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 element s of mathematics teaching, three operation s, 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.