Students should be able to use what they have learned to solve practical problems. Both the Mathematics Curriculum Standards of the United States and the mathematics education in other countries generally attach importance to solving practical problems. China's new curriculum standard requires: "let every student learn valuable mathematics;" Everyone can get the necessary mathematics; Different people get different development in mathematics; Everyone can use what they have learned to solve simple application problems in life. "Learning is the application of mathematical knowledge to solve practical problems. Therefore, teachers should collect the background related to new knowledge in real life and other disciplines and create mathematical problem situations. When students master the relevant knowledge and skills, they can guide students to explore and apply in the real world and build mathematical models to solve problems in real life. In this way, theory and practice are inseparable in the learning process, and teachers can connect with real life to cultivate students' awareness and ability to use what they have learned flexibly to solve practical problems. In addition, as a teaching form, "problem solving" emphasizes students' hands-on, so teachers should not just demonstrate the correct way to solve problems like coaches, but should choose appropriate questions, encourage students to discuss with each other, and let students exchange their own solutions and understanding, so it is more important to create the conclusion of the studied problem than to get the correct answer. In addition, let the students do their own work, do their own calculations, draw their own pictures and answer their own questions, and let the students do some small investigations and experiments, ask their own questions and solve their own problems. The following are my thoughts on this issue since I started teaching mathematics: 1. To cultivate students' awareness of applying mathematics in their lives, such as teaching the stability of triangles, students can explain: Why should the roof of the house where we live be framed into triangles? Why did the carpenter fix the desk for his classmates and nail a diagonal strip at the foot of the desk? Another example is teaching the characteristics of parallelogram. Ask the students to explain: Why should the gate be made into a parallelogram grid instead of a triangle? Through the explanation of some life phenomena, students can feel the close connection between mathematics and real life more deeply. In addition, students should use mathematical knowledge to solve practical problems. For example, in the initial understanding of teaching statistics, the teacher first shows a map of China and asks the students, "What map is this?" The student answered and asked, "Do you know the territory of our country?" After the student answered, he asked, "Do you know the population of our country?" On the basis of students' approximate figures, the teacher accurately stated that the population of China was1295.33 million, and introduced that this was the result of the fifth population census in China recently. At this time, students are interested in the census, and teachers can take the opportunity to introduce a new lesson: "There are many census items, but no matter which one needs to be applied to statistics, we will learn this knowledge today. Do you want to learn? " Then, under the students' strong thirst for knowledge, the topic was revealed. At the same time, practical homework was assigned at the end of this class: a "small census" was conducted in groups to investigate the number of students in the whole fifth grade of our school. This not only makes students realize the role of statistics, but also strengthens the impression of statistics in students' minds, makes students actually investigate and makes students understand that mathematical knowledge is actually used to solve problems in life. Second, arouse students' interest in learning with practical problems. Psychological research shows that the closer the learning content is to students' familiar life background, the higher the students' conscious acceptance of knowledge. Therefore, in classroom teaching, we should combine the teaching content with students' life background as much as possible, and introduce new lessons from practical problems close to students' lives to stimulate students' interest in learning. For example, when learning the concept of "vertical line", we can put forward such a question in combination with reality: "What is the relationship between the positions of two roads at the intersection of roads? For example, what is the relationship between telephone poles and the position of wires above them? " These are concrete examples of mathematics in real life, which can stimulate students' desire for knowledge, make students have the consciousness of "there is mathematics everywhere in life", understand the meaning of vertical line intuitively and realize the importance of learning this content. In teaching, teachers should make full use of modern educational technology to assist teaching, adopt modern teaching methods such as models, slides, videos, computers, etc., increase the interaction between teachers and students, visualize mathematics content, and visualize abstract knowledge at the same time. This can attract students' attention, stimulate students' interest in learning knowledge actively, deepen their understanding of knowledge and improve learning efficiency. Third, it is not a simple and natural thing to combine teaching with practice, find problems from life and ask questions from mastering knowledge to applying knowledge. Without adequate and conscious training, students' awareness of application will not be formed. In teaching, we should pay attention to extracting mathematical problems from concrete things and guide students to solve some problems in daily life with mathematical knowledge, which is helpful to the formation of students' awareness of mathematical application. For example, when talking about "travel application", we use such a problem that we often encounter in life: there are three roads connecting A and B. Under normal circumstances, we choose the shortest road from A to B (saving time and road); Under special circumstances, if the shortest road is too crowded, we will choose another road to get from A to B within a certain period of time. We would rather walk more and speed up the pace (speed) to ensure the time (time is fixed, distance is proportional to speed). Analyzing this problem for students from the perspective of mathematics is the practical application of the relationship between distance, time and speed. Fourth, carefully compile questions to cultivate students' application ability. At present, most of the questions and test questions in mathematics textbooks in China are pure mathematics questions divorced from the actual background, or applied mathematics questions with no background. Such training, over time, makes students have a strong ability to solve ready-made mathematical problems, but their ability to abstract practical problems into mathematical problems is very weak. Mathematics takes the spatial form and quantitative relationship of the real world as the research object, and many of its concepts, theorems and methods are derived from reality. But it has more conclusions to serve all walks of life in production and society. Therefore, under the premise of following the teaching requirements, teachers can carefully compile some questions related to life and science, which can make students feel that mathematics is everywhere around them, thus making them sprout the desire to learn mathematics well and solve practical problems, and combining learning with application to improve students' application ability. In teaching, we can gradually guide students to solve problems according to their own knowledge and practice, and gradually enhance students' ability to learn and use mathematics. 5. Strengthen extracurricular practice and use mathematical knowledge to enter life. Mr. Hua, a famous mathematician, once said: "The universe is big, the particles are tiny, the speed of rockets, the cleverness of chemical engineering, the change of the earth, the complexity of daily use, and mathematics is everywhere." The extensive application of mathematics in real life is expounded wonderfully. It can be said that mathematical modeling has created many life problems. For example, ask students to help their parents calculate the cost of decorating flat tiles at home. First, let the students measure and calculate the area of the room. Understand the application of various calculation methods of graphic area in practice. Then understand the types of floor tiles on the market. For example, there are squares, regular hexagons and so on. We can discuss what type of floor tiles can be seamlessly inlaid. For example, regular triangles, squares and hexagons can be tiled, so can regular pentagons and octagons be tiled? As for the pattern of floor tiles, through the choice of color varieties, the axisymmetric pattern and the central symmetric pattern are obtained. Then, by understanding the unit price of floor tiles, the number of floor tiles, and how to pay the salary for installing floor tiles, the total cost needed is finally calculated. By letting students actively calculate the cost of tiling from a mathematical perspective, students can truly understand that mathematics is everywhere in real life, and can actively try to use the knowledge and methods they have learned to seek strategies to solve problems from a mathematical perspective. In short, teachers should not only create conditions and opportunities for students to apply what they have learned, but also consciously collect and sort out some practical problems that meet the needs of local life and production, pay attention to collecting practical materials related to teaching content, organize teaching activities, increase internship and inquiry activities, find a breakthrough point for the transition to practical problems, and let students understand the application value of mathematics, thus imperceptibly cultivating students' ability to apply mathematics. Students' learning mathematics means "using the learned mathematical knowledge and methods to solve some simple practical problems, which is a necessary tool for daily life." Faced with practical problems, students can actively analyze and explore solutions from the perspective of mathematics, which is also the foundation of cultivating students' application consciousness in mathematics teaching. It is far from enough to cultivate students' mathematical application ability only through classroom teaching. It is also necessary to extend mathematics learning from in-class to out-of-class, gradually train students to understand things, think and solve problems with mathematics, and at the same time create more opportunities for students to use their mathematical knowledge, skills and experience to solve new or difficult problems. This can not only broaden students' horizons and enrich their knowledge, but also make the process of applied mathematics interesting and vivid.