This study aimed to increase efficacy for teaching mathematics in pre-service early childhood teachers through the presentation of five video lessons on topics in early childhood mathematics. Each lesson entailed reading a short essay on a topic related to children's mathematical thinking and then watching a short video of a child engaged in a relevant task and a clinical interview with an adult. This study also examined pre-service teachers' knowledge of mathematical development (KMD) and intellectual modesty, or the awareness of the limits of one's knowledge, as possible mediators of change in efficacy. Results showed that the video lessons did significantly increase efficacy for teaching mathematics, but that KMD and intellectual modesty were not significant mediators of the change in efficacy. In effect, confidence appeared disconnected from competence. Follow-up analyses revealed the importance of rich mathematical content within the videos in producing increased confidence and competence.

Education plays a vital role in any society; so much so, that countries strive to have not only adequate, but excellent educators in their classrooms. The aim of this study was to understand how beginning secondary mathematics teachers define success and to what experiences they attribute that success. Specifically, the central research question addressed was, "To what degree were significant attributes or experiences, important to the success of the first year teaching, learned pre-teacher education program, during a program, or post-program?" The practical goal of filling classrooms with great educators needs to be informed by research on how best to recruit highly qualified candidates into the field of mathematics education and how best to facilitate the teacher preparation process. This study employed a mixed methodology, using a sample of beginning secondary mathematics teachers to gather both quantitative and qualitative data on when they reported gaining influential knowledge or experiences. In particular, input from those who have had some success as beginning mathematics teachers was desired. The interview protocol designed for these participants added depth to the survey responses. Emphasis was placed on the relative importance of the three stages, pre-, during, and post-program, in developing common attributes associated with good teaching. Two characteristics were generally discussed as developing pre-program: being a self-starting and hard-working individual, and holding a belief that every student can learn. Beginning teachers viewed these traits as important for their success. Participants also felt that they acquired both practical classroom tools and educational theory from their teacher education program; having program instructors model pedagogy and mathematical instruction, and having opportunities to practice incorporating theory into their teaching were also seen as important. These aspects distinguished particularly prominent roles that the teacher education program played in shaping its graduates. Classroom management and being flexible and adaptive to different contexts were the most notable qualities frequently reported as being learned post-program. The study's results have implications for informing the types of students a mathematics education program should try to attract or recruit and defining areas where practicum or internship components might be incorporated into the teacher education process.

The purpose of this study is to determine how well traditional elementary preparation programs and alternative elementary certification programs are perceived by teacher candidates, to prepare them to teach mathematics to the standards required today. Using a qualitative design, this study examines how various ranked elementary teacher preparation programs and alternative certification programs are preparing elementary teachers to teach the mathematics envisioned in the CCSSM. Participants in this study all attended an undergraduate elementary teacher preparation program or an alternate route certification program. To paint a holistic picture of elementary teacher preparation in mathematics, each undergraduate elementary teacher preparation programs was ranked in a different level in the NCTQ Teacher Preparation Review. Qualitative surveys and interviews were used to gather data on participants' perceptions of their preparation in mathematics. Twenty-five participants agreed to take part in this study. Participants filled out a two-part survey. The first part of the survey asked background questions on their coursework and field experiences in mathematics along with a survey on their beliefs about their ability to teach mathematics. The second part was a pedagogy survey that asked participants how they would teach particular mathematics concepts that now require a conceptual understanding in the CCSSM. Seven participants agreed to participate in a follow up interview to further investigate their experiences in mathematics preparation in their teacher education programs. The data showed that there is little consistency in the mathematics education of elementary teachers within a teacher preparation program and across different teacher preparation programs. There is little standardization in the coursework for participants from different preparation programs and participants within the same program. The interviews revealed that the degree to which participants were able to teach mathematics in their field experiences also varied within and across teacher preparation programs. Furthermore, the interviews also unveiled that the CCSSM were also studied and utilized in different capacities within and across institutions. Lastly, the data from the surveys disclosed that the majority of participants feel that they have the ability to be effective teachers of mathematics yet the majority of participants teach mathematics for a procedural understanding.

王倩婷 = The conception of mathematics among Hong Kong mathematics teachers / Wong Qian Ting. / "2003年12月". / 論文(哲學碩士)--香港中文大學, 2003. / 參考文獻 (leaves 107-113). / 附中英文摘要. / "2003 nian 12 yue". / Wang Qianting = The conception of mathematics among Hong Kong mathematics teachers / Wong Qian Ting. / Lun wen (zhe xue shuo shi)--Xianggang Zhong wen da xue, 2003. / Can kao wen xian (leaves 107-113). / Fu Zhong Ying wen zhai yao. / Chapter 第一章 --- 緒論 / Chapter 1.1 --- 硏究背景 --- p.1-3 / Chapter 1.2 --- 硏究意義 --- p.3 / Chapter 第二章 --- 文獻回顧 / Chapter 2.1 --- 香港小學數學教育的現況 --- p.4-7 / Chapter 2.2 --- 學生的數學學習 --- p.8-11 / Chapter 2.2.1 --- 學生的數學學習與其數學觀 --- p.8 / Chapter 2.2.2 --- 數學學習、課程改革及數學觀的關連 --- p.9 / Chapter 2.2.3 --- 學生的數學學習與教師的數學觀 --- p.10 / Chapter 2.3 --- 教師的數學觀 --- p.12-18 / Chapter 2-3.1 --- 信念的定義 --- p.13 / Chapter 2.3.2 --- 信念的形成 --- p.16 / Chapter 2.3.3 --- 信念的結構 --- p.17 / Chapter 2.3.4 --- 小結 --- p.18 / Chapter 2.4 --- 教師數學觀的理論框架 --- p.19-25 / Chapter 2.4.1 --- 學者們提出的數學觀觀點 --- p.19 / Chapter 2.4.2 --- Ernest ( 1989)的數學觀理論框架 --- p.20 / Chapter 2.4.2.1 --- 對數學本身的觀念 / Chapter 2.4.2.2 --- 數學教學觀 / Chapter 2.4.2.3 --- 數學學習觀 / Chapter 2.4.3 --- Thompson (1991)的數學教學觀理論框架 --- p.23 / Chapter 2.4.4 --- Perry et al ( 1998，1999 )的數學教學觀理論框架 --- p.24 / Chapter 2.5 --- 教師的數學觀與其教學 --- p.26-28 / Chapter 2.6 --- 教師的背景、專業知識與其教學 --- p.29-30 / Chapter 2.7 --- 教學策略 --- p.31-36 / Chapter 2.7.1 --- 教學策略分類 --- p.31 / Chapter 2.7.2 --- 過往硏究綜述 --- p.33 / Chapter 2.8 --- 教師的數學觀與其教學策略的硏究 --- p.37-43 / Chapter 2.8.1 --- 過往硏究方法綜述 --- p.37 / Chapter 2.8.1.1 --- 質化硏究 / Chapter 2.8.1.2 --- 量化研究 / Chapter 2.8.1.3 --- 同時以質化及量化進行的硏究 / Chapter 2.8.2 --- 本港其他的數學教學計劃 --- p.40 / Chapter 2.8.3 --- 過往硏究的限制 --- p.42 / Chapter 第三章 --- 硏究方法 / Chapter 3.1 --- 硏究問題 --- p.44 / Chapter 3.2 --- 硏究工具 --- p.44-46 / Chapter 3.2.1 --- 背景資料 --- p.44 / Chapter 3.2.2 --- 數學觀訪問 --- p.45 / Chapter 3.2.2.1 --- 假設處境訪問 / Chapter 3.2.2.2 --- 數學教學觀訪問 / Chapter 3.2.2.3 --- 教學策略 / Chapter 3.3 --- 硏究對象 --- p.47-49 / Chapter 3.3.1 --- 硏究對象的選取 --- p.47 / Chapter 3.3.2 --- 硏究對象的個人資料 --- p.47 / Chapter 3.4 --- 硏究程序 --- p.49 / Chapter 第四章 --- 教師的一般數學觀 / Chapter 4.1 --- 數學觀 --- p.50-55 / Chapter 4.1.1 --- 強調運算 --- p.50 / Chapter 4.1.2 --- 講求理解 --- p.51 / Chapter 4.1.3 --- 與曰常生活有關 --- p.51 / Chapter 4.1.4 --- 訓練思考 --- p.52 / Chapter 4.1.5 --- 特定內容 --- p.53 / Chapter 4.1.6 --- 建構而成 --- p.54 / Chapter 4.1.7 --- 數學特性 --- p.54 / Chapter 4.2 --- 數學教學觀 --- p.55-60 / Chapter 4.2.1 --- 做中學習 --- p.55 / Chapter 4.2.2 --- 初學較嚴謹 --- p.56 / Chapter 4.2.3 --- 教師角色 --- p.51 / Chapter 4.2.4 --- 考試影響 --- p.59 / Chapter 4.2.5 --- 解難教學 --- p.59 / Chapter 4.3 --- 數學學習觀 --- p.60-61 / Chapter 4.3.1 --- 判斷對錯 --- p.60 / Chapter 4.3.2 --- 學生角色 --- p.61 / Chapter 第五章 --- 數學教師的三種類型 / Chapter 5.1 --- 實用型 --- p.62-75 / Chapter 5.1.1 --- 數學觀 --- p.62 / Chapter 5.1.1.1 --- 學校數學 / Chapter 5.1.1.2 --- 課題間關係薄弱 / Chapter 5.1.1.3 --- 與日常生活有關 / Chapter 5.1.1.4 --- 獨特性低 / Chapter 5.1.1.5 --- 權威判斷 / Chapter 5.1.2 --- 數學教學觀及其教學 --- p.66 / Chapter 5.1.2.1 --- 例題教學 / Chapter 5.1.2.2 --- 著重形式 / Chapter 5.1.2.3 --- 訓練思考和解難能力 / Chapter 5.1.2.4 / Chapter 5.1.3 --- 數學學習觀及其學生學習 --- p.72 / Chapter 5.1.3.1 --- 做中學習 / Chapter 5.1.3.2 --- 模仿者 / Chapter 5.2 --- 理解型 --- p.76-86 / Chapter 5.2.1 --- 數學觀 --- p.76 / Chapter 5.2.1.1 --- 理解和明白 / Chapter 5.2.1.2 --- 溝通工具 / Chapter 5.2.1.3 --- 數學思維 / Chapter 5.2.1.4 --- 學校數學以外 / Chapter 5.2.1.5 --- 逐步建構 / Chapter 5.2.2 --- 數學教學觀及其教學 --- p.81 / Chapter 5.2.2.1 --- 強調槪念 / Chapter 5.2.2.2 --- 反例突顯重點 / Chapter 5.2.2.3 --- 不同形式教學 / Chapter 5.2.2.4 --- 連繫已有知識 / Chapter 5.2.2.5 --- 一題多解 / Chapter 5.2.3 --- 數學學習觀及其學生學習 --- p.85 / Chapter 5.2.3.1 --- 內化教師教學 / Chapter 5.2.3.2 --- 因時制宜 / Chapter 5.3 --- 訓練思考型 --- p.87-98 / Chapter 5.3.1 --- 數學觀 --- p.87 / Chapter 5.3.1.1 --- 訓練思考 / Chapter 5.3.1.2 --- 嚴謹客觀 / Chapter 5.3.1.3 --- 情感態度 / Chapter 5.3.1.4 --- 持續發展 / Chapter 5.3.2 --- 數學教學觀及其教學 --- p.91 / Chapter 5.3.2.1 --- 數學性 / Chapter 5.3.2.2 --- 源於理解 / Chapter 5-3.2.3 --- 重組內容 / Chapter 5.3.2.4 --- 多種教學 / Chapter 5.3.2.5 / Chapter 5.3.2.6 --- 前後連繫 / Chapter 5.3.3 --- 數學學習觀及其學生學習 --- p.96 / Chapter 5.3.3.1 --- 表逹想法 / Chapter 5.3.3.2 --- 判斷對錯 / Chapter 第六章 --- 討論 / Chapter 6.1 --- 硏究結果 --- p.99-104 / Chapter 6.1.1 --- 實用型 --- p.99 / Chapter 6.1.2 --- 理解型 --- p.101 / Chapter 6.1.3 --- 訓練思考型 --- p.103 / Chapter 6.1.4 --- 小結 --- p.104 / Chapter 6.2 --- 總結 --- p.105-106 / Chapter 6.2.1 --- 實用層面 --- p.105 / Chapter 6.2.2 --- 學理層面 --- p.105 / Chapter 6.2.3 --- 未來硏究及發展方向 --- p.106 / 參考資料 --- p.107-113 / 附錄 / 附件一 實際教學片段 --- p.114-115 / 附件二 背景資料問卷 --- p.116-117 / 附件三 假設處境訪問大綱 --- p.118 / 附件四 數學教學觀訪問大綱 --- p.119 / 附件五 教學常見問題訪問大綱 --- p.120 / 附件六 觀課訪問大綱 --- p.121 / 圖表目錄 / 圖一 數學觀硏究框架 --- p.2 / 圖二 教師的數學觀與學生學習的關係 --- p.11 / 圖三 教師信念的架構 --- p.13 / 圖四 以情感度和認知度去劃分信念 --- p.14 / 圖五 數學觀的兩個度向：「傳遞」及「以學生爲中心」 --- p.25 / 圖六 影響教師數學教學行爲的因素 --- p.26 / 圖七 數學教師信奉的觀念與實際情況之關係 --- p.27 / 圖八 數學教學策略分類 --- p.33 / 圖九 硏究框架 --- p.44

過去二十多年，亞洲國家的學生在一些國際數學能力測試 (如 TIMSS、PISA) 中表現傑出，因此，許多學者嘗試找出這些學生取得優異成績的原因。根據經濟發展與合作組織的報告，在眾多變項中，教師的質素是影響學生學業成果的最重要因素。究竟一個能使學生有效學習的數學課堂，教師應擁有什麼數學知識? 教師應抱持什麼教學信念？ / 很多學者(如Ball, Thames, & Phelps、Shulman等)為鑽研教師的教學知識建立了不少理論，其中Ball和她的團隊利用Shulman有關教師知識的架構而發展出一項針對數學教學所涉及知識的類別，稱為「教學所需的數學知識」(mathematical knowledge for teaching，簡稱MKT)。此外，不少研究顯示除了知識之外，教師信念同樣影響教師的數學教學質素(Mathematical Quality of Instruction, 簡稱 MQI)。 / 本研究旨在了解香港高小經驗數學教師的MKT 和教學信念之現況，同時亦希望找出擁有高MKT及持不同教學信念的教師對其自身MQI之影響。 / 資料蒐集分兩階段進行，第一階段邀請105位擁有五年或以上數學教學經驗的教師參與，透過MKT測試卷和信念問卷分別量度他們的MKT和信念現況。至於第二階段，從第一階段參與的教師中挑選出八位經過測試結果屬於高水平的MKT的教師進行個案研究，研究員先觀察他們四節課堂教學，然後進行課後半結構訪談，測量他們的教學表現及進一步了解他們的教學信念。 / 研究結果顯示：(1) 在職經驗數學教師在圖形空間範疇的MKT成績高於數範疇的MKT成績；(2) 雖然信念問卷結果反映全部教師傾向抱持非傳統的教學信念，但是部分參與個案研究的教師卻抱持傳統教學信念的特徵；(3) 教師的教學質素並非全受著MKT的影響，擁有高MKT水平的教師而又持非傳統信念的教師的教學質素，比持有傳統信念特徵的教師的教學質素好；而(4) 教師在忙碌的教學生活下，大多沒有靈活多變的教學方法。本研究建議政府應推行政策減輕教師的工作量，而師訓機構宜開辦課程讓教師能掌握具體設計(尤其是數範疇) 的學習活動課程，協助教師建立專業交流網絡，創造機會讓教師進行反思，從而提高他們自身的教學能力。 / Over the past two decades, students from Asian countries have outperformed their counterparts in a number of international mathematics achievement studies such as TIMSS and PISA. Many scholars are therefore interested in investigating the reasons for Asian students’ higher performance. According to a research report released by the Organization for Economic Development and Cooperation, among the school variables which affect students’ learning outcomes, the quality of teachers play the most vital role. To provide a classroom environment for students that enables effective learning in mathematics, what kind of knowledge does a teacher need? And what kind of beliefs should a teacher hold? / Many scholars (e.g., Ball, Thames, & Phelps; Shulman, etc.) have proposed theories about the construction of teachers’ knowledge. Ball and her team, based on Shulman’s framework of teachers’ knowledge, developed a framework for "Mathematical Knowledge for Teaching" (MKT). Moreover, research studies have shown that in addition to MKT, a teacher’s beliefs also play an important role in a teacher’s mathematical quality of instruction (MQI). / This study aims to examine the MKT levels and beliefs of teachers who possess 5 or more years’ experience in teaching senior primary level mathematics, and to explore the influence of beliefs about teaching and learning on their MQI for teachers who have a high MKT level. / This study has undergone two stages in collecting data. During the first stage, 105 in-service experienced primary mathematics teachers were invited to complete an MKT instrument and a survey on beliefs about teaching and learning. It aims to explore their MKT levels and types of beliefs. At the second stage, eight teachers from the high MKT score group were selected for lesson observations and semi-structured interviews. Its aims were to explore their teaching performance and further verify their types of beliefs. / Results showed that (1) in-service experienced mathematics teachers generally scored higher MKT scores in the dimension of Shape and Space than in the dimension of Number. (2) They also showed that the scores of all 105 in-service teachers’ beliefs were identified as non-traditional. However, some teachers who were selected to take part in the subsequent case study held the characteristics of traditional transmission-oriented beliefs as revealed in the interview. Moreover, the findings also indicated that (3) the teachers’ instructional ability was not only affected by their MKT, their beliefs also played a part in shaping their pedagogical practices. Among the teachers with high MKT level, those teachers who held non-traditional beliefs outperformed their counterparts in terms of MQI. (4) It was also shown that teachers did not have a rich repertoire of teaching strategies to be used in classroom teaching because they lacked sufficient time to prepare their lessons. / In light of the findings, the Government should revise the current policy to reduce teachers’ workload. In addition, teacher training institutions should offer courses for teachers to design activities facilitating students’ learning in general, and strengthening the learning activities in the dimension of Number in particular. They should help teachers to establish professional exchange networks. By providing more chances for teachers’ to reflect, their teaching proficiency will be improved. / 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. / 陳詠心. / Parallel title from added title page. / Thesis (Ed.D.) Chinese University of Hong Kong, 2015. / Includes bibliographical references (leaves 132-149). / Abstracts also in English. / Chen Yongxin.

Abstract not available

Thesis (M.Ed.)--University of Hong Kong, 1980. / Includes bibliographical references (leaf 70-74). Also available in print.

Thesis (M.Ed.)--University of Hong Kong, 1980. / Includes bibliographical references. Also available in print.

Thesis (M.A.)--University of Toronto, 2006. / Source: Masters Abstracts International, Volume: 44-06, page: 2527. Includes abstracts in English and Hungarian.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Penny J. Gilmer, Florida State University, College of Education, Dept. of Middle and Secondary Education. Title and description from dissertation home page (viewed Sept. 23, 2004). Includes bibliographical references.