The rapid development of society requires that school education should teach students "useful mathematics", apply what they have learned and cultivate students' awareness of applying mathematics. Mathematical knowledge comes from nature and people's actual needs. In fact, many important concepts, theorems, formulas and laws in mathematics textbooks are produced by application and developed for application. How every concept of mathematics is put forward, discovered, abstracted, generalized, deduced and judged in the long river of its development contains rich thinking factors and values. Only in the process of revealing its occurrence can we deeply understand the concept, and only in the meaningful mathematical activities that reflect practical application can we master the "living" mathematical concept. For students, the most common source of difficulties is that the mathematical knowledge used rarely appears in the form of the founder's original function. After concentrating and polishing, they hide the tortuous, abstract and complicated mathematical process, and present a rigorous, abstract and refined mathematical conclusion after processing. An important task of our teaching work is to excavate mathematics knowledge as vividly as possible from the concrete world that conforms to students' psychology, so that students can personally participate in the process of "knowledge rediscovery", experience the tempering of the exploration process, absorb more thinking nutrition, and prepare for interesting and nostalgic mathematics applications. So how to cultivate students' awareness of mathematics application in mathematics classroom teaching?

First, provide a "prototype" of mathematics, and turn hard study into enjoyable study. Mathematics truly reflects a certain relationship in practice. Learning mathematics should be good at finding "prototype" in practice and getting inspiration. If you study geometry knowledge, you can tell students that the concept of human geometry first comes from the direct understanding of nature, and obtains the concepts of "circle" and "bend" from the sun and the moon; The concept of "straightness" is derived from the number and straightness of solar rays; Get the concept of "ping" from a still lake. In the process of making various tools and utensils, human beings have deepened their understanding of geometric figures: a tight string can get a straight line; Make round utensils and understand the nature of circles. This concept, which is abstracted from the surrounding world and summarized in practical activities, is the original geometric concept. Therefore, when explaining boring and simple geometric concepts, we should closely connect with examples in nature and real life, so that students can feel that geometric knowledge is not a simple concept, but a real life, within reach. The real world is the source of mathematical knowledge, and rich mathematical practice, after accumulation, induction, screening and refining, finally rises to mathematical theoretical knowledge. Now, when we spread the knowledge of mathematics, we should restore and regress the knowledge again, and integrate it into rich life practice, so that students can understand middle school mathematics and better understand mathematical concepts in use. For example, when talking about the concept of number axis, let students know the common thermometers in real life, observe the positions of positive numbers, zero numbers and negative numbers on the thermometers, and then ask questions. If the thermometer is regarded as a straight line, then the rational number can be expressed by a straight line, which leads to the concept of number axis, which is more acceptable to students. Spreading knowledge in this way, it seems that mathematics is in front of us, so intimacy arises spontaneously, and students will turn hard study into happy study.

Second, constructing mathematical background and stimulating students' interest in learning abstract generalization are the key steps to form concepts and the core link of "mathematicization". Students' difficulties in learning mathematics often occur at this "key point" in the process of abstract thinking from concrete and intuitive "words" to "mathematical symbols". At this time, students should build bridges for them and help them tide over the difficulties. In this way, students' understanding of abstract knowledge has a rich and concrete background and vivid and intuitive experience. For example, it is valuable to change subtraction into addition in mathematics, but it is difficult for students to understand. We can construct the following life background-the general cashier's account has three columns of income, expenditure and balance, but the cashier who likes to simplify can change it to only two columns of income and balance, and expenditure is regarded as income, so "+"and "-"should be added before the figures. Balance of payments is simplified as: income balance +9+9-5+4+4+8-3+5. The above process contains an equation: 9-5+4-3 = (+9)+(-5)+(+4)+(-3), so addition and subtraction are unified. Many such concrete examples can be introduced into mathematics teaching. Because these examples are intuitive and vivid, attractive to students, easy to understand and accept, so students learn lively and interesting. Students have changed from hating and fearing mathematics to loving mathematics. It not only stimulated their interest in learning mathematics, but also learned the ability to solve practical problems.

Third, reproduce the process of mathematical knowledge and stimulate students' desire to explore.

Living space is a magical mathematics kingdom. If you carefully observe and know the food around you from the perspective of mathematics, you will find that the laws of mathematics skillfully arrange your life, and life is full of mathematical principles. For example, when the sum of the external angles of the N-polygon is 360, the new textbook no longer gives strict logical reasoning, but draws conclusions through incomplete induction. Students may have doubts about this conclusion. Teachers can give an example: there is an N-sided road, a car runs around this road and then returns to the starting position. Because it only turns once, the total angle it changes is 360 degrees. A triangle is 360 degrees, so are hundreds of polygons. This value is a constant. The above process provides students with the actual background for the generation of new knowledge, so that students can experience the joy of rediscovering and "recreating" knowledge. We should pay attention to the setting of problem scenarios in teaching, and the new textbooks provide us with a stage to show. On the basis of flexible use of teaching materials, we should attach importance to the occurrence and development of knowledge, pay attention to connecting with real life, provide a free and broad world of activities, let students feel the need for creation, and thus stimulate their desire for exploration. Fourth, strengthen the application of mathematical knowledge to stimulate students' creativity. The purpose of learning mathematics is to use mathematics. From the perspective of developing application ability and cultivating students' innovative spirit, teachers should design some unconventional math problems that are more related to teaching materials and can be understood and liked by ordinary students. These questions are not a simple imitation of the textbook content, and can not be completed by skilled operation. They need more creativity and attach importance to the application of scenes, that is, the problems given are often not pure mathematical "known and verified" models, but realistic environment and realistic needs, marked by overcoming a realistic difficulty. They are exploratory, the problem does not necessarily have a solution, the answer is not necessarily unique, the conditions can be irrelevant to solving the problem, and the model can be designed by itself. This often requires hands-on, experiments and discussions with others, and does not require individuals to do it independently. In addition, practical problems closely related to real life account for the majority in the new textbooks. When using textbooks, teachers can change the conditions or requirements of the topics on the basis of the original topics, so that students can flexibly use what they have learned when solving practical problems, and truly feel that the mathematics knowledge in textbooks and after-school exercises is essentially to use what they have learned to solve their own life problems, and realize that mathematics is closely related to real life. In a word, there are many math problems in practical application, so we should try our best to introduce them into our classroom teaching, inspire students' imagination, cultivate their interest and make math really vivid. Through creative mathematics activities, the consciousness of mathematics application will gradually flow to students' skin along the flowing water of knowledge, melt into students' blood, turn it into faith, become the wealth that students enjoy for life, and consciously use mathematics in their lives.