Modern educational theory holds that the teaching goal is the expected learning result of students or the standard to be achieved in learning activities. The teaching goal is student-centered, aiming at students' physical and mental changes, and based on directly observable behavioral indicators. Therefore, the teaching goal is the learning goal of students. We can understand it this way: it expresses students' learning achievements, not what teachers will do; Its expression should be clear and concrete, observable and measurable, and avoid using vague or unrealistic language.

Teaching goal is the direction of classroom teaching. In the whole teaching process, mathematics teachers must be clear about students' expected learning results from beginning to end, or the degree that students should achieve through learning. The basic function of high school mathematics classroom teaching goal is to locate and point out the direction for teaching activities.

High school students are in the mature period of thinking activities and begin to transition to dialectical thinking. For senior high school students, the designed teaching objectives should not only conform to the students' thinking level, but also have appropriate difficulty. The depth and progress of mathematics teaching should be strictly controlled, so that most students can digest and accept it, so that students can achieve the predetermined goals in knowledge, ability, skills, psychology, ideology and morality, so as to improve their comprehensive quality.

2. Can highlight key points and resolve difficulties.

Every class should have a key point, and the whole teaching is gradually carried out around this key point. In order to make students clear about the key points and difficulties of this class, teachers can simply write these contents on the corner of the blackboard at the beginning of the class to attract students' attention. The key content of the lecture is the climax of the whole class. Teachers should stimulate students' brains by changing sounds, gestures, writing on the blackboard, application models, projectors and other visual AIDS, so that students can get excited, have a strong impression on what they have learned, stimulate students' interest in learning and improve their ability to accept new knowledge. For example, in the first lesson of Chapter 8 Ellipse, the focus of teaching is to master the definition and standard equation of ellipse, and the difficulty is the simplification of elliptic equation. Teachers can talk about the direct view of the circle, the slice of radish, the shadow of the disc on the ground in the sun, the earth and artificial earth satellites, so that students can have an intuitive understanding of the ellipse. In order to emphasize the definition of ellipse, the teacher prepared a thin line and two nails in advance. Before giving a strict definition of ellipse in mathematics, the teacher first takes two fixed points on the blackboard (the distance between the two fixed points is less than the length of thin lines), and then asks two students to draw an ellipse on the blackboard according to the teacher's requirements. After painting, the teacher drew two more pictures on the blackboard.