Li Toi-wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 105-113). / Abstracts and appendices in English and Chinese. / Table of Contents --- p.1-2 / List of Tables --- p.3 / List of Figures --- p.4 / Chapter Chapter 1 --- Introduction --- p.5-8 / Chapter Chapter 2 --- Literature Review --- p.9-41 / Chapter 2.1. --- Historical Views of Empathy --- p.9-10 / Chapter 2.2. --- Contemporary Views of Empathy --- p.11-14 / Chapter 2.3 --- Historical Thinking and Historical Understanding --- p.15-19 / Chapter 2.4. --- Historical Empathy --- p.20-36 / Chapter 2.5 --- Assessment of Empathy and Historical Empathy --- p.37-41 / Chapter Chapter 3 --- Method --- p.42-55 / Chapter 3.1 --- Hypotheses --- p.42-45 / Chapter 3.2 --- Participants --- p.45 / Chapter 3.3 --- Material and Procedure --- p.46-53 / Chapter ´Ø --- Preliminary Considerations of the Research --- p.46-49 / Chapter ´Ø --- The Actual Research Design --- p.50-53 / Chapter 3.4 --- Analysis --- p.54-55 / Chapter Chapter 4 --- Results --- p.56-84 / Chapter 4.1 --- "Samples of Memoirs that Scored ""2"", ""1"" and ""0"" in Each of the Three Aspects of Historical Empathy" --- p.56-65 / Chapter 4.2 --- Assessment of Inter-rater Agreement and Inter-rater Reliability on the Historical Empathy Score --- p.66-67 / Chapter 4.3 --- Descriptive Statistics --- p.67-71 / Chapter 4.4 --- Correlational Analysis of the Three Categories of Historical Empathy --- p.71-73 / Chapter 4.5 --- Results of Hypothesis One --- p.73-75 / Chapter 4.6 --- Results of Hypothesis Two --- p.75-77 / Chapter 4.7 --- Interview Results --- p.77-84 / Chapter Chapter 5 --- Discussion --- p.85-100 / Chapter 5.1 --- Discussion of the General Findings --- p.85-88 / Chapter 5.2 --- Discussion of Hypothesis One --- p.89-95 / Chapter 5.3 --- Discussion of Hypothesis Two --- p.95-97 / Chapter 5.4 --- The Follow-up Interview --- p.98-99 / Chapter Chapter 6 --- Conclusion --- p.100-104 / References --- p.105-113 / Appendix / Chapter A. --- Multiple source documents for Case 1: Chang Hsueh-liang --- p.114-115 / Multiple source documents for Case 2: Shang Yang --- p.116-117 / Chapter B. --- Textbook Materials for Case 1: Chang Hsueh-liang --- p.118-119 / Textbook Materials for Case 2: Shang Yang --- p.120-121 / Chapter C. --- Guided questions for the cases of Chang Hsueh-liang and Shang Yang --- p.122 / Chapter D. --- Remarks of Table 3.1 to 3.3 --- p.123-132 / Chapter E. --- "Excerpts of memoirs which obtained the highest score (i.e., “2´ح）in the three aspects of historical empathy respectively" --- p.133-136 / Chapter F. --- Excerpts of students' original writings --- p.137-142 / Chapter G. --- "Full original version of the written memoirs that got the highest score (i.e., ""2"") in all the three aspects of historical empathy (i.e., total score=6)" --- p.143-145

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本研究以"教学性解释"这一课堂会话形式为研究对象，调查小学数学课堂教学中教学性解释的数学丰富性特征和结构特征，以及它们与学生学习的关系。其中，数学丰富性是指课堂教学活动与数学内容的相关程度,以教学性解释中的学术词汇比例和教学性解释的概念水平为指标。 / 本研究数据源于项目"课程改革的成效──教师课堂教学实践变化"（Ni, Li, Cai, & Hau, 2009），选取使用新课程教材的17名小学数学教师及其1013名学生作为研究样本。教学性解释来源于这17个班级的51节课录像（每个班级3节课录像，教学内容为"分数运算"）。同时，也对学生的认知学业表现（计算、简单问题解决和复杂问题解决）和数学学习的情感表现（学习兴趣、课堂参与、数学观、交流素养）进行了两次测查。 / 研究一考察了教学性解释的结构特征。研究结果表明：小学数学课堂中教学性解释主要是教师进行引导，由学生来提供解释，教师的引导方式包括提问引导和回应性引导。就引导水平而言，教师将选择性引导、产品性引导、过程性引导和元过程引导这四种不同水平的引导方式相结合，其中高水平的引导方式（过程性引导和元过程引导）所占比例近四成，教师倾向于让学生表达观点和看法，提供解释，并且对自己的观点进行论述。 / 研究二考察了教学性解释的数学丰富性特征。研究结果表明：教学性解释的学术词汇比例和概念水平可以作为数学丰富性的两个有效指标。小学数学课堂中教学性解释的丰富性水平较高：绝大部分教学性解释是数学解释，并且原理性解释是比例最高的数学解释。 / 研究三考察了教学性解释的结构特征与丰富性特征与学生学习结果的关系。研究结果表明：教学性解释的丰富性对学生简单问题解决能力表现具有正向预测作用，但与学生计算能力表现呈负相关，同时，与学生复杂问题解决能力表现的关系更为复杂，受到学生原有的知识和技能水平的调节作用。教学性解释的丰富性与学生的数学兴趣、数学观和交流素养呈现负性相关。 / The main purpose of the present study was to investigate the mathematical richness and structural features of instructional explanation in 17 primary mathematics classrooms, and their relations to students’ cognitive and affective performance in learning mathematics. Mathematical richness in the present study refers to the extent to which classroom instruction is related to mathematics, or the extent of doing or talking mathematics in classroom instruction. The indicators of mathematical richness of instructional explanation included the ratio of academic words and conceptual level of instructional explanations. / The data source of the study was from the project "Has curriculum reform made a difference? Looking for change in classroom practice" (Ni, Li, Cai, & Hau, 2009). The current study selected 17 primary mathematics classrooms and the 1013 students from the database. 477 episodes of instructional explanation were identified from the 51 videotaped lessons of the classrooms (3 lessons for each class). The content of all 51 lessons was about division with fractions. The identified episodes of instructional explanation were analyzed in terms of the indicators of mathematical richness. The students’ achievement data included two times of assessment on three aspects of cognitive performance (calculation, simple problem solving, complex problem solving) and four aspects of their indicated attitude towards mathematics and learning mathematics (interest in learning mathematics, classroom participation, views of mathematics, literacy about mathematical communication). / Study One analyzed the structural features of instruction explanations in the 17 primary classrooms. The results indicated that teachers were used to guiding the students to provide explanations when constructing instructional explanation in the mathematics classrooms. Teachers’ elicitations consisted of questions and responsive elicitations. Four levels of elicitation were identified. They were choice elicitation, product elicitation, process elicitation and metaprocess elicitation. The higher levels of elicitations (process and metaprocess elicitation) accounted for a significant amount in the classrooms. The teachers tended to let students express their views, provide explanations and arguments of reasoning. / Study Two investigated the mathematical richness of instructional explanations. The results showed that the ratio of academic words and conceptual level of instructional explanations could be valid and useful indicators of mathematical richness. The mathematical richness of instructional explanation was high for the observed classrooms in terms of the two indicators. Majority of the instructional explanations were mathematical and involved mathematical concepts and principles. / Study Three examined whether the richness and structural features of instructional explanation were able to predict student learning outcomes in the cognitive and affective domain. The results indicated that the mathematical richness positively predicted students’ simple problem solving performance, but was negatively related to students’ computation performance. Furthermore, its relation to students’ complex problem solving performance was complicated, which was moderated by the students’ prior status in the knowledge and skills. Lastly, mathematical richness was negatively associated with students’ indicated interest in learning mathematics, view of mathematics and literacy about mathematical communication. / 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. / 鄒君. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 148-172). / Abstracts also in Chinese. / Zou Jun.

Thesis (Ph.D.)--University of the Witwatersrand, Faculty of Science, 2004 / This research is in the field of ethnomathematics. The study was carried out in three phases with the Tchadji-game being its principal focus. Tchadji is a traditional game played at Ilha de MOyambique, a small Island situated on the northeast coast of Mozambique. Tchadji belongs to a class of board games known as Mancala, which are thousands of years old and are played throughout the African continent as well as in other parts of the world. Mancala games have only recently received due attention as a topic for research. The first phase of the research was carried out in the school mathematics classroom. The outcomes of this phase indicated that games like Tchadji and the three stones (a variant of the Muravarava game) as a part of Mozambican culture are also rich in providing opportunities for activities in the mathematics classroom related to the development of key probabilistic concepts. Quasi-experimental research involving the researcher, 4 mathematics teachers and 162 students showed statistically significant positive effects on attitude towards the learning of, and performance in probability. These outcomes were corroborated by qualitative research. The second phase of this study consisted of ethnographic research amongst master Tchadji players, which explored the mathematical ideas embedded in the Tchadji-game and in the procedures for playing the game. The results of this phase of the research revealed that, the Tchadji-players had mathematical knowledge, skills and ways of thinking such as counting, logical thinking, calculation, visualisation, recognition of different numerical patterns and infinity. These results are described in terms of examples taken from different critical moments of the recorded matches of Tchadji. This way of iii Abstract (PhD thesis) presenting the results gives insight into the complexity of the methodology used. It also uncovers different aspects of playing Tchadji, like rules, strategies and tactics. A need for further investigations of this nature for uncovering mathematical ideas in traditional culture is also indicated by this research. As advocated in ethnomathematical research an intervention with (pre and in-service) student teachers formed the third phase of the research. The results of this phase indicated that the 24 teachers, who participated in the research, showed enthusiasm, satisfaction and excitement in experiencing the mathematical richness of Tchadji and in appreciating possibilities for the use of Tchadji in the mathematics classroom. They were able to analyse the game independently and to identify embedded mathematical ideas in the game, like logical thinking, counting and empirical and mental calculation. The research makes contributions to the field of ethnomathematics itself, to ethnographic research methodology and to the pedagogy of mathematics.

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Thesis (M.Ed.) --University of the North, 1990 / Refer to the document

As a young and dynamically evolving discipline, statistics evokes many conceptions about its purpose, the nature of its development, and the tools and mindset needed to engage in statistical work. While much research documents the perceptions of statisticians and experts on these matters, little is known about how the disciplinary perspectives of statistics instructors may interact with the work of teaching. Such connections are likely relevant since research has shown that teachers’ and instructors’ views about the discipline they teach inform their instructional approaches. This work specifically focuses on the disciplinary views of graduate teaching assistants (GTAs), who continue to serve a critical role in undergraduate instruction. Using multiple case study design, I document the views, experiences, and teaching practices of four statistics GTAs over the course of a full year—from their induction into the department in the fall, until their first solo-teaching opportunity the following summer. From the literature, I organized important disciplinary themes in statistics, including disciplinary purpose, epistemology, and disciplinary engagement. Targeting issues and questions stemming from these areas, I documented the various perspectives, models, and tensions that characterized the disciplinary views of the participants. I also documented the relevant experiences and influences that motivated these views. Additionally, I explored the GTAs’ pedagogical views and vision for teaching introductory statistics while looking for possible connections (and glaring disconnects) between these views and their disciplinary views. Finally, I observed their instruction and considered the participants’ teaching reflections as I looked for alignment between their expressed views and actual instructional decisions. From the data, I found that several of the GTAs expressed sophisticated views and expert notions about the discipline. There was a clear disconnect, however, between their perceptions of disciplinary work and the work of students in an introductory statistics course. Despite recognition that statistical questions typically do not have right answers, that statistical methods are often quite flexible and contextually-driven, or that many disciplinary elements developed through community negotiation rather than discovery, the GTAs struggled to bridge these considerations to the tasks being posed and the practices being emphasized in introductory courses. The participants also expressed a basic desire to engage students in practice problems and activities, yet their instructional visions were not specific and well-grounded in rich classroom experiences that modeled student-centered pedagogy. As a result, all four GTAs converged on a singular vision for introductory statistics. This vision involved focusing on “the basics,” acquainting students with a wide array of procedures, honing students’ computational abilities, and emphasizing statistical problem-solving as a pursuit for right answers. This dissertation study provides insights into disciplinary tensions that may be of value in developing an instrument for assessing the disciplinary views of instructors and students alike. GTAs without well-developed views may need opportunity to engage in rich, open-ended tasks that serve to develop their disciplinary perspectives. Additionally, this work reveals how GTAs may struggle to bridge their perceptions of advanced disciplinary work to the work of their own students. Acquaintance and experience engaging in tasks that promote informal inferential reasoning or exploratory data analysis, coupled with connections to situated and constructivist learning theories, may enrich GTAs’ instructional visions as they see how disciplinary and instructional spaces may interact and inform one another. / A Dissertation submitted to the School of Teacher Education in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / March 28, 2019. / Disciplinary Views, Epistemology, Statistics Education, Teaching Assistants / Includes bibliographical references. / Ian Whitacre, Professor Co-Directing Dissertation; Elizabeth M. Jakubowski, Professor Co-Directing Dissertation; Eric Chicken, University Representative; Lama Jaber, Committee Member; Jennifer J. Kaplan, Committee Member.