Mathematics comes from life and is applied to life. Bruner said: "Learning is an active process. The best internal motivation for students to learn is their interest in the materials they have learned, that is, the internal motivation mainly comes from the learning activity itself, that is, the psychological motivation that directly promotes students' active learning." The famous mathematician Hua once said: "For a long time, people have a boring, mysterious and difficult impression on mathematics, one of the reasons is that it is divorced from reality." Therefore, teachers should be good at creating teaching situations from students' familiar real life, let mathematics enter life, let students see and contact mathematics in life, and stimulate students' interest in learning mathematics. For example, when teaching comparative scores, create a good learning situation for students and fully mobilize the enthusiasm and initiative of students' thinking. Teachers use multimedia to lead into teaching, and good results have been achieved. Its practice is to make up the story of "Tang Priest and his apprentice sharing watermelons". At the beginning of the class, the teacher turned on the screen, and four priests and tutors of Tang appeared on a grassy road, scorched by the sun. Wukong skipped to the master and said, "Master, I am so drunk. I'll find something to quench my thirst! " Tell Pig and Friar Sand to watch the master. Soon Wukong came back with a big round watermelon in his arms. Wukong said, "Master and Friar Sand eat watermelon 1/4, Bajie eats watermelon 1/3, and I eat watermelon 1/6. Bajie glared at me and said unhappily, "Monkey, knowing that I have a big belly and eat a lot, you give me the least and you eat the most." As soon as his voice fell, Wukong laughed and said, "What an idiot, idiot, idiot …" At this time, the teacher seized the opportunity and asked, "Why is Wukong called an idiot?" Because students especially like Journey to the West, at the beginning of the course, students are attracted by vivid pictures and personalized dialogues. Every plot is very vivid. When asking questions, the students rushed to answer: "Bajie didn't know that he took the most." "How stupid he is!" Wait a minute. The teacher then asked, "Why didn't Bajie know he got the most?" At this time, the students are eager to try, but they can't say anything. Teachers use doubts to guide situations and reveal topics. In this way, the effect of "a stone stirs up a thousand waves" has been achieved. The introduction of novel and interesting topics has aroused students' desire for knowledge, ignited the sparks of students' thinking and paved the way for learning new knowledge. In this way, knowledge is closely linked with real life, teaching situations are skillfully created, students' interest in learning and desire for knowledge are stimulated, and students' thinking is released.

2. Feel the "abstract beauty" of mathematics with effective inspiring and guiding teaching methods.

Mathematical knowledge is abstract, so we should use scientific and effective teaching methods to fully inspire and guide students to learn independently in mathematical activities such as active observation, experiment and discussion. Starting from the actual situation of students, we should take various effective forms, first inspire, let students observe more activities, actively participate in the whole teaching process, discover laws through their own efforts, communicate the close relationship between old and new knowledge, and fully mobilize students' enthusiasm and initiative in learning. For example, when a teacher was teaching congruent triangles, he put forward such a situation: Xiao Ming drew a triangle, how could he draw a triangle that is identical to his triangle? We know that congruent triangles has three equal sides, three equal angles and six equal elements, so two triangles must be congruent. However, must the six conditions be met? Can the conditions be as few as possible? Guide students to conduct classified research on this. Teachers should correct the unreasonable classification of students; Different strategies put forward by students should be affirmed and encouraged to meet their diverse learning needs and develop their individual thinking. According to the classification of triangle's "edge and angle" elements, teachers and students can get: 1. One condition: one corner, one side. 2. Two conditions: two angles; Both parties; One corner and one side. 3. Three conditions: triangle; Trilateral; Two corners on one side; Corners on both sides. Think, operate and verify according to the above classification order. The teacher collected and compared the students' works, and came to the conclusion that the triangle drawn can not be guaranteed to be congruent when only one or two conditions are given. Practice has proved that teachers' timely guidance and proper teaching can help students learn better, faster and more effectively.

3. Give full play to students' main role in autonomous learning and actively build a mathematical knowledge system.

Bruner once said: "Exploration is the lifeline of mathematics. Without exploration, there will be no development of mathematics. " Mathematics curriculum standards also point out that hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. Mathematics classroom teaching should provide students with the opportunity to "do" mathematics, so that students can turn abstract into concrete in concrete operation, arrangement, analysis and exploration and exchange activities, gain rich experience in mathematics activities, and thus realize effective learning. It is very beneficial for students to gain knowledge through personal experience. For example, in the teaching of "parallelogram area calculation", most teachers will use demonstrations to guide students to learn new knowledge, but teachers still talk a lot and move a lot, often leaving no time and space for students to fully explore. When teaching this course, a teacher first instructed the students to draw a parallelogram with a base of 20 cm and a height of 10 cm, and cut it out with scissors. Then it is proposed whether this parallelogram can be converted into a learned plane figure to calculate its area. Secondly, students' group cooperative learning. In teaching, teachers only prompt, guide and cooperate in time, without too many demonstrations and words, giving students the initiative to learn. In the process of self-exploration, some students found that everyone was holding a parallelogram with equal base and equal height. Their shapes are not necessarily the same, but they can spell the same rectangle, and they have a deep understanding of knowledge and actively build a mathematical knowledge system. Therefore, in mathematics learning activities, teachers should change their roles, give students more opportunities to think, operate and communicate, and let students explore new knowledge, ignite wisdom, build confidence and feel the charm of mathematics in an atmosphere of democracy, equality, trust and tolerance, so as to realize "everyone learns valuable mathematics".

4. Let different students get different development in mathematics and enjoy the "fun of success" in mathematics.

Due to the different levels of intellectual development and personality characteristics, there must be obvious differences in the angle and depth of cognitive subjects' understanding of the same thing, and the cognitive structure thus constructed must be diversified, personalized and imperfect. Students' individual differences are manifested in cognitive styles and thinking strategies, as well as differences in cognitive level and learning ability. As a teacher, we should know the individual differences of different students in time and positively evaluate their innovative thinking, so as to establish a harmonious teacher-student relationship of equality, trust, understanding and mutual respect, create a democratic classroom teaching environment, and let students express their opinions boldly and show their personality characteristics. For students with difficulties, teachers should give timely care and help, encourage them to actively participate in mathematics learning activities, try to solve problems in their own way, and express their views; Teachers should affirm their little progress in time, patiently guide them to analyze the causes of mistakes, encourage them to make efforts to correct and strive for progress, thus enhancing students' interest and confidence in learning mathematics. For example, when solving equations: ①x+y=7②3x+y= 17, most students first subtract the two equations to eliminate y, but one student thought of changing the second equation to 2x+(x+y)= 17, and then substituting it into the first equation x+y=7 to get 2x. In the process of teaching, students put forward completely different opinions from teachers, and teachers should not simply deny students. When students make even a little progress in their studies, they should be warmly encouraged. Different students express different languages, whether strict or not, we should actively encourage and guide them to be strict step by step. Let students create opportunities to show their research results, gain successful experience, stimulate their enthusiasm for learning, and enjoy the "fun of success" in mathematics learning. Paying attention to differences and encouraging different learning processes embodies that "different people get different development in mathematics."