Xianggang xiao xue jing yan shu xue jiao shi de jiao xue xin nian, jiao xue suo xu de shu xue zhi shi he shu xue jiao xue zhi su zhi guan xi: A study of the relationships among Hong Kong primary school experienced mathematics teachers' beliefs about teaching and learning, their mathematical knowledge for teaching and the quality of mathematics instruction.

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