In the catalog issue of the Bulletin of Florida State University, to be published sometime during 1950, will appear a challenging innovation: the General Education course in mathematics, titled mathematics 105, will be listed under the general area of Communication through Language. This, so far as the writer is able to ascertain, will be the first time a course in mathematics has been so listed in any university catalog. It will be the purpose of this paper to examine some aspects of the historical development of mathematics to justify such a classification and to explore some of the implications of such an approach for the teaching of mathematics. / Typescript. / "July, 1950." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Includes bibliographical references (leaves 26-30).

The results reported here are the product of the research titled: Using history in the teaching of mathematics. The subjects are students in two classes of algebra II course at Florida State University High School-- 36 students-- makes and females whose ages are mostly 18 and a few 17 and 16 years old. Algebra II is a course that is usually taken by high school seniors in 12th grade and a few 11th or 10th grade students which explains why the ages of the students are mostly 18 and a few 17 and 16 years old. In this investigation, both quantitative study and qualitative study were employed. The quantitative study was the main study-- a teaching experiment using quasi-experimental methodology that involves two groups-- group 1 and group 2. Group 1 is the control group, where various algebraic/mathematical concepts, or topics were taught or explained to students with the necessary formulas. Group 2 was the experimental group in which the accounts of the historical origin of algebraic/mathematical concepts and the mathematicians (Lewis Carroll, Archimedes, Pythagoras, and Sophie Germain) who brought forward or created the concepts were used to augment pedagogical lessons and exercises used for this study as the main feature of pedagogy. The qualitative study augmented the main quantitative study; it was a follow-up interview for students to probe further an in-depth rationale for the research theme, using history in the teaching of mathematics. The statistical analysis results indicated that there is a significant difference in the mean of score for the control group students and the mean of scores of the experimental group is greater than the mean on scores of student's performance in the control group; and the interview questions responses indeed corroborate the fact that the use of history in teaching mathematics does improve learning and understanding of algebraic/mathematical concepts. / Typescript. / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisors: Elizabeth Jakubowski, Herbert Wills III, Professors Co-Directing Dissertation. / Includes bibliographical references (leaves 202-205).

A research report submitted to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand in partial fulfilment of the requirements for the degree of Master of Education by combination of coursework and research / Percent is a familiar, yet complex topic that is found to be difficult for both adults and children. The question of why percent has been persistently difficult has spurred much research, the most notable of which was conducted in the early 1990’s. Those studies have adopted a cognitive perspective. This study adds a commognitive perspective to the discussion by proposing a model for the development of percent discourse (PD-Model). The model rests on Sfard’s premise that learning mathematics is synonymous with modifying and extending one’s discourse. I begin by employing a cognitive framework of percent for the design of written tests to identify the areas of percent that first-year university students experience difficulty with. The quantitative analysis of the written tests shows that less than half the students obtained a score of 50% or more. Later, in search of the features of students’ discourse that hinder their access to percent discourse, I examine the discourse of two pairs of students in interview sessions. I illustrate the application of the PD-Model as an interpretive analytical tool that offers an explanation for the insufficiency in their objectification of percent as a comparative ratio. This study confirms the results of Parker’s (1994) study, that is: percent is difficult for students to work with. The key findings of the discursive analysis show that students’ discourse of percent is narrow and deeply rooted in a percent-as-fraction notion. The students’ discourse is predominantly additive in nature and does not show signs of recognising the underlying multiplicative structures of percent tasks. As such, a fully-fledged objectification of percent as a comparative ratio is not evident in the students’ discourse of percent. / NG (2020)

Research Report submitted to the School of Education,Faculty of Humanities, University of the Witwatersrand, Johannesburg In partial fulfillment of the requirements For the degree in Master of Education (Inclusive Education) July 2019 / NG (2020)

Geometric proof-writing is a widely known cause of stress for secondary school students and teachers alike. As the textbook is the primary curricular tool utilized by novice teachers, a two-part qualitative study was conducted to determine (a) the types of proofs presented in a typical high school geometry textbook and (b) teachers’ preparedness and confidence to teach proof and proving. I conducted a qualitative analysis of the selected textbook based on its presentation of proofs and proof tasks, and then used said analysis to inform the creation of a five-question content assessment on proof, which was administered to 29 preservice and in-service secondary mathematics teacher participants. During the administration of the assessment, I interviewed each participant regarding their thought processes, as well as their knowledge, beliefs, and preparedness to teach proof and proving. The data were analyzed using a qualitative coding system to categorize participants’ responses to the interview questions according to their beliefs and attitudes, as well as issues with mathematical language and content that they encountered. The qualitative analyses indicated that the selected textbook largely underemphasizes the role of proof in the secondary school geometry curriculum, and that most participants are largely underprepared to teach proof at the secondary level. Participants expressed sentiments about the nature of proof and proving, verifying trends from the literature and providing the impetus for future study. The findings support that more studies are needed to analyze the intersection between curricular knowledge and content knowledge for secondary mathematics teachers.

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在國際評鑑計劃中，東亞地區學生的數理能力往往較西方國家為佳。現有學術文獻已就這個現象作深入探討，並提出東亞學生的文化特徵和模型。然而，鮮有研究以縱向的歷史角度，討論東亞教育制度下對於「學習者」的文化概念如何因應全球化的影響而演變。本文嘗試以香港的數學教育為研究個案，探討本地數學課程在教學重心及組織上的轉變。研究發現，該學科在教學上的轉變緣於現代個人主義的制度化過程 ── 社會整體愈益視學習者作為充權和自省的行動者。本研究致用縱向文本分析的研究方法，綜析四十二本於戰後出版的香港高小數學教科書的教學內容。研究結果顯示，歷年來課本及課程的教學愈加著重參與式教學、興趣啟發以及與扣連學生生活等概念。另外，政府官員、老師、本地壓力團體及學術專家等亦援用「以學生為本」的話語，推動課程改革。綜合而言，本研究認為世界政體理論相比歷史主義式的理論視野更有力地解釋數學課程內容的轉變。 / East Asian learners usually outperform their Western counterparts in international mathematics assessment programs. Although the cultural traits of East Asian learners are well documented and analyzed, the cultural dynamics of the changing conception of “learner“ in East Asia, especially under the influence of globalization, is under-explored. Taking Hong Kong as a case study, this paper explores the changes within the emphasis of instruction and organization of local mathematics curriculum across time. I contend that the shift of instruction within the school subject is due to the institutionalization of modern individualism, the process in which the conception of “learner as an empowered and self-reflexive actor becomes culturally legitimate in the society. I employ a longitudinal content analysis to track the changes of the instructional emphasis within 42 senior primary mathematics textbooks published in Hong Kong since World War II. It is revealed that despite the unique cultural and historical trajectory of educational development in Hong Kong, the curriculum embraces the ideas of participatory pedagogical approach, interest stimulation, and social relevance to students. Furthermore, it is found that governmental officials, teachers, local pressure groups and academic professionals draw scripts and models from the discourse of student centrism to drive curricular reforms. Results suggest that world polity theory is more applicable than the historicist perspective in accounting for the changes of the curriculum content. / Detailed summary in vernacular field only. / Yip, Chun Ting Patrick. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 60-66). / Abstracts also in Chinese. / Abstract --- p.iii / Abstract (Chinese) --- p.iv / Acknowledgement --- p.v / Table of contents --- p.vi / List of tables, figures and charts --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature review --- p.7 / Chapter 2.1 --- Endogenous explanation I: cultural essentialism --- p.7 / Chapter 2.2 --- Endogenous explanation II: historicist perspective --- p.8 / Chapter 2.3 --- Exogenous explanation: world polity theory --- p.9 / Chapter 3 --- Framework and hypotheses --- p.12 / Chapter 4 --- Method --- p.14 / Chapter 4.1 --- Longitudinal content analysis of textbook --- p.14 / Chapter 4.2 --- Textbook data --- p.15 / Chapter 4.3 --- Measures for trend analysis --- p.16 / Chapter 4.4 --- Textual analysis --- p.18 / Chapter 4.5 --- Secondary analysis of the process of curriculum development --- p.18 / Chapter 5 --- Result --- p.21 / Chapter 5.1 --- Trend analysis --- p.21 / Chapter 5.2 --- Textual analysis --- p.28 / Chapter 5.3 --- Explaining the rise of student centrism in Hong Kong --- p.38 / Chapter 6 --- Conclusion --- p.52 / Chapter Appendix A. --- Textbooks sampled --- p.56 / Bibliography --- p.60

published_or_final_version / Education / Master / Master of Education