Mathematics education must attach importance to the teaching of mathematics application, put the cultivation of application consciousness and the development of application ability in an important position, let students adapt to life and society, and let them use their own knowledge and thinking methods to think and deal with problems. This requires us to focus on students' life experience and practical experience, open students' horizons, broaden students' learning space, tap students' potential, let students experience the close relationship between mathematics and daily life, cultivate students' ability to find mathematical problems from surrounding situations, apply what they have learned to solve practical problems, and cultivate students' application consciousness. Keywords: mathematics application consciousness; Mathematical application problems; Mathematics classroom teaching

1 Let students experience the process of "problem situation-modeling-explanation, application and expansion"

1. 1 Does the mathematics content in the classroom deviate from the reality seriously, which makes students' awareness of mathematics application weak? It is almost recognized that our students (even college students) have a weak sense of mathematics application. I have consulted some documents and combined with our classroom practice, can I draw the following conclusions: the mathematics content in the classroom is seriously divorced from reality, which makes students' awareness of mathematics application weak. The answer should be yes, which is the result of rational thinking. Of course, it depends on our further investigation and study in the end. Combined with my own teaching practice,

Should our teacher ask himself: What should I do with the content of the textbook? What needs to be declared is that the author does not think that the serious disconnection of mathematics content in class is the only reason for students' weak sense of mathematics application. On the contrary, we must consider this issue from the whole education link, not just from a certain link or a certain angle. 1.2 Can asking students to do more application problems really cultivate students' awareness of mathematics application? The appearance of application problems in the classroom can be said to meet the needs of society, parents and teachers to some extent, that is, to expect students to learn useful mathematics. Some people even made statistics on the proportion of application problems in junior and senior high school textbooks, and found that the proportion of application problems was obviously low, thus drawing a conclusion: we should vigorously strengthen the teaching of application problems. Undoubtedly, this has a positive side, that is, application problems create good conditions for students to cultivate their awareness and ability of mathematics application. But we can't easily draw the following conclusion: let students do more application problems and cultivate students' awareness of mathematics application. Whether students can really cultivate their awareness of mathematics application depends on how teachers rely on the whole process of teaching application problems. It is a foolish teaching method to teach students only skilled skills, and at the same time teach them a lot of application modes and some special memory methods. Just to cope with the exam, it is impossible to cultivate students' awareness of mathematics application. In fact, this is more harmful, that is, to let students firmly establish such a wrong concept: the so-called mathematical application is to do more application problems; If you can't apply mathematics, it's because you have done too few application problems. Therefore, we can naturally draw the following conclusion: the cultivation of students' mathematics application consciousness mainly involves not whether they rely on application in teaching, but an important change in teaching thought, that is, emphasizing the openness of the teaching process, completely changing the passive state of students in the learning process, and prompting them to explore more actively and actively. Can the noisy class of 1.3 help to cultivate (or awaken) students' awareness of mathematics application?

As the saying goes, "Spirit needs the nurturing of spirit and personality needs the shaping of personality", can we also put forward that "consciousness needs the nurturing of consciousness"? The answer is yes. As Spencer said: "If you have no compassion for children, they will become unsympathetic, but treating them with the friendship they deserve is a means to cultivate their friendship." Teachers should cultivate students' awareness of mathematics application, and students should also have a certain awareness of mathematics application. It's hard to imagine how strong the students' sense of mathematics application is and how smart their ability is under the education of a teacher who doesn't know what mathematics is for. The consciousness of mathematics application lurks in students' minds, and of course it needs the subtle education of "sneaking into the night with the wind and moistening things silently". But apart from this quietness, especially in class, should we advocate a "vigorous" atmosphere? In other words, is the "noisy" classroom more conducive to the cultivation of students' awareness of mathematics application? Of course, the "noisy" classroom mentioned here does not mean that the classroom order is chaotic, but that students have a heated debate around a certain issue. They have no distinction between good and bad, only freedom of thought. Starting from the first case, combined with the current relatively boring classroom reality, we look forward to this "noisy" classroom to wake up students. In order to make students experience the process of applied mathematics, the teaching should adopt the process of "problem situation-modeling-explanation, application and expansion". The basic idea of this process is to arouse students' discussion with realistic, interesting or related questions. In the process of solving problems, new knowledge points or skills to be formed appear, and students understand knowledge with a clear purpose of solving problems, form new skills, and then solve the plaintiff's problems. In this process, students experience the integrity of mathematics and the diversification of strategies, and initially form the consciousness of evaluation and reflection, thus improving their ability to solve problems.

For example, the problem of "folding a cuboid with square paper to maximize its volume" begins with the origami activities that students are familiar with, and then forms the algebraic expression of the problem through operation, abstract analysis and communication; Then, by collecting relevant data and summarizing different data, guess the relationship between volume change and side length change; Finally, through communication and verification activities, the solution to the problem is obtained and the process of solution is reflected. In this process, students realize the connection and comprehensive application of knowledge such as "unfolding and folding graphics", "letter representation" and "making and analyzing statistical charts". 2. Cultivate students' ability to ask and solve problems.

In order to make mathematics help to improve students' ability to solve problems, we should first give students the opportunity to ask questions, know problems and understand problems from the perspective of mathematics, so that students can be good at asking questions and discovering problems from the perspective of mathematics when studying. Secondly, let students learn to use a variety of methods to solve problems and develop diversified methods to solve problems. Because different students have different cognitive methods, different solutions and problem-solving strategies, they should be encouraged to think and solve problems from different angles and in different ways. For example, when understanding quadrangles and trapezoids, students can be encouraged to look at the characteristics of edges and corners and the differences between such figures and other figures (rectangles, etc.). ). This can expand students' thinking and deepen their understanding of what they have learned. For another example, when students are organized to explore "determining the position of an object with different reference objects and drawing a schematic diagram" and "connecting lines of points represented by several pairs on a square paper" through cooperation, how to complete such tasks can be discussed in groups of several people. One student describes the main buildings that pass from home to school. Other students draw a schematic diagram according to what he says. Students can discuss whether the description is accurate or not, whether the schematic diagram is clearly drawn, and put forward suggestions for revision, and finally form a description method and schematic diagram acceptable to everyone. In this process, on the one hand, students can understand the significance of cooperation in a job, on the other hand, they can understand different students' different views on the same problem.

3. Guide students to find math problems

Guiding students to discover mathematical problems is the most basic premise and condition for students to explore the value of mathematics and cultivate their awareness of mathematical application. Imagine that if students can't find math problems, they can't apply what they have learned to solve them well. In this way, the cultivation of students' mathematics application consciousness may become an empty talk. Then, in mathematics teaching, how to guide students to learn to find mathematical problems?

3. 1 Guide students to find math problems from their daily lives. The serious defect of traditional mathematics curriculum is to design mathematics into a strict and abstract deductive system. But in any case, you can't deny the role of mathematics in society. You know, from the past, present and future, the classroom that teaches mathematics can't float in the air, and the students who study mathematics must belong to society. As Comenius said: Everything one learns should be full of connections. Mathematics also has rich connections. While emphasizing the internal connection of mathematics, we should also attach importance to the connection between mathematics and the outside world. What we emphasize is the reality related to students' personal experience, rather than the artificial false reality as an application example. However, at present, what is not good in our mathematics education is that we have obtained the internal connection (whether it is really unknown) but sacrificed the external connection. Therefore, the primary problem we math teachers face is: how do we introduce the math problems in our lives into our classroom? Here, Friedenthal provides us with a good method. He believes that analogy is an extremely effective means to establish the internal and external relations of mathematics, because through analogy between objects, one can explain the other, thus making students interested, convincing and forming abstract imagination. But no matter how our teacher transforms the math problems in life into the classroom, we must understand that it doesn't seem to matter which math students learn, as long as they are full of connections. Because only connection is the most dynamic. There are a lot of math problems in daily life. It is particularly important to analyze and solve some simple problems in combination with mathematics content, which is especially important for cultivating students' awareness of mathematical application and mathematical concepts from an early age and promoting students' further understanding of what they have learned. For example, after the third-grade students know the perimeter of the rectangle, I do this: let three or four students measure the length and width of rectangles such as door frames, window frames and picture frames in the classroom, and how much materials are needed to design and make these items. It is best to indicate the unit price of each different material, and let them calculate what kind of material to choose and what kind of scheme to use, which is both economical and practical and meets the needs. Through these activities, students can have the consciousness of solving mathematical problems and solve some simple problems.

3.2 Guide students to discover mathematical problems from the inside of mathematics full of various problems. Although many problems have been solved through the efforts of predecessors for many years, students' learning, as a process of re-creation, still has a process of constantly exploring and solving new problems. In mathematics, the problem that students are most exposed to is problem-solving exercise, which is a special form of problem-solving. Teachers can guide students to correctly understand the problem from the perspective of the problem, make clear the known conditions and the goals to be achieved, make reasonable assumptions, seek possible ways to achieve the goals, and determine the optimal solution. It is necessary for students to form habits and skills and transfer them to other aspects, so that they have the consciousness of solving problems and improve their thinking level.

3.3 Guide students to actively participate in family mathematics practice activities. Mathematics comes from practice and serves practice. In students' life, most of the time they live with their parents, and all the construction in the family can not be separated from the application of mathematics. Let students participate in it, which is undoubtedly conducive to cultivating students' awareness of mathematics application. Teachers should guide students to actively participate in practical activities in the family from two aspects: on the one hand, students are required to actively participate; On the other hand, we should contact parents to cooperate with teachers and boldly let students participate. For example, let students participate in family management activities. Let them go home to know the basic living expenses such as oil, grain, non-staple food, water, electricity and gas in a week, and then sort out the collected data under the guidance of the teacher and ask related questions: How much does your family need to spend in a week? According to this calculation, what is the basic expenditure for one month? What is the monthly income of the family? How much is the monthly balance at home? I want to buy a water heater of about 800 yuan at home. According to your monthly balance, I can buy one in a few months. Through these practical activities, students are encouraged to discover mathematical problems from the special family situation, reflect the thinking mode in mathematics in a popular and life-like way, and gradually develop good mathematical thinking habits through collection, communication, analysis, sorting and application in simple problem situations, cultivate and strengthen the application consciousness of mathematics, so that students can feel the joy of mathematical creation in application and enhance their confidence in learning mathematics well.

3.4 The ultimate criterion for the formation of mathematics application consciousness is whether students can creatively use mathematics to solve practical problems. Mathematics application consciousness emphasizes that students can consciously and actively apply mathematics to solve problems in real life. It focuses on students' consciousness and initiative, refers to a psychological state, and belongs to the category of concept and consciousness. In other words, it is a "hidden" state of mathematics. It is precisely because of "invisibility" that it is difficult for us to have a scale to measure whether students' awareness of mathematical application has really formed. However, if our students can creatively use mathematics to solve practical problems, can this behavior or process provide the most valuable basis for students to form their awareness of mathematics application? Furthermore, is that the ultimate criterion for the formation of mathematical application consciousness? Of course, the so-called "creatively using mathematics to solve practical problems" includes two aspects: one is to find mathematical information from practical problems; Two, can creatively use mathematics to solve problems containing mathematical information. What needs to be emphasized here is that "creativity" does not require students to have superb mathematical skills, but mainly depends on whether the results obtained after using mathematics are closer to reality. Maybe we will have a better understanding of the concept of "creativity". Unfortunately, our teaching pays more attention to students' mathematical skills than whether the results are feasible in practice. In fact, let's not discuss whether the ultimate criterion for the formation of mathematics application consciousness is whether students can creatively use mathematics to solve practical problems, but it also opens the following perspective for our teachers: the quantity and quality of students' questions raised and solved in class are the most important reference indicators for the formation of students' mathematics application consciousness. Of course, the cultivation, improvement and development of primary school students' awareness of mathematical application cannot be achieved overnight, nor can it be solved by teaching several special courses on mathematical application. Don't expect to cultivate students' awareness of mathematical application in one or two problem solving; Don't think that simple math problems (including problems in life) are of no help to the cultivation of students' awareness of math application. It will take a long time. Teachers should consciously stimulate students' application consciousness at an appropriate time, and go through the process of infiltration, repetition, crossing, gradual, spiral rise and deepening. Make students' application consciousness gradually change from unconscious or purposeless state, and then develop into conscious and purposeful application. In short, through various carriers to enhance students' awareness of mathematical application, effectively stimulate students' enthusiasm for applying mathematical knowledge to practice, increase the frequency of students' experience of success, improve students' ability to solve problems by using mathematics, achieve the purpose of "applying what they have learned" and promote the improvement of students' mathematical quality.

References [1] Zheng Yuxin and Liang Guancheng. Constructivism of cognitive science and mathematics education. Shanghai: Shanghai Education Press, 2002 [2] Zheng Yuxin. Mathematics education: from theory to practice. Shanghai: Shanghai Education Press, 200 1 [3] Friedenthal, compiled by Chen Changping and Tang Ruifen. As an educational task. 1999 [4] Ji Suyue. Cultivation of Innovative Consciousness and Reconstruction of Mathematics Learning Environment [J]. Journal of Mathematics Education, 200 1(4)