements for the degree of Doctor of Philosophy Johannesburg 2017 / MT2017

Li, Xiaoqing. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 161-179). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

手稿本. / Thesis (M.A.)--香港中文大學. / Shou gao ben. / Includes bibliographical references (leaves 62-66). / Thesis (M.A.)--Xianggang Zhong wen da xue. / Chapter 第壹章 --- 問題說明 --- p.1 / Chapter （一） --- 研究問題 --- p.1 / Chapter （二） --- 有關文獻 --- p.5 / Chapter （三） --- 假設 --- p.11 / Chapter （四） --- 執行定義 --- p.12 / Chapter 第貳章 --- 研究方法 --- p.14 / Chapter （一） --- 設計 --- p.14 / Chapter （二） --- 樣本 --- p.17 / Chapter （三） --- 研究工具 --- p.19 / Chapter （四） --- 實驗程序 --- p.26 / Chapter （五） --- 資料分析 --- p.31 / Chapter 第叁章 --- 結果與討論 --- p.35 / Chapter （一） --- 結果 --- p.35 / Chapter （二） --- 討論 --- p.51 / Chapter 第肆章 --- 摘要及建議 --- p.56 / Chapter （一） --- 摘要 --- p.56 / Chapter （二） --- 建議 --- p.60 / 參考文獻 --- p.62 / Chapter （一） --- 英文 --- p.62 / Chapter （二） --- 中文 --- p.64 / 附錄 / Chapter （一） --- 本研究應用之第一類中文辭句 --- p.67 / Chapter （二） --- 本研究應用之第二類中文辭句 --- p.68 / Chapter （三） --- 本研究應用之第三類中文辭句 --- p.69 / Chapter （四） --- 中文辭句默寫測驗卷 --- p.70 / Chapter （五） --- 两项因素重複測量設計電腦計算程序 --- p.71 / Chapter （六） --- 鄧肯統計法分析結果 --- p.77

Bidirectional Translation, devised by the author, is a structured approach to the teaching of addition and subtraction which aims to give children greater understanding of arithmetical operations. The approach systematically involves both: the translation of numerical representations into hypothetical, real world contexts; and the extraction of the appropriate numerical operations from hypothetical, real world contexts. It is this emphasis on translation from and to both the numerical representation and realistic contexts which gives rise to the name, Bidirectional Translation. An experimental group of 90 primary one children were taught to add and subtract (within 10) by the method of Bidirectional Translation. Post-test comparison of the experimental subjects' performance with that of a control group showed significantly superior performance on the part of the experimental subjects in terms of the utilizability of addition, the evocability of addition, the utilizability of subtraction and the evocability of subtraction for five different classes of verbal context, namely: Part-Part Whole, Separating, Joining, Equalizing and Comparison contexts. In all instances the probability of the results being chance ones were less than 5% and in most, were less than 1%. In both the experimental and control groups, most children performed better when they were required to utilize concepts than when they were required to evoke concepts. Similarly they performed better when they were required to add than when they were required to subtract. The differences, however, were not always significant. It is suggested that the effectiveness of the methodology of Bidirectional Translation is rooted in a structure which allows the child to make his/her thinking explicit and which allows the teacher to monitor this.

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