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 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, for the newly learned mathematics knowledge, teachers should collect the background related to the new knowledge in real life and other disciplines in many ways, and create mathematical problem situations. When students master relevant knowledge and skills, they will be guided to explore and apply in the real world and build mathematical models to solve problems in real life. In this way, in the learning process, theory and practice are inseparable, and teachers will come into contact with real life again, thus cultivating 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, the students are interested in the census, and the teacher 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 this knowledge. 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, guide students to contact some problems in daily life and solve them 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. How to train students to use mathematical knowledge to solve practical problems in life "Mathematics Curriculum Standard" emphasizes that mathematics teaching should reflect life, starting from students' existing life experience and knowledge, so that students can personally experience the process of explaining and applying practical types. As the saying goes, life is inseparable from mathematics, and mathematics is inseparable from life. Therefore, in mathematics teaching, teachers should actively create an experiential environment for students, so that students can feel the close connection between mathematics and real life, integrate the "mathematical world" into the "life world", and guide students to use the mathematical knowledge and methods they have learned to solve practical problems in life. How to guide students to use mathematical knowledge to solve practical problems "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, for the newly learned mathematics knowledge, teachers should collect the background related to the new knowledge in real life and other disciplines in many ways, and create mathematical problem situations. When students master relevant knowledge and skills, they will be guided to explore and apply in the real world and build mathematical models to solve problems in real life. In this way, in the learning process, theory and practice are inseparable, and teachers will come into contact with real life again, thus cultivating 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, the students are interested in the census, and the teacher 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 this knowledge. 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, guide students to contact some problems in daily life and solve them 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, let them germinate and learn mathematics well, and solve practical problems in life with mathematical knowledge. Mathematics learning report is rich in connotation, which is reflected in its flexible application. Especially primary school mathematics, as a basic subject, has its special application value. Flexible learning is not enough. We should learn to use it flexibly on the basis of flexible learning, so that mathematical knowledge can really serve our study and life.
1. Mathematical knowledge is close to life and used in life.
After learning the unit of volume, volume and how to measure and calculate it, let students use their own mathematical knowledge to solve practical problems in life. For example, the paper used to calculate the length, width and height of the shoe box and its volume are measured, so as to deepen students' understanding of volume and area, consolidate the method of measuring the length of objects with a scale, and calculate tomorrow's area and volume. At the same time, students can get some common sense information in daily life. This activity not only improves students' interest, but also cultivates students' practical ability, so that students can learn something useful in life.
2. Enhance strategic awareness and improve the efficiency of solving practical problems.
In modern society, in order to improve efficiency, we should attach importance to strategy, so we should attach importance to strategy research in mathematics teaching. For example, when he was teaching Possibility, he designed such an exercise: "Today is Children's Day, and Xiaoming is going to prepare a lottery game for his classmates, in which six white balls, two yellow balls and three green balls are prepared. There are three prizes: the first prize, the second prize and the third prize; The prizes are pencils, pencil boxes and a football. Now Xiaoming is going to ask his classmates to help him design a prize-winning game rule. Can you help him? " After seeing the topic, students can be sure that the ball that touches the green is the first prize, the ball that touches the yellow is the second prize, and the ball that touches the white is the third prize. However, there are differences in the distribution of bonuses. At this time, the teacher, as the instructor, told the students to consider the price of the prize in the distribution of the prize. After another heated discussion, the students finally determined the rules of the game with prizes for touching the ball. In this practical application, middle school students' thinking is more active, their creative consciousness and strategic consciousness are enhanced, and their ability to solve practical problems is also improved.
These are some examples of my exploration. It can also be explained by such a process: "life experience (solution) → mathematical problems (acquisition) → mathematical knowledge (solution) → practical problems"
It aims to make mathematics teaching closer to students' life, make learning interesting, vivid and easy to understand, apply mathematics to practice and make mathematics more dynamic. Use colorful activities to guide more students to like mathematics, learn mathematics well and use mathematics well; Actively promote the reform of primary school mathematics teaching and the overall improvement of teaching quality; Provide a good atmosphere for students with high mathematical quality to give full play to their mathematical talents. How to find and solve practical problems in life by using the mathematics knowledge of junior two? I don't think learning math is necessarily for solving problems. It is important to learn his thinking method, that is, the general spatial imagination. If your geometry is good, your spatial imagination should be good too. Learning mathematics can make us smart, that is, know how to judge a thing better. If you are in Grade Two, you may not really have much knowledge to use to solve problems in life. I think about the problems you should encounter in your life, and then think that you can use what you have learned to solve them, which is the best use. Because what we have learned is to solve problems when we encounter them, of course, it may be difficult if you can think of problems to solve. . Thank you. How to use mathematical knowledge to solve practical problems in life How to use mathematical knowledge to solve practical problems The success of scientific teaching depends largely on whether students' mathematical ability is cultivated, and the strength of mathematical ability depends largely on whether students can use what they have learned to solve practical problems. Therefore, in mathematics teaching, how to make students "understand" that mathematics knowledge comes from and serves life, how to observe the reality of life from a mathematical perspective and cultivate the ability to solve practical problems should become a problem that every mathematics teacher attaches importance to. The newly compiled mathematics textbook has created good conditions for teaching in this field from the aspects of concept formation, method induction and knowledge application. However, how to make use of these conditions, creatively exert teachers' subjective initiative, make mathematics teaching closer to the reality of life, and cultivate students' ability to solve practical problems needs our constant practice and exploration. Learning is for application. Therefore, teachers should integrate with practice and cultivate students' awareness and ability to solve practical problems with mathematical knowledge. Let's talk about this experience
1. Improve students' mathematics consciousness by combining with practice.
Mathematical knowledge is widely used in daily life, and there is mathematics everywhere in life. After learning the stability of triangles, students can observe where the stability of triangles is used in their lives. After learning the knowledge of circle, ask the students to explain why the shape of the wheel is round and triangular from a mathematical point of view. Why? Students can also find out where the center of the basin bottom, pot cover and so on is. By understanding the extensive application of mathematical knowledge in practice, students are trained to see problems with mathematical eyes and think with mathematical minds, and their awareness of solving practical problems with mathematical knowledge is enhanced.
2. Create situations to cultivate students' ability to solve practical problems.
After students have mastered certain mathematical knowledge, they can consciously create some environments and apply what they have learned to real life. For example, after learning the knowledge of "proportional distribution", ask students to help calculate the electricity bill that each household in this residential building should pay; After learning the knowledge of "interest", calculate how much principal and interest you can get after the money deposited in "emerging small banks" expires.
After learning percentage knowledge, I played a game with my students. The method is: put six identical balls in a cloth bag and mark them with 1~6 respectively. Teachers and students take turns taking two balls out of the bag at a time. If the sum of the two numbers on the ball is even, the student wins and the teacher wins. The result of the competition is that the teacher won many times, and then led the students to discuss and list all kinds of situations one by one. It is understood that the sum is even in six cases and odd in nine cases. The teacher's chances of winning are 60% and the students' chances of winning are 40%, so the teacher has won many times. Finally, it is pointed out that some gambling activities in the streets and lanes engage in this kind of deception, so don't be easily deceived.
3. Strengthen the operation and cultivate the ability
Applying the mathematics knowledge learned in class to real life is often stumped by the complicated reality of life. We should strengthen practical operation and cultivate the ability to apply what we have learned. For example, after teaching "Ratio and Proportion", I intend to take the students to the playground and let them measure and calculate the height of Metasequoia glyptostroboides beside the playground. Metasequoia towering, how to measure? Most of the students shook their heads, and a few of them whispered to each other and proposed to climb up and measure, but how can they measure with their hands on the tree? Some people suggest taking the rope, measuring the tree with the rope first, and then measuring the rope after getting off the tree. It's a good idea, but there's nothing to climb. How can I get up? The teacher took a 2-meter-long bamboo pole at the right time and inserted it straight in the playground. At this time, the sun is shining, and the shadow of the bamboo pole appears immediately, and the shadow length is measured to be 1 meter. Inspire students to think: since the length of the pole is twice that of the shadow, can you think of a way to measure the height of the tree? The student calculated that the height of this tree is twice as high as its shadow. (The teacher added "at the same time". After this idea was affirmed, the students quickly calculated the height of the tree by measuring the length of the shadow. Then, the teacher said, "Can you write a formula for finding the height of the tree in proportion?" So it is concluded that: rod length: rod shadow length = tree height: tree shadow length; Or: tree height: rod length = tree shadow length: rod shadow length. In this activity, students have increased their knowledge and exercised their abilities. An experimental report on using mathematical knowledge to solve practical problems in life. Isn't the interest in the bank very practical? How to use mathematical knowledge to solve mathematical problems in life "New Curriculum Standard" emphasizes that students should learn to observe and analyze reality by using mathematical thinking mode, solve problems in daily life, enhance students' awareness of applying mathematics, make students truly realize the close relationship between mathematics and human society, understand the value of mathematics, and enhance their understanding of mathematics and confidence in learning mathematics well. It can be seen that students should find problems in real life, use their own knowledge and methods to solve problems, and cultivate their application consciousness. The ultimate goal of learning mathematics is to apply what you have learned to real life. I actively encourage students to use what they have learned to solve simple practical problems and gain successful experience, thus stimulating students' interest in learning mathematics and enabling them to have initial innovative spirit and practical ability. 1. Combination of calculation and problem solving 1. In primary school mathematics textbooks, calculation accounts for a large proportion. Students' computing ability is the basic knowledge that primary school students must master. However, some students feel that simple calculation is boring and their enthusiasm for learning is not high, so I pay special attention to connecting with students' daily life when teaching calculation. For example, when I teach addition and subtraction, I ask students to collect their own shopping materials. As a result, students pay special attention to the price of goods and the payment. Students are very enthusiastic when they show the application problems written by their collected materials in class. When students master calculation, they can find that mathematics is around them. How to cultivate primary school students' ability to solve practical problems with mathematical knowledge is rich in connotation, which is embodied in flexible application. Especially primary school mathematics, as a basic subject, has its special application value. Flexible learning is not enough. We should learn to use it flexibly on the basis of flexible learning, so that mathematical knowledge can really serve our study and life.
1. Story-based and life-oriented problem situations to stimulate students' interest in learning and solve problems in life.
After learning Unit 5 "Cuboid and Cube", according to the knowledge characteristics of the unit textbook, starting from the overall knowledge of the unit, let the students collect a large number of long and cubic objects first, and then let the students investigate and recall what problems they have encountered in their daily life, such as "How long does it take me to make a cubic birdcage frame with thick wire?" ; "I want to make a beautiful cubic flower bed with a fence against the wall. How long is the fence? "
2. Create scenarios to improve the ability to solve practical problems.
For example, after the lecture on "Understanding of Yuan, Jiao and Fen", the teachers set up a simple daily necessities store on the podium, which was marked with "3 1 yuan schoolbag, 8 yuan 70 pencil case, 50 eraser, 1 pencil sharpener, 28 yuan 30". And everyone has good change in their hands, so that the deskmate can take turns to play the role of salesman and customer and buy the products you want most. The teacher asked, "The teacher gave you money from 40 yuan. Who can tell the teacher what kind of goods you can buy at most? " Students' interest is stimulated again, and they will be eager to participate in activities.
Life is the source of mathematics. Without life, mathematics will become "passive water" and "a pool of stagnant water", which will eventually dry up and lose its life. Teachers should be good at digging the source of "life" and attracting the living water of "mathematics". With the nourishment of life, mathematics learning will be more interesting, more challenging and more energetic. Cultivating students' mathematical thinking in primary school will help them step by step to the profound mathematics hall.