First, cultivating interest is the driving force to overcome "thinking inertia".

Einstein said, "Interest is the best teacher". Therefore, students should first be interested in the subject of mathematics, so as to open the door to the treasure house of mathematics. The way to overcome students' long-standing mathematical "thinking inertia" is not only to urge and correct, but also to change students' subjectivity. Only by improving students' interest in high school mathematics learning can we fundamentally change students' "thinking inertia". Interest is the driving force to overcome "thinking inertia".

For example, there is a female student in the first year of high school where I teach. When she was in junior high school, she was not interested in mathematics and stayed away from it. Every time she has a math problem, she only does it twice. Once she couldn't hold on, she gave up and never had the courage to do similar problems again. Through several exchanges and discussions with her, I understood the crux of her laziness, so I first shared with her her several experiences of getting high marks in mathematics, and at this time her look showed brilliance and her eyes sparkled. Due to some personal experiences, her interest in mathematics has gradually increased. She admitted that she was more relaxed and confident in learning math. Since then, once students have subjectively overcome the inertia of thinking and become interested in mathematics, they will take the initiative to enter the hall of mathematics and gradually feel the sense of satisfaction and accomplishment in learning. It can be seen that interest is the driving force to overcome students' "thinking inertia".

Second, the step-by-step setting problem is a stepping stone to overcome students' "thinking inertia".

Psychological research shows that people's thinking begins with problems. The problem points out the direction of research, which can mobilize people's accumulated knowledge and think boldly and actively, thus solving the problem. Many students' thinking inertia is not formed overnight. This is also a problem that some teachers are eager to achieve success in class or don't set the difficulty according to the actual situation of students, which leads to the bad habit of students' fear of difficulties or disdain for thinking, thus resulting in thinking inertia. According to my teaching experience of more than ten years, I guide students to learn step by step in the form of writing a learning guidance outline. Students gradually lead to the deep level of the problem in the problem setting from shallow to deep and from easy to difficult. After a period of time, students gradually learned to imitate and summarize in their studies, and they were able to list the outlines on their own initiative and think deeply. Once they find a problem, they don't want to think deeply as before, but they will pursue it, feel it in exploration, understand it, and never give up until they reach their goal. It can be seen that setting questions step by step is a stepping stone to overcome students' "thinking inertia".

For example, if we don't pay attention to the step-by-step guidance and ask students to prove and memorize formulas in the content of "N items and formulas before geometric series", many students will dabble in it, unwilling to study and think deeply, and will only stick to formulas in the future. When I was dealing with this category, I listed the following questions to guide my inquiry: I am willing to give you 100 yuan every day for one month, but you must return me 1 cent on the first day of this month, 2 cents on the second day and 4 cents on the third day ... that is, the money returned to me the next day is twice as much as that of the previous day. When the students saw this question, they all thought the teacher was ridiculous. But I calculated and found that the money returned to me reached10 million (far exceeding the 3000 I gave). Students' thinking is strongly stimulated, and they find the close relationship between mathematics and life, so they think deeply, summarize abstractly, establish a mathematical model, turn practical problems into mathematical problems, further explore the conclusions of problems, and discover the relevant laws of geometric series, which makes it obvious to master this knowledge point.

This is the role of setting questions step by step in overcoming "thinking inertia" in learning. The problem is a stepping stone to overcome the "thinking inertia".

Third, encouraging practice is a catalyst to overcome "thinking inertia".

There is also a very important factor in the emergence of thinking inertia, that is, "attack." The failure of the attack and the disapproval of the teacher's peers lead to students' unwillingness to think, thus forming thinking inertia. Therefore, we must let students taste the joy of learning and success to encourage them to think positively. In fact, mathematics learning is a lively, proactive and personalized process. Learning mathematics knowledge should start from students' existing life experience and let students experience the process of abstracting practical problems into mathematical models and explaining and applying them. The cultivation of active thinking quality is inseparable from the participation of "practice". Generally speaking, "practice" includes the following four processes: (1) observation (2) operation (3) calculation or demonstration (4) summary. Among them, "calculation or demonstration and summary" is an important link to cultivate students' thinking quality.

For example, geometry learning is very abstract and difficult. If students are afraid of difficulties at first, or just passively learn this knowledge point, they will give up lazily when they encounter problems in the future. This is a great obstacle to the cultivation of students' problem-solving thinking. Therefore, when studying geometry, I let students get in touch with the real world, build an intuitive model, and participate and practice by themselves. First of all, students combine daily life and experience the characteristics of graphic transformation through observation; Secondly, students personally participate in the operation, through folding, cutting, drawing, measuring and even independent design activities, deepen their personal experience in all aspects of graphics, master relevant knowledge and methods, and lay the foundation for geometry learning; Thirdly, students can participate in calculation or demonstration by themselves to solve specific mathematical problems; Finally, summarize the law and draw relevant conclusions. Through these practical steps, our students not only have intuitive and perceptual knowledge, but also have more rational knowledge, which greatly enhances their interest in geometric problems and improves their ability to understand geometric problems. They are no longer passive in thinking quality, but actively explore and extend, which is of great help to students in learning geometry.

Therefore, practice is like a "catalyst" to promote students' thinking and overcome the "thinking inertia" in the process of solving problems.

Fourth, initiative and good thinking are the core of overcoming "thinking inertia".

The formation of thinking inertia is the expression of passive thinking. If students develop good thinking habits, then the important link of solving mathematical problems can be completed. Cheng Yi, an educator in the Song Dynasty in China, said: "The way to learn lies in thinking, and thinking can be obtained, but thinking cannot be obtained." Active thinking is one of the important thinking qualities for students to solve problems. If students want to overcome the inertia of thinking, they must form thinking habits, so as to complete the inquiry activities in mathematics.

For example, the concepts that are easily confused in mathematics (positive and non-negative, empty set and set {0}, acute angle and the angle of the first quadrant, necessary and sufficient conditions, function and mapping, etc. ), if students learn passively, their thinking stops at rote memorization of concepts, and they are not good at induction, discrimination and comparison, and they are not good at distinguishing the connections and differences between concepts, it will be difficult for them to have a profound understanding of knowledge, thus affecting its relevance.

In short, in order to prevent students from "thinking inertia" in the process of solving problems, high school students need to develop the thinking quality of interest, diligent questioning, emphasis on practice, good thinking and diligent memory, and correct their lazy habits. If we can persist in doing these things well, students will swim in the ocean world of mathematics and eventually feel the joy and satisfaction of success.