本研究的主要目的在於發展中學教師數學教學專業知能結構、項目與指標。本研究乃 一為期四年的發展性研究，研究方法主要採問卷調查法及焦點團體討論法，樣本包括75位中 學數學教師、53位數學師資培育者、全國性隨機抽樣之2，077位國中生及2,437位高中生。本 研究發展出一個包含數學教學元素、運算、核點的數學教學專業知能結構，其中共有20個元 素，3個運算與3個核點，每一運算作用在一或多個元素上，搭配核點的選擇，可產生許多數 學教學知能專業項目，數量龐大無法窮盡，以此結構可做出有系統的數學教學知能項目選 擇，可供教師檢定、甄選、評鑑使用。除此，研究結果顯示不論國中或高中，從學生的觀點 來看，數學教學最重要的專業指標是要能替學生解惑，而重視公式與性質的推導過程也是另 一項重要的指標。

This study is a four-year study that aims at developing the structure, items and indicators of mathematics teaching competence (MTC) in the high school level. A total of 75 secondary school elite mathematics teachers and 53 mathematics teacher educators either participated in focus group sections or be surveyed with questionnaires. A national random sample of 2077 junior high school students and 2437 senior high school students were surveyed. This study develops a structure of MTC which is structured around three objects: element, operation, and kernel. With these, a total of twenty elements of mathematics teaching, three operations, and three kernels are engaged. Any operation may act on any element with a certain kernel focus, and this process may generate unlimited MTC items. The structure of MTC may properly help classifying, organizing and selecting MTC items in the teacher recruitment, qualification assessment, and evaluation settings. This study also finds that from the student points of views at both junior and senior high school levels, the foremost indicator of MTC is being able to resolve students’ doubts. Emphasizing how a formula or rule is derived is another important MTC indicator.