1. The importance of strengthening mathematics application consciousness 1. Paying attention to the application of mathematics is a basic trend of mathematics education reform. Since 1980s, the reform of international mathematics education has been in the stage of in-depth exploration and intensive experiments. Developed countries in the world have promulgated a series of outlines for the development of mathematics education and blueprints for the reform of mathematics courses. Participants believe that "information technology" and "mathematics application" have become the focus of mathematics education reform. There are three major trends in international mathematics education reform, namely "popular mathematics", "problem solving" and "mathematics application". Emphasizing the application of mathematics in essence and cultivating the consciousness and ability of mathematics application have become the common characteristics of mathematics curriculum standards in various countries. For example, the American Federation of Mathematics Teachers (NCTM) 1989 "Principles and Standards of School Mathematics" published in 2000, and one of its basic features is the most famous UCSMP textbook (short for School Mathematics Project of University of Chicago) which emphasizes the application of mathematics in American modern mathematics textbooks. It is characterized by the application and modeling of mathematics as the main line. British mathematics education has its remarkable characteristics in application. The cockcroft Report, a programmatic document of mathematics teaching reform published by 1982, emphasizes that the fundamental purpose of mathematics education is to meet the needs of students' adult life, employment and further study in the future. Emphasize the connection between mathematics teaching and students' daily life experience. Based on the cockcroft Report, the National Curriculum Committee of the United Kingdom put forward some suggestions to strengthen the cultivation of students' mathematical application ability. At present, British mathematics curriculum attaches great importance to cultivating students' mathematical application ability, and has formed a systematic system, which is mainly manifested in four aspects: first, mathematics application is determined as a separate teaching goal in British mathematics curriculum standards; Second, all schools should attach importance to the cultivation of mathematical application ability; Third, the requirements for students' mathematical ability are reflected in the curriculum standards and the national unified examination syllabus; Fourthly, the ways to cultivate students' application ability are put forward. Looking at the reform and development of mathematics education in the world, it has become a common understanding to attach importance to the application of mathematics, and cultivating the awareness and ability of mathematics application has become a new feature of the reform and development of international mathematics education. 2. Strengthening the consciousness of mathematics application is the slogan of mathematics quality education in China. Firstly, the international comparison of mathematics education was put forward at the National Senior Teachers' Teaching Conference in Ningbo in June 1992. It is considered that mathematical quality includes four parts: mathematical consciousness, problem solving, logical reasoning and information exchange. 1At the Qingdao meeting in June, 1995, the connotation of mathematical quality education was comprehensively defined, and it was considered that a person's mathematical quality refers to the innate foundation. Mathematics quality education refers to fully respecting students' subjectivity, paying attention to tapping students' potential, cultivating students' basic mathematics quality, laying a solid foundation for their future development and forming a good mathematical mind. Obviously, the implementation of mathematics quality education is for all students to develop; It is to solve the tendency of attaching importance to theory and neglecting application in the reality of mathematics education in China. In recent years, with the in-depth development of China's mathematics education reform, people gradually attach importance to the cultivation of middle school students' application ability. 1993 applied questions first appeared in the college entrance examination questions, and then the number of questions and scores gradually increased. The baton of the mathematics college entrance examination has gradually emphasized students' application consciousness. More importantly, in examining students' practical ability, the "Full-time Senior High School Curriculum Plan (Trial)" promulgated by the Ministry of Education in 200 1, 1 added a section of "comprehensive practical activities" to the basic education curriculum in China for the first time; The recent national mathematics curriculum standard also emphasizes the importance of strengthening the cultivation of practical ability of mathematics application, and makes specific provisions and puts forward teaching suggestions and requirements. Therefore, it is necessary to strengthen the consciousness of mathematics application and improve and cultivate students' ability to solve practical problems. 3. Strengthening the consciousness of mathematical application is the need of mathematical science and social development. The extensive application of mathematics is its outstanding feature. With the development of society, the status of mathematics is improving day by day, and its application is becoming more and more extensive, almost infiltrating into all scientific fields and every aspect of people's lives. The in-depth development of natural science depends more and more on mathematics, while social science and humanities depend more and more on the extensive application and development of mathematical knowledge and its thinking method. It is required that mathematics education must strengthen the consciousness of mathematics application and cultivate students' consciousness and ability of mathematics application, which can help students have an intuitive, vivid and profound understanding of mathematics content, ideas and methods, help students correctly understand the development path of mathematics and even science, understand the thinking mode used in mathematical analysis and problem solving, and make students truly understand what mathematics is. Therefore, it has a far-reaching impact on their lifelong development. Second, the cultivation of mathematics application consciousness is a kind of thinking tendency to observe and analyze the problems in the surrounding life from a mathematical point of view, which is mainly reflected in the following aspects: on the one hand, students can actively try to find strategies to solve problems from a mathematical point of view when facing practical problems; On the other hand, in the face of new mathematical knowledge, we can find and understand the mathematical information contained in real life and actively seek its practical background and application value. The cultivation of mathematics application consciousness mainly permeates the routine teaching process. Through the "life-oriented" treatment of classroom content, students gradually realize the importance of mathematics application. Thus forming an idea and gradually transforming it into consciousness 1. Considering that mathematics is the balance between theory and application in the sense of mathematical application, it must be based on certain mathematical knowledge and ability. Without the training of mathematical knowledge and the cultivation of mathematical application ability, the significance of mathematical application will lose its meaning. Therefore, the balance between theory and application must be maintained in teaching as a middle school education. It is necessary to provide students with some basic formula theorems to lay a foundation for students to understand and apply mathematics, and at the same time, it is necessary to provide students with opportunities to solve practical problems in various fields by using mathematics, such as using mathematics to analyze the consumption and purchase problems of some natural and social sciences and some other problems encountered in daily life, which are both abstract theoretical derivation and concrete practical content, so that students can form a complete mathematical concept and truly reflect that mathematics comes from practice. The process of responding to practice with greater motivation. Connecting with practice and paying attention to the ins and outs of mathematical knowledge. The formation of mathematical knowledge stems from the actual needs and the inherent needs of mathematics, but mathematics itself is an abstract and boring subject. To cultivate students' awareness of mathematics application, students must have a strong interest in learning, and the cultivation and development of mathematics application awareness will not happen overnight. This is a deepening process. Therefore, in mathematics teaching, the introduction of new knowledge should be linked with the reality of life and pay attention to the ins and outs of knowledge. Introducing new knowledge from real life helps students understand the application value of mathematical knowledge and provides a demonstration for students to actively analyze and solve practical problems from the perspective of mathematics. Starting from cultivating students' interest, it can also provide students with interesting topics of mathematics development. Through reading comprehension and other activities, let students see the development track of mathematics. In practical teaching, teachers should pay special attention to the application of mathematics in the real world, find mathematical problems from real life, link "reality" with "knowledge", pay attention to collecting examples of mathematical application and introduce them to students, so that students can understand the extensive application of mathematics. This will not only help students understand the development of mathematics and appreciate its application value, but also stimulate their interest in learning. It can also help students understand the application process of mathematical knowledge. 3. Adopt flexible and diverse classroom teaching modes and teaching methods. Classroom teaching modes are divided into the following three types (1). Modeling topic is the main mode to cultivate students' application consciousness in classroom teaching. The process of mathematical modeling is the process of applying mathematical theoretical knowledge to practical problems. Mathematical modeling provides us with an opportunity to combine mathematics with real life and an opportunity to use mathematics. Through the study and research of modeling subject, create an environment for students to learn mathematics. Students can personally participate in the whole process of exploring, discovering, analyzing, learning, solving and testing such a problem, and gain practical experience in learning mathematics. Then, by observing and analyzing the things and phenomena around us with the knowledge of mathematics, the consciousness of mathematics application is enhanced. (2) The study of research topics, that is, special research, is an important supplementary form to cultivate students' application consciousness in classroom teaching. Take research topics as a beneficial form to cultivate students' application consciousness, organically combine in-class learning with after-class learning, and appropriately expand the knowledge of teaching materials. It is more helpful to combine the usual study and training with the practical hot issues in social production and life with classroom teaching, which is of great significance to change the traditional closed discipline concept, pay attention to the combination of the cultivation of subject ability and interdisciplinary comprehensive ability, and cultivate students' ability and quality. (3) In the introduction and teaching process of micro-application project, teachers can put some minor mathematical application and mathematical modeling problems, and do them in all local links of teaching according to the problem-solving process, and pay attention to doing them often. Compared with modeling and research projects, micro-application projects are very helpful for mastering knowledge and understanding mathematics because they are short and flexible. From the above three types, the main way to cultivate students' application consciousness through classroom teaching is to solve some practical problems close to life as the basic material, so that students can realize the great role and value of mathematics in solving problems.