Based on the classification from quantitative studies, total six teachers, two in each category, were interviewed to construct six individual qualitative case studies. The results suggested that teacher professional knowledge about function and beliefs about mathematics had impacts on their teaching approaches. The teaching approaches can be classified into three categories, i.e, content-centered with performance focus, contentcentered with understanding focus and student-centered with cognitive focus, which constituted traditional content-centered and student-centered perspectives on teaching approaches. Emphasizing process or product is still dichotomy for teachers. / In conclusion, this study showed the significance of subject matter knowledge, pedagogical content knowledge and beliefs about mathematics to teaching approaches of mathematics teachers, which pave the way for future education researches in this field. This study has also provided some valuable experiences in applying hypothetical situations to education researches. In the future, further explorations can be conducted in finding the effect of contextual factors to teaching approaches and how teaching approaches influenced student learning. / In past 30 years, under the global trend of curriculum reform, new requirements on teacher professional knowledge and belief were put on teachers. Accordingly, the focus of research on teaching was shifted from finding effective teaching behavior to in search for teacher professional knowledge, beliefs and cognitions behinds their behaviors. Before, the literatures on teacher professional knowledge were mainly focused on what professional knowledge that teachers have and/or should have. Only few literatures were interested in the effect of teacher professional knowledge and beliefs to teaching approaches. / The main objective of this study is to fill in the missing pieces and investigate the effect of teacher professional knowledge and mathematics beliefs on teaching for inservices mathematics teachers. Mixed method was applied in this study in order to build up some comprehensive understandings to the effects. In quantitative part, this study has surveyed ninety one high school mathematics teachers in M city to find out the deepness of professional knowledge and mathematical beliefs that teachers held. For professional knowledge, the results showed that teachers had different levels of subject matter knowledge and pedagogical content knowledge. For beliefs about mathematics, the results echoed with Ernest's (1989) classification of teacher mathematical beliefs, i.e. instrumentalist, Platonist, and problem-solver. / 張侨平. / Adviser: Ngai-Ying Wong. / Source: Dissertation Abstracts International, Volume: 73-03, Section: A, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 184-209). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in Chinese and English. / Zhang Qiaoping.