How to make students use mathematics knowledge to solve practical problems in life

Students should be able to use what they have learned to solve practical problems. Both American Mathematics Curriculum Standards and 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 to create mathematical problem situations. When students master 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 flexibly apply what they have learned to solve practical problems. In addition, as a teaching form, "problem solving" emphasizes students' practical ability, 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 understandings, so that it is more important to create the conclusion of the studied problem than to get the correct answer. In addition, students should be allowed to do their own work, calculate, draw and answer questions, and let them do some small investigations and experiments themselves, and ask and solve problems independently. The following are my thoughts on this issue since I started teaching mathematics: First, after cultivating students' awareness of applying mathematics in life, such as teaching the stability of triangles, students can explain: Why is the roof of the house where we live framed into triangles? Why did the carpenter nail a diagonal strip at the foot of the table to help his classmates repair 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? By explaining 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, teachers first show a map of China and ask 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?" According to the approximate figures of students, the teacher accurately stated that the population of China was1295.33 million, and introduced that this was the result of the fifth census in China recently. At this time, students have become 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, today we will learn these knowledge. Do you want to learn? " Then reveal the theme under the students' strong thirst for knowledge. At the same time, at the end of this class, practical homework was assigned: a "small survey" 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, and makes students actually investigate and make students understand that mathematics 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 a road intersection? 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", and can intuitively understand the meaning of vertical lines 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 and computers, increase the interaction between teachers and students, visualize mathematics content and abstract knowledge at the same time. This can attract students' attention, arouse students' interest in learning knowledge actively, deepen their understanding of knowledge and improve learning efficiency. Thirdly, 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 often encounter such a problem 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 roads); 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 problems divorced from the actual background, or applied mathematics problems with no background. Such training, over time, enables students to 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 elaborate some questions related to life and science, which can make students feel that there is mathematics everywhere around them, thus making them sprout the desire to learn mathematics well to solve practical problems, combining learning with application, and achieving the effect of improving students' application ability. In teaching, we can gradually guide students to put forward and solve problems according to their own knowledge and practice, and gradually enhance their 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 small, the rockets are fast, the chemical industry is clever, the earth is changing, the daily life is complicated, and mathematics is everywhere." The extensive application of mathematics in real life is expounded wonderfully. It can be said that mathematics models many life problems. For example, ask students to help their parents calculate the cost of decorating flat tiles in their house. 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 which types 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 required 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 in mathematics, 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 make students understand the application value of mathematics, thus imperceptibly cultivating students' mathematical application ability. 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 root of cultivating students' application consciousness in mathematics teaching. It is far from enough to cultivate students' mathematical application ability only by 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 will not only broaden students' horizons and enrich their knowledge, but also make the process of applied mathematics interesting and vivid.