by Wong Ka-Ming. / Thesis (M.A.Ed.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 164-173.

Digitized by Kansas Correctional Industries / Department: Music.

The goal of this treatise is to examine elements of jazz pedagogy that can be applied to improve musicianship in the undergraduate classical lesson setting. I have identified areas of classical pedagogy that would benefit most from these elements and have corroborated them with information from respected classical pedagogues. These concepts are addressed by examining both the classical and jazz pedagogical traditions and determining which approaches from the jazz methodology are conducive to supplementing the undergraduate classical lesson experience. I have provided suggestions for adapting and implementing these methods, with examples of supplemental exercises that may be incorporated by classical teachers included at the end of each section. The aspects of pedagogy that were chosen for this research were aural skills, harmonic awareness and application, and improvisation. More specific topics relevant to each to each of these are discussed within each chapter. All of the above are areas in which jazz musicians typically excel, so I studied their pedagogical methods to see what could be applied to the classical lesson structure for undergraduates. I conducted the research for this project primarily through interviews with pedagogues and performers of each style. Further evidence was gathered through lesson observations and examination of syllabi, articles, dissertations, and books. / A Treatise submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Music. / Summer Semester 2018. / May 1, 2018. / Clarinet, Classical, Jazz, Lessons, Pedagogy / Includes bibliographical references. / Jonathan Holden, Professor Directing Treatise; William Fredrickson, University Representative; Deborah Bish, Committee Member; Jeffrey Keesecker, Committee Member.

Given the reality that active and competitive participation in the 21st century requires American students to deepen their scientific and mathematical knowledge base, the National Research Council (NRC) proposed a new conceptual framework for K-12 science education. The framework consists of an integration of what the NRC report refers to as the three dimensions: scientific and engineering practices, crosscutting concepts, and core ideas in four disciplinary areas (physical, life and earth/spaces sciences, and engineering/technology). The Next Generation Science Standards (NGSS), which are derived from this new framework, were released in April 2013 and have implications on teacher learning and development in Science, Technology, Engineering, and Mathematics (STEM). Given the NGSS's recent introduction, there is little research on how teachers can prepare for its release. To meet this research need, I implemented a self-study aimed at examining my teaching practices and classroom outcomes through the lens of the NRC's conceptual framework and the NGSS. The self-study employed design-based research (DBR) methods to investigate what happened in my secondary classroom when I designed, enacted, and reflected on units of study for my science, engineering, and mathematics classes. I utilized various best practices including Learning for Use (LfU) and Understanding by Design (UbD) models for instructional design, talk moves as a tool for promoting discourse, and modeling instruction for these designed units of study. The DBR strategy was chosen to promote reflective cycles, which are consistent with and in support of the self-study framework. A multiple case, mixed-methods approach was used for data collection and analysis. The findings in the study are reported by study phase in terms of unit planning, unit enactment, and unit reflection. The findings have implications for science teaching, teacher professional development, and teacher education.

In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and performance in the MCM and ICM: the Chinese government's support, pertinent organizations' efforts, support from initiators of Chinese mathematical modeling education and local resources, Chinese teams' preferences in selecting competition problems to solve, and influence from the Chinese National College Entrance Examination (NCEE). The data made clear that (1) the policy support provided by the Chinese government laid a solid foundation in popularizing mathematical modeling activities in China, especially in initial stages of the development of mathematical modeling activities. (2) Relevant organizations have been the main driving force behind the development of mathematical modeling activities in China. (3) Initiators of mathematical modeling education were the masterminds of Chinese mathematical modeling development; support from other local resources served as the foundation of mathematical modeling popularity in China. (4) Chinese teams have revealed a preference for discrete over continuous mathematical problems in the Mathematical Contest in Modeling. However, in general, the winning rates of these two problem types have been shown to be inversely related to their popularity — while discrete problems have traditionally had higher attempt rates, continuous problems enjoyed higher winning rates. (5) The NCEE mathematics examination seems to include mathematical application problems rather than actual mathematical modeling problems. Although the extent of NCEE influence on students' mathematical modeling ability is unclear, the content coverage suggests that students completing a high school mathematics curriculum should be able to apply what they learned to simplified real-world situations, and pose solutions to the simple models built in these situations. This focus laid a solid mathematics foundation for students' future study and application of mathematics.

The purpose of this dissertation is to clarify the emergence of quaternions in order to make the history of quaternions less opaque to teachers and students in mathematics and physics. ‘Quaternion type Rotation Groups’ are important in modern physics. They are usually encountered by students in the form of: Pauli matrices, and SU(2) & SO(4) rotation groups. These objects did not originally appear in the neat form presented to students in modern mathematics or physics courses. What is presented to students by instructors is usually polished and complete due to many years of reworking. Often neither students of physics, mathematics or their instructors have an understanding about how these objects came into existence, or became incorporated into their respected subject in the first place. This study was done to bridge the gaps between the history of quaternions and their associated rotation groups, and the subject matter that students encounter in their course work.

Geometry is an essential branch in mathematics that helps students learn to grasp their environment and leverage that grasp into abstract understanding and reasoning. There has been an observable decrease in geometrical content in secondary education curricula, and particularly a “puzzling scarcity” in three-dimensional geometry, which has led to a decline in students’ geometrical abilities, spatial thinking and deductive reasoning abilities. This study addresses this issue by scrutinizing the enacted curriculum standards and the most influential textbooks related to three-dimensional geometry in two prominent countries, the US and China, both of which embrace the interplay of both conventional and innovative practices. This qualitative study used both content analysis and cross-cultural comparison methods to inquire about and to understand the current situation of three-dimensional geometry in high school. I focused on probing the communication types, objects, concepts, and spatial thinking abilities related to three-dimensional geometry in the standards and texts. To understand spatial abilities, I synthesized a spatial thinking abilities framework with six attributes and used this framework to exam the affordance of these abilities in the texts and requirements in the standards. The result and analysis reveal the details of each text and standards individually and offer an examination of the alignment between the standards and texts. The comparison of the two countries’ different approaches also sharpens the understanding of the issue. I also worked to unveil students’ multiple ways of making sense of geometry concepts by two geometry learning models, Piaget’s model and van Hiele’s model, as well as spatial thinking abilities.

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Typescript (photocopy). / Digitized by Kansas Correctional Industries

本研究透過分析四十多份數學史教學實證研究，發現過往的研究較少以了解數學歷史演變及發展作為研究內容、亦鮮有對學生的數學觀進行分析。為了填補這些研究上的缺口，本研究從了解演變及發展的角度出發，在設計函數的課程時，以歷史角度及學重演法則，由接觸巴比倫列表，到不連續函數，探討在學習過程中加入數學史怎樣影響學生的數學觀，包括數學趣味、數學人性化量表、數學演變、對數學的看法。 / 本研究於一所中學內進行，以兩班數學成績相近的中四學生為測試對象，一班是實驗組，一班是參照組。實驗組使用的教材由研究者設計出來，參照組則使用教科書。 / 透過認知測試、問卷調查、訪談、概念圖、教師日誌等量化、質化的研究方法，探討是次在教學上使用數學史教學怎樣影響學生的數學觀及老師對是套教材的建議，例如：數學史如何影響學生的數學認知層面、又如何影響學生的數學態度、老師使用這套教材時的困難、老師認為是次數學史教學與平常的教學有何不同、任教老師有否對數學史觀感上的改變、老師會否把數學史在高中教學上使用等。 / 是次研究發現，數學史對不同數學能力學生產生不同層次的效用。在選取數學史材料時，需要注意學生的數學能力及興趣，教學時應作出適切的調整，才能讓不同數學能力的學生之數學觀獲得不同層次的擴展。 / This study, with an analysis of over 40 empirical researches about the history of mathematics teaching, discovered that only a few studies conducted research about the evolution and development of history of mathematics and they seldom analysed students’ mathematical beliefs. In order to fill the gap, this study is aimed to design the topic of function through the perspective of the evolution and development, namely from the Babylonian tables to discontinuous function. It also seeks to explore how that affects students' mathematical beliefs including math fun, math humane scale, mathematical evolution, and students’ views of mathematics. / The study was conducted among two classes of F.4 students who have the similar mathematics abilities in a local secondary school. One is the experimental group and another one is the reference group. The teaching materials developed by the researcher were used in the experimental group while the textbooks were used in the reference group. / Through cognitive tests, questionnaires, interviews, concept maps and teacher journals, the way in which the history of mathematics affects students’ mathematical beliefs is explored .The subsequent analysis of the data attempts to answer the following questions: How the history of mathematics affects students' mathematical cognitive level? How history of mathematics affects students' mathematics attitudes? What difficulties the teacher suffers when using this teaching material? Are there any differences between the normal teaching and history of mathematics teaching? Are there any changes in teacher’s mathematical belief? Is it appropriate to conduct history of mathematics teaching in senior form? / This study discovers that history of mathematics has different effects on students of various mathematical abilities. When selecting the material of history of mathematics, stakeholders need to pay attention to students’ mathematics abilities and interests as well as make appropriate adjustments to teaching, so that students of different mathematical ability canobtain different levels of expansion on their mathematical beliefs. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / 張慧珊. / Parallel title from added title page. / Thesis (Ed.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 134-143). / Abstracts in English and Chinese. / Zhang Huishan.