First of all, we should pay attention to determining the key points and difficulties in teaching: according to the students' cognitive level, we should determine the difficulties from the key points. The focus of mathematics teaching is related to students' cognitive structure, which is caused by the contradiction between students' original mathematical cognitive structure and new learning content. Judging from students' cognitive level, it is difficult to master things through assimilation. Of course, in actual teaching, due to the differences of students' individual cognitive level. Careful design of classroom exercises is an important guarantee to improve teaching quality. Teachers can know the effect of classroom teaching in time through classroom practice, so that the information of teaching and learning can get immediate feedback and avoid "mending after the sheep is dead". In short, according to the reality of students, the difficulties should be determined on the basis of grasping the key points.
Secondly, grasping the key points and difficulties is the premise of breaking through the key points. Through the above analysis, we can draw a conclusion that in order to highlight the key points and difficulties in teaching, we must first dig deep into the teaching materials and grasp the key points and difficulties in each chapter and lesson from the knowledge structure. Secondly, prepare enough students. According to students' actual cognitive level, considering the differences of different students' cognitive structures, grasping the key points and difficulties in teaching, making good preparations before class and positioning correctly provide favorable conditions for highlighting key points and breaking through difficulties in teaching. The focus of teaching comes from knowledge itself. Because of the inherent logical structure of mathematical knowledge, knowledge exists objectively, so it is consistent for every student. However, the teaching difficulty is different, depending on the students' own understanding and acceptance. Practice has proved that students of different levels have different breakthrough speeds and levels in the same knowledge point. Because of the different bases of teaching emphasis and difficulty, some teaching contents are both teaching emphasis and teaching difficulty, some are teaching emphasis but not necessarily teaching difficulty, and some are teaching difficulty but not necessarily teaching emphasis. However, the teaching emphasis and difficulty are determined by the teaching objectives of the same teaching content. I think the only way to explore the road of mathematics is to dig deep into the teaching materials, grasp the key points and difficulties of each chapter, and prepare lessons carefully according to the characteristics of knowledge and the laws of students' understanding of things, so as to achieve twice the result with half the effort.
In short, there is no fixed model for how to highlight key points and break through difficulties in mathematics teaching. As long as every math teacher thinks more, spends more time preparing lessons, studies the syllabus carefully, studies the textbooks assiduously, finds out the key points and difficulties in combination with the students' reality, arranges the teaching links reasonably, carefully designs classroom questions, and devotes himself to teaching, we can find the "trick" to highlight the key points and break through the difficulties, thus optimizing the teaching effect.