Analytical geometry was an important course in high school mathematics learning, and innovative teaching was the main direction of curriculum reform. Therefore, how to innovate in analytic geometry teaching was one of the important problems in high school mathematics teaching. Based on the teaching content and practice, and comparing with the teaching methods of analytic geometry in foreign countries, the key and difficult points of analytic geometry teaching in senior high school mathematics are clarified by studying the main contents of analytic geometry in senior high school and its teaching significance. On the premise of paying attention to the knowledge base, it is proposed that geometric intuition should be taught in combination with reasonable reasoning and deductive reasoning. On this basis, the geometric sketchpad should be fully utilized as a supplement, and mathematical stories should be appropriately interspersed to arouse students' interest.

Learning from thinking, thinking from doubt, People's thinking begins with problems, and they think only when they have problems. As a hot spot of educational research nowadays, the core accomplishment of mathematics leads the new direction of educational reform, puts forward higher requirements for solving mathematical problems, and pays more attention to cultivating students to solve mathematical problems with the thinking of core literacy of mathematics. Through discussing the meaning of mathematics core accomplishment and the recognition of "problem solving" under the background of mathematics core accomplishment, this paper discusses three methods of cultivating students' problem consciousness: creating situation, arousing problem consciousness, making students want to ask questions; The democratic atmosphere, the cultivation self-confidence, causes the student dares to ask; the positive appraisal, the body Test the sense of achievement, make the students happy to ask, so as to arouse teachers pay attention to cultivating students' problem awareness and ability, and stimulate students' creative thinking.