Abstract The main purpose of this study is to analyze the professional knowledge of an mathematics expert teacher, who teaches mathematics in a junior high school. Qualitative data were collected by employing observations, interviews, and document analysis. The purposes of this study was as follows: analyze and discuss the performed professional teaching knowledge underlies the teacher's teaching performance of the case study; discuss the contents of the expert teacher's professional teaching knowledge; integrate and generalize and interpret successful factors of the teacher's teaching of the case study, and hope for a complete understanding of the teacher's teaching of the case study, furthermore, to bring the teaching inspiration and innovation to teachers in general, and also induce teacher's power to make teaching innovation development. The researcher exams, analyzes and generalizes the data in connection with the teacher of the case study, in addition to interpret the realized professional teaching knowledge, the researcher also analyzes the factors of the teacher's teaching performance and teaching specialty, teaching performance and main form. Combine the above study outcomes, the researcher proposed high school mathematic teacher with following recommendations: fulfill professional teaching knowledge unceasingly, introspect teaching progress continuously and has the courage to change and hold the ideal of lifetime learning. Moreover, the researcher recommends the teacher education institution of mathematics and the researcher also recommends approach and subject for the future study.

摘要 本研究是在探讨一位澳门初中数学专家教师的教学专业知識之內涵。本研究採用質性的個案研究，針對個案教師，利用觀察、訪談、文件採集等方式，分析個案教師的教學專業知識內涵。本文的研究目的有：分析、討論個案教師教學表現背後所展現出的教學專業知識；探討專家教師教學專業知識之內涵；綜合歸納、說明個案教師教學成功之要素，期能對個案教師教學有完整的了解，並為一般從事教學之教師，帶來教學靈感與創新教學，引發教師教學創新發展的動力。 研究者在檢核、分析、歸納與個案教師有關的資料以後， 除說明其所理解的教學專業知識外，並分析該個案老師教學表現的成因與教學特質、及其教學表現的主要型態。 綜合上述研究的結果，研究者提出了對中學數學教師的建議﹔不斷充實 教學專業知識、不斷反省自己的教學歷程、勇於改變具終身學習的理念。另外，研究者對數學師資培育單位和後續研究的方法以及對象等方面，提出建議事項。