Keywords Primary School Students' Mathematics Application Life Practice
Mathematics Curriculum Standard points out in the overall goal that through mathematics learning in compulsory education, students can initially learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, and enhance their awareness of applied mathematics. This goal requires educators to pay attention to cultivating students' mathematical literacy in the teaching process. Mathematical application ability is an important part of mathematical literacy, and improving students' mathematical application ability is the key to improve mathematical literacy.
First, experience life and let students feel the application value of mathematics.
Mathematics originates from life, and life is full of mathematics. How to give students a pair of eyes to observe and understand mathematics around them is particularly important. Close to the textbook, aiming at the problems closely related to the textbook and life, we choose to process the problem scenarios, and put forward assumptions and conjectures that are in line with students' actual abilities, thus attracting students' attention and thinking. For the problems created, because students want to solve them, their application of mathematical knowledge and interest in mathematics arise.
In traditional primary school mathematics teaching, teachers seldom talk about the source and practical application of knowledge. Even in the application problem teaching, they only show the ready-made problems compiled in advance to the students. Students only apply the methods and steps to solve application problems according to several necessary conditions, and they don't know what information and data are needed to solve a problem, let alone the unique significance of mathematics to this problem. Therefore, in mathematics teaching, we should first guide students to feel the application value of mathematics.
1, using living materials for teaching, so that students can clearly understand the practicality of mathematics knowledge.
The application of mathematical knowledge is extensive, from macroscopic celestial movement to microscopic proton and neutron research, and even the vitality of some disciplines depends on the application degree of mathematical knowledge. Marx once pointed out: "Only when mathematics is successfully applied to a subject can it truly reach perfection". Life is full of mathematics. As a math teacher, we should be good at abstracting math problems from students' lives, so that students can feel that math is around them and realize the practicality of math knowledge, thus generating interest.
For example, when teaching "line segment", I designed such a problem: how to divide the curved road and how to take the shortest road. Inspire students' interest in exploring problems with the problems they often encounter in their daily life, and thus sum up an axiom: between two points, the line segment is the shortest. For example, when I teach "Calculating the sum of edges of a long cube", let the students think about how the workers weld the long cube, and then let the students make the border of the long cube with iron wire, and then let them find ways to calculate the sum of edges. Through practical operation, students can find out the law of calculating the sum of edges of a long cube and a cube. Through the mathematical prototype in life, students can easily master these mathematical knowledge.
When I was teaching Jiao Yuanfen in the lower grades, I realized that fen is a unit of RMB and the relationship between them. According to the requirements of the book, I created a game: I simulated a store, hired a child as a salesman, and other children as customers, and bought things with copied RMB. In the relaxed and lively teaching atmosphere, students happily consolidated their knowledge, further understood the quantitative relationship between Jiao Yuanfen, and improved the application ability of mathematics in the scene.
There is mathematics everywhere in life, and mathematics permeates every corner of life. In mathematics teaching, we should always connect with the reality of life, guide students to understand mathematics and be close to life materials. Mathematics teaching should follow the law of "from life to life" and fully embody the practicality of mathematics.
2. Collect application cases to deepen students' understanding and experience of mathematics application.
With the rapid development of science and technology, the development of mathematics involves more and more fields. High definition multimedia series, aerospace engineering, clinical medicine, market research and forecast, meteorology and so on all reflect the extensive application of mathematics. Let students collect this information, which can not only help students understand the development of mathematics, appreciate the value of mathematics, stimulate students' courage and confidence in learning mathematics well, but also help students understand the application process of mathematics knowledge.
For example, in the teaching of "the meaning and basic nature of proportion", an episode was arranged: Do you know many interesting proportions of our human body? The ratio of head height is about 1: 7, and the ratio of foot length to height is also about 1: 7. When your fist rolls once, the ratio of its length to the length of the sole is about 1: 1 ... It is useful to know these interesting ratios: when you buy socks in the store, you only need to wrap them around your fist for a week to know this pair. If you are a policeman, as long as you find the footprints of criminals, you can estimate the height of criminals ... In this way, using the life phenomenon of "interesting proportion of human body", the study of "proportion" can make students have a strong interest, actively participate in the exploration of new knowledge, and experience that mathematics is around us while gaining knowledge, so that students can experience a process of knowledge discovery and cultivate their innovative ability.
Mathematics teaching should closely link mathematics with life, embody that mathematics comes from life, resides in life and is used in life, guide students to apply mathematics knowledge to students' life practice to experience feelings, make students fully realize that mathematics comes from life and is the basic tool to solve life problems, and achieve "mathematical problems of life" and "mathematization of life problems".
Creating real life situations can make students feel the connection between mathematics and reality. When mathematics is closely combined with children's life, mathematics is vivid and full of vitality. Only the mathematical problems from life can make students feel more cordial and natural, stimulate children's interest in learning and solving problems, and stimulate the source of children's thinking and creation.
Second, 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.
1, to guide students to find math problems from their daily lives.
Rogers believes: "If students want to devote themselves to learning activities, they must face their own meaningful or related problems. But our education is trying to isolate students from all the realities of life, which constitutes an obstacle to meaningful learning. However, in order for students to become free and responsible individuals, they must be directly faced with various practical problems. " 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, in the course of "Understanding Triangle", let students draw triangles from familiar red scarves, bicycle racks, telephone pole racks and bridges, and then let students know the stability of triangles through practical activities such as pushing and pulling, and use it to solve some real-life problems, such as repairing a rickety chair. Students will immediately think of applying the "triangle stability" they have just learned, adding wood blocks to the chair to form a triangle, thus stabilizing the chair. In this way, students can learn easily and deeply, and get twice the result with half the effort.
In real life, numbers and shapes can be seen everywhere. Teachers should, according to teaching practice, let students connect what they have learned with the surrounding living environment, help them form knowledge and skills, and feel the extensive application of mathematics.
2. Instruct students to discover mathematical problems from inside mathematics.
Mathematics is full of all kinds of 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.
When teaching the simple algorithm of adding and subtracting decimal numbers close to the whole hundred, there is such a problem as "165-97 =165-100+3". It is difficult for students to add 3 when subtracting 100, which makes them think about shopping and change in real life. She paid the clerk a hundred-dollar bill (100 yuan minus 165 yuan), and the clerk asked 3 yuan (plus 3 yuan). So, if you subtract more, you have to add 3.
Mathematical concept comes from practice, is the result of rational thinking and high abstraction of practical problems, can accurately reflect the nature of science, and has universal significance. It is also the result of this generalization and abstraction that forms an insurmountable gap between mathematics learning and mathematics application, which leads to students learning a lot of knowledge but not knowing how to use it. What do we do? This requires that the principle from practice to practice can be embodied in the teaching of mathematical concepts, so that students can understand the occurrence and development process of mathematical concepts, let students experience the formation process of concepts, and find out what the prototype of concepts is in reality and what the general meaning is after evolution, so as to trace back to the source and keep constant.
Third, mathematical modeling to improve the efficiency of children's problem solving
There is a lot of mathematical information in real life, and mathematics has a wide range of applications in the real world. There are many problems in mathematical modeling, which involve all aspects of life. When determining the topics of mathematical modeling, we should consider the practical ability and knowledge and experience of primary school students, and choose those topics that are suitable for primary school students and can arouse their enthusiasm. When primary school students have some experience in modeling, it is a research process and a sign that students' awareness of mathematical application has been developed to encourage them to independently discover the problems to be studied and put forward a meaningful question. You can choose topics from the following angles to carry out mathematical modeling activities among primary school students.
1, combined with classroom teaching content, cut into practical problems in time.
Mathematics teaching in primary schools in China often overemphasizes accuracy and rigor, ignoring the open imagination space for students, which can easily stifle students' creative thinking. We should change the traditional concept of mathematics teaching and design open, life-oriented and real mathematics problems. For example, after learning "Direction and Location" in the second grade of primary school, the after-class practice of "Talking about the route from school" [3] can be further expanded, requiring students to "draw a road map from home to school". This task seems very complicated, and students will indeed encounter many problems in actual operation, such as how to measure the length of each section of the road, what proportion to draw and so on. Teachers and parents should not rush to help students get results, but should give students some time to think independently and point out the direction of their confusion. As long as students can finish it, let them do it boldly. In the process of measurement, some students measure the distance step by step, some students think of measuring with a ruler, and some students calculate the distance through the odometer in the car. In this process, students should be reminded to record the data and direction. In the process of drawing the road map, students can determine the orientation according to their own learning experience and adjust the length of each road according to the measured data. Under the correct guidance of teachers or parents, students can finish this work. In the process of completing this assignment, the students measured, calculated and drew by themselves, and experienced the whole process of mathematical problems from putting forward to solving, and also had some experience on the accuracy and rigor of mathematics itself and the difference between fuzzy mathematics used in practical work and life.
2. Extract mathematical problems from the colorful activities of the school.
Mathematics teaching should provide interesting materials related to children's life background and present them in colorful forms. The school life that students are most familiar with is also a resource library, which can provide students with more learning materials. At the end of each semester, the school will select outstanding students. According to the regulations, the number of outstanding students in a school should be 15% of the total number of students in the school, and the school will allocate places to all grades and classes according to this ratio. You can present the actual problem of quota allocation to students, let students investigate the number of students in each class by themselves, and allocate quotas through statistics. For junior students, they can only be required to complete the quota allocation of this grade. Quota allocation should embody the principle of fairness to the maximum extent. The ranking calculated by the ratio of 15% per class is often not an integer, which involves some rounding rules, such as rounding method and tail cutting method. And these two methods are likely to lead to insufficient points or excessive total places, which requires students to seek a more reasonable distribution method. Let each class get the integer part of its share first, then allocate the first remaining quota to the class with the largest fractional part of its share, and so on until the allocation is completed. This method is actually the Hamilton method used to allocate the number of members in American history. After such a distribution activity, students not only understand the reasons for the different number of outstanding students in each class, but also have a certain understanding of the application of mathematics in social life.
3. Strengthen multidisciplinary integration, and reflect the value of mathematics as a basic discipline.
With the rapid development of science and technology, mathematics has become more and more closely related to various disciplines, and its position as a basic tool has become more and more prominent. Let students realize this from the beginning of primary school, which is very helpful to the study of other subjects and is very beneficial to the all-round development of students. In addition to the content required by the syllabus, there are few materials related to other disciplines in primary school mathematics in China, and there are few links with other disciplines. The application of mathematics in other disciplines in primary schools is almost blank. We should focus on the future and the all-round development of students, and we should not limit the mathematics teaching in primary schools to pure mathematics. Strengthen the connection between mathematics and other disciplines in the application of mathematics, show students the important role of mathematics as a basic discipline, and infiltrate the ideas and methods of mathematics into the study of other disciplines. For example, in mathematics and society, China is the most populous country in the world, so it is of great significance to control population growth. Let students know the history and significance of the census, use mathematical statistics knowledge, and put forward some mathematical problems related to population data through investigation and data collection, such as population growth rate and growth trend, and describe the population structure and development trend with statistical charts, and put forward their own suggestions.
4. Based on students' personal experience and family life environment, encourage students to find problems independently and take the initiative to practice.
Because of the different cultural environment, family background and their own way of thinking, students' mathematics learning activities should be a lively, proactive and personalized process. We should encourage students to find problems from their own lives and solve them with the idea of mathematical modeling. For example, after the Spring Festival, every student has a lucky money. If you deposit the lucky money in the bank, you can design a suitable deposit method by investigating the bank interest rate. After buying a house at home, participate in the decoration budget and design of the house.
Cultivate the consciousness of applied mathematics in the usual teaching process, and let students learn the spirit, thoughts and methods of mathematics through scientific processing, processing and re-creation of teaching content.
Fourth, be flexible and innovative, and improve application ability.
The outline points out that students should be able to understand and master what they have learned, and use this knowledge to solve some practical problems in daily life and productive labor. In today's market economy, students often get information such as commodity discounts and changes in bank interest rates. How to use what you have learned to solve such questions as "What is the current price of this commodity?" "I saved 200 yuan's money in the red scarf small bank. How much interest is there after one year? " And other problems in life. At this time, the teacher can arrange for students to investigate the original price of goods and the percentage of price reduction, and record the one-year interest rate of the bank at that time, and then return to the classroom to exchange and discuss with the students, so that they can draw a conclusion and solve the previous problems, which is actually to solve the application problem of "What is a number", and finally let the students answer it continuously. Facts have proved that as long as teachers deliberately design problem-solving contents according to teaching needs, students can seek methods and steps to solve problems, thus solving problems. In this way, students' mathematical application ability can be continuously cultivated and improved.
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. It can't be cultivated by solving problems once or twice. Don't think that simple math problems (including problems in life) are of no help to students' awareness of math application. It takes a long time for teachers to 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, to cultivate students' independent innovation ability and problem-solving ability, we must actively create conditions and strive to cultivate students' subjective consciousness. In class, we should create vivid and interesting situations to inspire and induce, and actively use mathematical knowledge to solve practical problems outside class to stimulate students' strong thirst for knowledge, so that students can explore, discover and solve problems themselves and truly become the masters of learning.