Application of computational power in primary school mathematics

1. Estimation is based on the basic calculation theory and knowledge and experience in daily life and proction to make a general inference about the quantity or result of things. To a large extent, it embodies a kind of approximate oral calculation. It is an important part of calculation ability and has a very wide application in daily life. Having the ability of estimation can make people have an overall, comprehensive and general understanding of quantity, time and space. It is one of the directions of international ecation reform to strengthen the teaching of estimation and improve students' estimation ability, and it is also an important goal of primary school mathematics teaching< In mathematics teaching, strengthening the awareness of estimation can enhance students' interest in learning, activate their thinking, broaden their thinking, and improve their ability to deal with and solve practical problems with various methods. Therefore, the teacher should be the person who inspires the students to use the estimation, consciously combine the relevant teaching content, connect the estimation with the relevant problems in real life, graally strengthen the infiltration, let the students feel the practical application value of this knowledge in the psychological experience, so as to actively explore the estimation method, enhance the estimation consciousness, and cultivate the interest in estimation
for example, after learning the calculation of rectangular area, students can try to estimate the number of students in a certain square array and the practical area of their home; After learning the knowledge of kilogram, students can try to estimate the quality of related articles in daily life; After learning the knowledge of millimeter, students can estimate the length, width or thickness of some objects, so that students can feel the fun of estimation, experience the practicability and convenience of solving problems with estimation, and highlight the value of estimation application< Second, combining with calculation training, forming the habit of estimation
as a calculation method, estimation is one of the basic skills that students should have. Everyone can use the estimated quantity to estimate at any time, so it is necessary to make students form a good habit of estimation. Oral and written calculation provide sufficient "material" for estimation. Teachers should seize the opportunity to combine oral and written calculation to train estimation, which in turn promotes the proficiency of import and written calculation. Therefore, ring the training, whether it is to estimate first and then calculate, or to calculate first and then estimate and test, the results of estimation and calculation should be recorded truthfully, and the differences between them should be compared and analyzed, so as to continuously improve the estimation skills. As estimated, 51 × 2.04, 51 as 50, 2.04 as 2, you will find 50 × 2 = 100, the result of the original formula is larger than 100; Another example is 9 + 99 + 999 + 9999 =? The students who have the habit of estimation will change the data slightly in their minds and almost blurt out the results. Of course, if students want to have such ability, teachers should consciously and regularly guide students to estimate their own calculation results, so as to form a good habit< Third, master the estimation methods and improve the estimation skills
in teaching, teachers should dig into the estimable contents in the teaching materials and guide students to master some estimation methods in examining, solving and verifying problems, which can not only help students improve the estimation speed and check whether the calculation results are correct, but also an important way to improve the estimation skills
1. Teach students basic estimation methods, such as approximation method, observation method, etc
approximation method is often used in estimation, that is, rounding (or according to the actual situation) to get the approximate value and then calculate the result. For example, calculate: 1137 + 5044-3169, take their approximate numbers by omitting the mantissa after the highest order, and then add and subtract the approximate numbers to get the estimated value, that is: 1137 + 5044-3169 ≈ 1000 + 5000-3000 = 3000, so the value of the original formula should be around 3000
observation method, that is, observing the characteristics of formula, data and graph, analyzing or reviewing the results from the whole or part to judge the conclusion. For example, a curve divides a rectangle into two parts: A and B. It is obvious that the area of a is larger than that of B; Then let the students compare the perimeter of part a and Part B. the students often get the conclusion that the perimeter of part a is greater than that of Part B by feeling, and the perimeter of part a and part B is equal by careful observation and analysis
2. Advocate the use of different estimation methods. Since the estimated results are approximate, errors should be allowed. This provides space for reflecting different estimation methods and training students' innovative consciousness. Therefore, in the process of teaching, we should break the routine, encourage students to give full play to their imagination, take different methods to estimate, as long as within a reasonable range of error, can quickly calculate, estimate the answer, should be affirmed. The standard answer should provide an error range, not a specific number
3. Flexible use of estimation methods. After mastering certain estimation methods, we should flexibly select appropriate estimation methods to make the estimation results more reasonable and realistic. For example: the fourth grade students' autumn outing, each set of tickets is 49 yuan, a total of 104 sets of tickets, how much should be prepared to buy tickets? The formula is: 49 × 104, estimate 1: 49 ≈ 50104 ≈ 100, 50 × If 100 = 5000, 5000 yuan should be prepared; Estimate 2: 49 ≈ 50, 104 ≈ 110, 50 × 110 = 5500 yuan, 5500 yuan should be prepared. After solving the problem, students should be guided to think: who is better and why? Although the first estimation method is the correct calculation according to the "rounding" method, the practical problems need to be analyzed in detail. It is more reasonable and practical to regard 104 as 110. Through such a comparison, students can make it clear that the use of estimation in solving practical problems should proceed from reality
in a word, strengthening the estimation is a requirement of the new curriculum for the teaching reform of primary school mathematical calculation. Teachers should timely reflect the estimation teaching in classroom teaching, so as to improve students' preliminary estimation ability and broaden students' ability to use mathematical knowledge and mathematical thinking mode to solve relevant problems.

2. Abstract: number runs through people's mathematics learning and plays an important role. It affects students' learning of various subjects, and also lays a foundation for students' further learning in mathematics. Today's society is a digital society, number plays a very important role in people's life. Number can be used to express and communicate, can help people understand things around, can also help people solve problems in life. Therefore, it is an important task to cultivate students' number sense in primary school mathematics teaching

key words: number sense accumulation, infiltration, formation and mastery

& lt& lt; Mathematics curriculum standard puts forward the number sense as one of the core contents for the first time, and is placed in the first place among the six core concepts. It can be seen that the new curriculum standard emphasizes and attaches importance to the number sense. Therefore, we must make some thinking and exploration in the new field of establishing and cultivating students' number sense effectively. Number sense is a basic quality of human beings. It is an understanding and feeling of numbers and their operations. This understanding and feeling can help people put forward useful strategies for solving complex problems in a flexible way. It is a mental skill of human beings. The purpose of cultivating students' sense of number in primary school mathematics teaching is to make students learn to think mathematically, understand and explain practical problems with mathematical methods, and consciously establish the relationship between practical problems and quantity. Therefore, every student should establish a certain sense of number. How to cultivate students' number sense in primary school mathematics teaching< First, accumulate the sense of number in life

children's learning mathematics often starts from recognizing numbers. Therefore, when children begin to recognize numbers, they should make full use of the mathematical materials around them, create teaching situations that help children understand mathematics, and unconsciously let children accumulate the sense of number. For example, when teaching "lovely campus", ask the students to look at the beautiful forest. The school of zoology begins. The lovely animals come into the school happily, which arouses the students' interest in counting the animals. The students can't help but count how many rabbits, butterflies, birds and flowers there are in the school. After counting, let him say a word with these numbers, Make children initially realize: if there is no number, it is almost impossible to say clearly where there is something. Another example is to guide the students to contact with the specific and interesting things around them. Through active observation and analysis of life phenomena, we can use numbers to express the things around us, talk about the numbers around us, and the numbers used in life, so that the children can count: there are several learning tools in the pencil box, and each learning tool has a few; Ask students to think about: home number, mother and father's phone number, mobile phone number, birthday, license plate number, etc., let students feel the meaning of number in colorful activities, experience the function of number used to express and communicate, make mathematics visible, touchable, and have a real role, lay the foundation for cultivating children's sense of number< Second, infiltrate the sense of number into the situation. The standard emphasizes that "students should be guided to contact with specific and interesting things around them. Through observation, operation, problem-solving and other rich activities, they can feel the meaning of number, experience the role of number in expression and communication, and initially establish the sense of number". In teaching, teachers should make full use of the resources of real life, create teaching situations that help children understand mathematics, awaken students' existing life experience, reproce the real source and practical application of the concept of number, so as to enable students to grasp the essence of the concept of number, truly understand the meaning of number, and establish a good sense of number. For example, when teaching "counting", it can guide students to observe the theme map in the book. The cheerful, warm and childlike pictures can bring students good memories of children's life, but also yearn for colorful primary school life. Because they usually have the learning foundation in kindergarten, the children will count with great interest: one wooden ladder, two swings, three Trojans, four airplanes... All of them are common things in their life. Mathematics is everywhere; After counting, the students will talk to each other about what is in the picture. So "number" has become an indispensable tool for students to communicate with each other, which plays a real role

for example, when teaching "simple operation of addition and subtraction method close to the whole hundred and thousand", in order to make students understand the difficulties in "345-198 = 345-200 + 2" and "345 + 198 = 345 + 200-2"“ ± 2 ", designed the situation of buying and selling goods. Student a plays the role of a salesman and student B plays the role of a customer. Student B originally paid 345 yuan, bought 198 yuan camera, paid two 100 yuan banknotes, and should get 2 yuan back. This explains the simple calculation process of "348-198": that is, if you pay more, you need to find. Then, taking the original 345 yuan as the base, he sold 198 yuan of goods, but received 200 yuan. If he received 2 yuan more, he should get 2 yuan back. In this way, we can explain the simple calculation process of "345 + 198": that is to say, if we collect too much, we should return it. On this basis, guide students to sum up the law of "simple algorithm of addition and subtraction close to the whole hundred and thousand"

for another example, when teaching division, let the students act as the group leader, distribute learning tools to the group members, understand the meaning of division and calculate by formula. When learning "Statistics", students should make their own tables according to the items and results of the class in the sports meeting, so as to master the method of statistics. For another example, when teaching the calculation of "nine plus a few", create the situation of "the salesperson arranges the counter, there is a box of table tennis is 9, the other box is 8, how many in total", let the students think of a way to calculate< Third, form the sense of number in the expression and communication

create the problem situation for students in the teaching, so that students can inspire each other, learn from each other and learn from each other in the process of discussion, and realize that number can be used to express and exchange information, so that students can expand their thinking, enrich their understanding of logarithm and realize the value of mathematics in the exchange of logarithm perception, So it can promote the formation of number sense

for example, when talking about "liter and milliliter", ask students to look at the scale and say the volume of water. The picture shows that one measuring cylinder contains 1000 ml of water, and the other measuring cylinder contains 700 ml of water. How much is it combined? After looking at the pictures, the students came up with a variety of methods, some said 1 liter 700 ml; Some say 1.7 liters; Some say 1700 ml and so on. Students use many methods to express the same quantity. Through discussion, we can judge that these methods are correct. It also shows that the integral of water in a picture can be expressed by integer, decimal and fraction. In this way, students establish a connection between fractions, decimals and integers, know that they can understand a number from many aspects, enrich the understanding of logarithm, and further develop the sense of number

learning to listen, finding and thinking about problems from other people's description of certain quantity is also a kind of communication. For example, in the actual measurement, I led the students to the playground to measure the length and width of the rectangular flower bed. The students measured the length and width of the flower bed in different ways. In the classroom communication, they showed a variety of measurement methods. Some students measured directly with tape measure; Some students first measure the length of a brick, then count the number of bricks in length and width, and multiply the length of each brick by the number of bricks to get the length and width; Some students first measured the length of the rope of 1 meter, then measured the length of the rope of 1 meter and 1 meter; Some students use the method of walking test. In the communication, we exchange our ideas with others, and also understand how others think and do. We perceive a certain length from different angles, develop a sense of distance, and enhance the sense of number< Fourth, it is necessary to master the sense of number in practice. The standard clearly points out that effective mathematics learning activities can not simply rely on imitation and memory. Hands on practice, independent exploration and cooperation are important ways for students to learn mathematics. Primary school mathematics practice activities should let students learn mathematics through personal experience, do and use mathematics in their hands, not just listen to and remember mathematics. Mathematics practice activities are the sky of students' active development, and the mathematics classroom focusing on practice activities will become the paradise of students' exploration and the cradle of innovation. Similarly, the cultivation and development of number sense is inseparable from practical activities. First grade children are curious and active. Simple practical activities such as operation, observation, guessing and communication are attractive to them. In the first volume of the experimental textbook of the new curriculum standard for grade one, many interesting practical activities are designed to cultivate students' sense of number. For example, when teaching "Statistics", the problem situation is designed according to the theme map in the textbook, "Xiao Ming has investigated the situation of the fruits that the whole class likes to eat most. My friends, guess which fruit most people like to eat?"“ What method can you use to let students see which kind of fruit most people like to eat at a glance? "“ What method can you use to let students see which kind of fruit most people like to eat at a glance. " Then let the students in each group discuss and talk about it, and then put it in the picture. And choose the best method from the students' works, leading to the statistical chart of fruit. In this way, in teaching closely linked to the actual life of students, in the specific operation activities to cultivate students' sense of number, can make students have a distinct appearance, and then encounter similar situations, they will have a specific reference in the mind, really establish a good sense of number&# 57348;< 5. Cultivate the sense of number in application. Mathematics curriculum standard puts forward that students' sense of number should be further cultivated by solving practical problems. Practice is the only criterion for testing truth. Students' mathematics learning ultimately lies in its application value. The key experience of application can not be taught, and must be experienced by children themselves. Therefore, teachers should guide students to "re create" knowledge after class to solve the real problems around them. In this process, students should start from the perspective of mathematics, learn from the experience of predecessors, flexibly choose appropriate mathematical methods and strategies, try to supplement, modify, reflect and summarize at any time, and evaluate their rationality. In this way, the students' learning experience can be transferred to a wide range of learning ability, so as to cultivate the sense of number

for example, after learning the average, how old is each member's grandmother and grandfather. Then ask the students to estimate the average age? Combined with the video of the 11th national young singers TV Grand Prix, let students estimate the final score of each singer according to the score of each judge. Let students understand why to calculate and what kind of calculation method to choose

another example: how many vegetables and meat dishes do you need to buy for your mother in the street? How much is the price of each dish and how much is the total<

after learning statistics, students are asked to make statistics on family expenses, water, electricity and TV programs, and then put forward suggestions for their own families

in a word, the process of cultivating students' number sense is graal. Cultivating students' sense of number can make students have more opportunities to contact society, experience reality, express their views on problems, and think and solve problems in different ways

3. In the process of primary school students' growth, mental health ecation is particularly important. It is not an additional ecation, but a complete ecation project, which should penetrate into the whole process of school ecation and teaching. The infiltration of mental health ecation in mathematics teaching is to eliminate all adverse factors harmful to students' mental health in teaching design, evaluation and management, prevent students' mental disorders, and enable students to study in a relaxed, harmonious and happy situation without excessive psychological pressure, so as to maintain and promote students' mental health. I think we should focus on the following aspects
first, we should pay attention to mining the psychological teaching content contained in the teaching materials, and carry out targeted infiltration
the orientation of the content in Chinese and ideological ecation textbooks is to teach students with good quality, while the content of mathematics tends to be more rational knowledge and less humanistic. However, we can still find many contents that are beneficial to the development of students' mental health. In the class of number and algebra, we mainly cultivate students' ability of calculation and estimation; In the course of comprehensive practice, we can let students explore actively and experience the joy and pride of finding their own conclusions; In the class of figure understanding, we can focus on cultivating students' space concept and space imagination ability; Statistics and probability courses, we can increase contact with social life, so that students learn to apply. For example, in the sixth volume, we can naturally penetrate the ideas of fairness, equality and mutual benefit, and cultivate students' peaceful mentality; For example, a lot of information such as gross national proct, raw coal output, per capita annual income and so on appear in many practical problems. Through these information, students can have a sense of pride, so as to cultivate students' noble sentiment of loving the motherland, the people and socialism< Second, pay attention to the learning process experience, ince students to actively participate in learning
psychological research shows that: intuitive, visual, novel things can attract students' attention. Pupils' interest in learning is always directly related to learning materials. And primary school students have strong curiosity, thirst for knowledge, easy to be attracted by new things. Therefore, in order to solve the contradiction between the abstraction of mathematical knowledge and the visualization of primary school students' thinking, teachers must organize students to operate more, inspire students' thinking with "movement", let them proce more new problems and ideas, and activate the classroom atmosphere. For example, in the class of "understanding objects", I first organized the students to play with building blocks, so that the students could understand the shapes and characteristics of squares, rectangles, cylinders and balls in the activities of playing with building blocks. In this way, students will not feel bored, but also interested in learning to play. Teachers often have a strong attraction to students by using vivid language and appropriate intuitive teaching methods, which can stimulate students' interest in learning and develop their interest at the same time
thirdly, teachers' own behavior is also a good channel for healthy psychological infiltration
Confucius said, "if you are upright, you should act without command; If he is not upright, he will not be able to do so. " Teachers are like a model for students. How teachers do it, they will guide students to do it. Sometimes, preaching over and over is not as good as a hint of eyes, a demonstrative action, a casual words. It can be said that many good moral qualities of students are taught by teachers imperceptibly. Therefore, in order to make students form healthy psychology, teachers must be upright
teachers don't need to talk a lot about their behaviors, they just need to start from the little things around them and show good quality from the little things. For example, a clean and tidy office can make students understand that their own place is clean, and it can also bring beauty to others, and understand the principle of "how to sweep the world without sweeping a room"; When you see the broom falling down, you can pick it up. It is a virtue to tell students to take good care of public property; In the face of other people's unreasonable noise, teachers can treat it peacefully, which can make students understand that peace of mind is also a kind of accomplishment; It can help students understand that "Lei Feng spirit is not on the wall, but on their lips"...
Fourth, to determine the evaluation orientation and pay attention to mental health ecation
evaluation refers to the value judgment of teaching activities and effects based on certain objective standards. The process of students' participation in evaluation is also the process of learning to be a person. In the process of evaluation, teachers should guide students to learn to use the step-by-step positive evaluation method instead of taking a perfect answer as the only standard of evaluation results. Many children are tired of school and play truant. The basic reason is that they are criticized and criticized by many people in their study and life, and even satirized and sarcastic, resulting in serious psychological problems. Therefore, when evaluating students, teachers should pay attention to more encouragement, more praise, less criticism and less criticism, pay attention to the equality and fairness of ecation, strive to find the shining point of students, and give guidance and training, so as to graally cultivate students' self-confidence and interest in learning.

4. In primary school mathematics teaching, attention should be paid to the cultivation of students' thinking preciseness
preciseness is the basic feature of mathematics class, and thinking preciseness is one of the keys to learn mathematics well. However, the phenomenon of imprecise thinking often occurs among teachers, and this kind of imprecise thinking directly affects the students' mathematics performance. For example, at the end of the first semester of a school year, there is such a judgment question in the sixth grade mathematics test paper: "if 1 / 3 of the number a is equal to 1 / 4 of the number B, then the number B is greater than the number a"

according to the reference answers, the questioner thinks that "√" should be marked. I think the original intention of the questioner is under the premise of "both a and B numbers are positive". At this point, a × 1 / 3 = b × 1 / 4 → A / 3 = B / 4 → a ∶ B = 3:4 → the number of B is greater than that of A. However, if there is no "both a and B numbers are positive", we should consider:

1. When both a and B numbers are zero, this should be considered under the knowledge system that primary school students have learned, at this time, a number is equal to B number

2. If we consider that the number a and B are both negative, although primary school students have not yet learned, they will soon learn when they enter junior high school. At this time, the number B should be less than the number a. For example, if a is - 3 and B is - 4, then (- 3) x 1 / 3 = (- 4) × 1 / 4, but - 3 & gt- 4< In conclusion, as far as the original proposition is concerned, the conclusion can be divided into three situations:

1

2. When both numbers a and B are zero, the number a is equal to the number B

3. When both a and B numbers are negative, the number of a is greater than that of B

therefore, in my opinion, the original topic is a proposition without major premise. As a judgment question“ ×”

some people may think that in the case of pupils not learning negative numbers, they can tick "√". I think this is unreasonable. First, pupils have learned zeros and know that natural numbers and zeros are part of integers. For the students with rigorous thinking, we should pay attention to the fact that the original proposition is a false proposition when a and B are both zero. Second, when a primary school student enters junior high school, he will encounter this problem. At that time, he will find that when the two numbers a and B are negative, the original proposition is false. Moreover, he will realize that the original knowledge of primary school is not contradictory to that of junior high school, and the content of the knowledge system is richer and more complete

speaking of this, I think a mathematics teacher should fully realize that mathematics is a subject with strong knowledge, strict logical reasoning and rigorous way of thinking. Therefore, in the usual teaching, we should pay attention to strengthen the cultivation of students' rigorous thinking. There are many other examples like this:

1. A group of paralleled quadrilateral is trapezoid

this is a false proposition. Because it ignores another set of non parallel conditions. "You" here is different from "only", "you" refers to existence, and "only" refers to uniqueness. Strict statement should be: there is and only one set of paralleled quadrilateral is trapezoid< The area of triangle is half of that of parallelogram. This false proposition ignores the premise of "equal base and equal height"< 3. The progressive rate of area unit is 100. This false proposition ignores the condition of "two adjacent"

if you divide 4.0 by any number, you get 0. "Any number" in this false proposition should not include 0

5

the "same number" in this false proposition should also be excluded from 0

there are so many such examples that you will see many in middle school. As long as we are a conscientious person in teaching and responsible for students, we should always pay attention to cultivating students' habit of comprehensive and complete consideration, so that students can graally develop the characteristics of rigorous thinking.

5.

For those pupils with poor grades, it is very difficult to learn primary school mathematics. In fact, primary school mathematics belongs to the basic knowledge, and it is relatively easy to master certain skills. In primary school, it is a period that needs to develop good habits. It is important to pay attention to the cultivation of children's habits and learning ability. What skills do primary school mathematics have

It can be seen from this that the skill of primary school mathematics is to do more exercises and master basic knowledge. In addition, it is mentality. If you can't be timid before the exam, it's very important to adjust your mentality. Therefore, you can follow these skills to improve your ability and make yourself enter the ocean of mathematics

6. Abstract: the cultivation of abstract thinking ability is an important learning task in primary school mathematics teaching. It is an effective way for students to understand mathematics, like mathematics and master mathematics. It is also the basis of cultivating students' innovative consciousness. It is a step-by-step process to cultivate students' abstract thinking. Teachers need to strengthen the teaching of students' basic knowledge of mathematics, dig deep into teaching materials, innovate teaching methods, fully mobilize students' learning initiative, guide students to think positively, and constantly improve their abstract thinking ability in the process of thinking
key words: primary school mathematics; Abstract thinking; Learning tools; Language; development; Indivial difference
the design concept of the new curriculum standard of primary school mathematics clearly stipulates: "mathematics is a science that studies the quantitative relationship and spatial form. Mathematics is closely related to human activities, especially with the rapid development of computer technology, mathematics is more widely used in all aspects of social proction and daily life. Mathematics, as a scientific language and tool formed by the abstract generalization of objective phenomena, is not only the basis of natural science and technological science, but also plays an increasingly important role in social science and humanities. " From this passage, we clearly know that the cultivation of abstract thinking ability plays a very important role in the future development of students. Abstract thinking is an indirect and generalized response to the objective reality by using concepts, judgments and reasoning. The cultivation of students' abstract thinking is concive to the training of students' thinking ability, which is the prerequisite for students to learn mathematics well. Now on the students' abstract thinking training methods, say a little bit of their own views< In the primary school stage, the students should be able to make full use of learning aids

7. Understanding mathematical thinking and methods, let the classroom shine charm, let the students show elegant demeanor Famous mathematician Zhang Jingzhong once pointed out: "primary school students learn mathematics very elementary, very simple. But despite its simplicity, it contains some profound mathematical ideas. " As the two clues of primary school mathematics learning, mathematical knowledge and mathematical thinking method support each other. Among them, mathematical thinking method prompts the essence and development law of mathematics, which can be said to be the essence of mathematics. Now let's talk about mathematical thinking. 1、 Why should we infiltrate mathematical thinking methods into teaching? 1. Basic mathematical thinking methods are of great significance to the development of students. An ecationist once pointed out: "mathematics as knowledge may be forgotten in less than two years after leaving school, but what is deeply remembered in the mind is the brilliant spirit of mathematics and the ideas, research methods and focus of mathematics, These can work anytime, anywhere and benefit students for life. " The thinking method of mathematics is the soul and essence of mathematics. Mastering the scientific thinking method of mathematics is of great significance to improve the quality of students' thinking, the subsequent learning of mathematics, the learning of other learning, and even the lifelong development of students. In primary school mathematics teaching, consciously infiltrating some basic mathematical thinking methods is the key to enhance students' mathematical concept and form good thinking quality. It can not only make students understand the true meaning of mathematics, understand the value of mathematics and learn to think and solve problems mathematically, but also organically integrate the learning of knowledge with the cultivation of ability and the development of intelligence. 2. Infiltrating basic mathematics thinking method is the need to implement the spirit of the new curriculum standard. Mathematics curriculum standard takes "four Basics": basic knowledge, basic skills, basic ideas and basic activity experience as the target system. The basic idea is one of the goals of mathematics learning, and its importance is self-evident. The new textbook is to present some important mathematical ideas and methods through the simplest examples in students' daily life, and solve these problems by means of operation, experiment and other intuitive means. So as to deepen students' understanding of mathematical concepts, formulas, theorems and laws, and improve students' mathematical ability and thinking quality, which is an important way for mathematics ecation to realize from imparting knowledge to cultivating students' ability to analyze and solve problems, and also the real connotation of the new primary school mathematics curriculum reform. 2、 What mathematical thoughts are permeated in the teaching materials? Dection and inction are the most superior thoughts in primary school mathematics, which is the main line of mathematics teaching. There are also some commonly used mathematical thinking methods: correspondence thought, - which refers to the grasp of the relationship between two set elements. Many mathematical methods come from the idea of correspondence. For example, students often have 10? twenty × 2 30 40 50 The appearance of form actually reflects the corresponding thought. For example, a point on the number axis corresponds to a number, any number can find the corresponding point on the number axis, one-to-one correspondence, showing perfect. Today, symbolic thinking and mathematics have become a world of symbols. The famous British mathematician Su once said: "what is mathematics? Mathematics is sign plus logic. " Symbolic thought refers to people's conscious and universal use of symbolic language to express the object of study. Symbolization thought has more penetration in the whole primary school, for example: Arabic numerals: 1, 2, 3, 5, 6,... +, -,, and other operational symbols& gt;、& lt;& lt;/ SPAN>、=、 And so on to indicate the sign of relation; (), [] Equal brackets; Letters for numbers: X, y, Z, etc. Letter expression formula: area of rectangle and square s = Ab s = A & # 178; The letter indicates the unit of measurement symbol: M & # 92; cm\ dm\ mm\ g\ Km, etc. The idea of set -- putting a group of objects together as the scope of discussion is the idea of set. For example, when teaching children how to recognize numbers in the first grade textbooks, some pictures are circled in a circle. This is the rudiment of collection that children first came into contact with, and it is also the first time that this idea of collection has been infiltrated into primary school students. In the later teaching, the ideas of union set, difference set and empty set are graally reflected. Limit thought -- the thought of limit thought in ancient China. Liu Hui's "circle cutting" is a typical example of using Ji Naizi's thought. The idea of limit is to study the changing trend of variables in infinite changes. With this idea, people's thinking can develop from limited space to infinite space, from static to dynamic, from concrete to abstract. Statistical thinking - the statistical thinking in primary school mathematics is mainly reflected in: simple data sorting and averaging, simple statistical tables and charts. While students can sort out, tabulate and draw charts, they should be able to find mathematical problems and mathematical information from data and charts, and draw relevant conclusions Hypothetical thinking is a kind of thinking method that first makes some assumptions about the known conditions or problems in the goal of the question, then calculates according to the known conditions in the question, and makes appropriate adjustments according to the contradictions in the number, and finally finds the correct answer. Comparative thinking is one of the common ways of thinking in mathematics teaching, and also a means to promote the development of students' thinking. In the practical problems of mathematics score, teachers are good at guiding students to compare the situation before and after the change of known and unknown quantity, which can help students find the way to solve problems quickly. Analogy thought refers to the thought that according to the similarity of two kinds of mathematical objects, it is possible to transfer the properties of one kind of known mathematical objects to another. Such as addition commutation law and multiplication commutation law, rectangle area formula, parallelogram area formula and triangle area formula. This idea not only makes the mathematical knowledge easy to understand, but also makes the memory of formula natural and concise. Transforming thought is a way of thinking in which one form is transformed into another, and its size is constant. For example, the geometric transformation of equal proct, the transformation of the same solution of the equation, and the deformation of the formula are also commonly used in the calculation. Classification idea - reflects the classification of mathematical objects and its classification standards, such as the classification of natural numbers, triangles divided by edges and angles. Different classification standards will have different classification results, resulting in new concepts. Number and form are two main objects of mathematical research. Number and form are inseparable from number. On the one hand, abstract mathematical concepts and complex quantitative relations can be visualized, visualized and simplified by means of graphics. On the other hand, complex shapes can be represented by simple quantitative relations. In solving practical problems, we often use the help of line diagram to analyze the quantitative relationship. Substitution thought -- it is an important principle of equation solution. When solving problems, one condition can be replaced by another. For example, the school bought four tables and nine chairs for a total of 504 yuan. The price of one table and three chairs is exactly the same. What is the unit price of each table and chair? Reversible Acacia -- it is the basic thought in logical thinking. When it is difficult to solve the problem in the forward thinking, we can find the solution from the condition or problem thinking, and sometimes can replace the line diagram. For example: a car from a to B, the first hour line 1 / 7, the second hour than the first hour more than 16 kilometers, there are 94 kilometers, seek the distance between a and B. The thinking method of transformation is to classify the problems that are likely to be solved or indicated to be solved into one category through the transformation process, so as to solve the problems that can be easily solved and obtain solutions. This is called "transformation". However, mathematical knowledge is closely related, and new knowledge is often the extension and expansion of old knowledge. Let the students face the new knowledge and think about problems with the method of transformation, which is undoubtedly of great help to improve the ability of acquiring new knowledge independently. The way of thinking of grasping invariability in the course of change -- how to grasp the quantitative relationship and grasp invariability as the breakthrough point in the complicated changes? For example, there are 630 scientific and technological books and literature and art books in total, of which 20% are scientific and technological books. Later, some scientific and technological books are bought. At this time, 30% are scientific and technological books. How many scientific and technological books are bought? The thinking method of mathematical model is a way of thinking for a specific object in the real world, starting from its specific life prototype, and making full use of the process of observation, experiment, operation, comparison and analysis to get simplification and assumption. It is a way of thinking for practical problems in life to be transformed into mathematical problem model. It is the highest level of mathematics to train students to understand and deal with the surrounding or mathematical problems with mathematical vision, and it is also the goal of students' high mathematical literacy. These mathematical thinking methods are the essence of mathematics and the essence of mathematics. Only by mastering the methods and forming the ideas can students benefit all their lives. Next, we will combine our own learning and practice of mathematical thinking methods to communicate with you. 3、 Let the classroom show the charm of thought. First of all, let's talk about lesson preparation: when preparing lessons, we should study the teaching materials, make clear the objectives, design plans, and fully explore the mathematical thinking methods. If the teacher knows nothing about the suitable thinking methods for the teaching of the teaching materials before class, then the classroom teaching can't have a definite aim. Therefore, when we prepare lessons, we should not only see the basic knowledge and skills of mathematics directly written in the teaching materials, but also further study the teaching materials, creatively use the teaching materials, excavate the mathematical thinking methods hidden in the teaching materials, clearly write out the infiltration of mathematical thinking methods in the teaching objectives, and design mathematical activities to implement in each link of the teaching presupposition, Realize the organic integration of mathematical thinking and methods in the formation process of mathematical knowledge. In fact, each textbook has the infiltration of mathematical thinking methods, and we choose representative units in each textbook. This is only the tip of the iceberg relative to all teaching content. Therefore, when I study the teaching materials, I often ask myself a few reasons, and internalize the idea of textbook arrangement into my own teaching ideas, such as: how to let students experience the process of knowledge generation and development? How to arouse students to think deeply about mathematics? How to stimulate students' initiative to explore new knowledge? How to infiltrate mathematics thinking methods timely according to teaching materials and so on. Only when I have a clear mind can I permeate the students with corresponding mathematical thoughts. Class 2: create situations, build models, explain applications, and infiltrate mathematical thinking methods. Mathematics is an organic combination of knowledge and thinking methods. There is no mathematical knowledge that does not include mathematical thinking methods, and there is no mathematical thinking methods that are free from mathematical knowledge. This requires teachers in classroom teaching, in revealing the formation of mathematical knowledge in the process of infiltration of mathematical thinking, in teaching students mathematical knowledge at the same time, also get the Enlightenment of mathematical thinking. Teachers actively infiltrate mathematical thinking and methods in class, reflecting the great wisdom of teachers in teaching and opening up a vast new field for students' learning.

8.

1. Floor plan

for the questions with abstract conditions and not easy to write answers directly according to the knowledge, you can draw a floor plan to help you think and solve the problems

For example, there are two natural numbers a and B. If a is increased by 12 and B is unchanged, the proct will increase by 72; If a is constant and B is increased by 12, the proct will be increased by 120

according to the abstract condition of the topic, we can use the rectangular graph to transform the condition into the relationship between factor and proct. First, draw a rectangle. The length represents a and the width represents B. the area of the rectangle is the proct of the original two numbers. As shown in figure (L)

from the chart, we can clearly see the different holding methods. There are seven ways to solve this problem

It can be seen from the above examples that drawing pictures can help to understand the meaning of the problem, which can simplify the complexity and make the difficulty easy. We might as well use it widely in solving problems

9. The following principles should be considered when choosing and applying teaching methods:
1. Adhere to heuristic teaching and oppose injection Teaching
heuristic teaching means that teachers start from the actual situation of students, regard students as the main body of learning, and use various ways and methods to mobilize students' learning enthusiasm, initiative and initiative, Guide students to master knowledge, form skills, develop ability and promote the healthy development of personality through their own active learning activities
the spirit of heuristic teaching is to respect students' main personality, emphasize guiding students' learning methods, and attach importance to students' skill formation, ability development and personality display. It regards students as both the object of ecation and the subject of learning, fully arouses students' initiative in learning, stimulates their interest in learning and thirst for knowledge, so as to actively carry out thinking activities and master knowledge on the basis of understanding. This kind of teaching is helpful to promote students' intelligence, especially the development of thinking ability, and cultivate students' ability to analyze and solve problems. It is a scientific and democratic teaching method
infusion teaching, also known as "cramming" or "indoctrination" teaching, refers to teachers' subjectivism, putting students in a passive position, ignoring students' subjective initiative, viewing students as a "container" of simply accepting knowledge, and only focusing on knowledge imparting in the teaching process. It can be seen that injection teaching is to treat students as passive objects of ecation, and not pay attention to mobilize students' initiative and enthusiasm. Teachers only instill knowledge into students, so that students can swallow it alive, read it blindly and memorize it, which inhibits students' thinking ability and innovative spirit. Injective teaching method is not concive to students' real understanding of knowledge, but also not concive to the development of their wisdom. It is an unscientific and undemocratic teaching method
2. The principle of reflecting the value of ecation
what is the basic value pursuit of primary school mathematics ecation? Different understanding will affect the choice and combination of specific mathematics teaching methods. If we simply understand the value of primary school mathematics ecation as mastering the most basic mathematics knowledge that has been found, we may think more about "what kind of way to explain is better for students to understand?"“ What kind of exercises can make students grasp the basic knowledge“ How to consider whether students have mastered the required basic knowledge? " Correspondingly, when we choose or combine teaching methods, we may focus more on "narrative explanation", "repetitive practice", "conclusive demonstration" and other methods; If we understand the value of primary school mathematics ecation as the development of students' mathematical literacy, we may think more about "what kind of organization can be more concive to students to experience a process of exploration and discovery?"“ Through which acquisition can students' knowledge and experience be applied to the real situation? "“ How to consider students' ability to solve mathematical problems "and so on, correspondingly, when choosing or combining mathematical methods, they may focus more on" heuristic dialogue "," exploratory experiment "," initiating problem solving "and other methods
3. Goal oriented principle
before any mathematics teaching activity starts, teachers will (and must) design specific teaching objectives according to curriculum objectives, learning tasks and students' characteristics. With the implementation of the new curriculum, the diversity and integration of teaching objectives have been deeply rooted in the hearts of the people. The new curriculum standard divides the teaching objectives into three dimensions: "knowledge and skills, process and method, emotion, attitude and values". This goal is to concretize the task of mathematics learning. It is the basic orientation of the whole classroom learning activities. In the classroom teaching, it dominates the methods and processes of teaching and learning, and is the starting point and destination of teaching. Therefore, teachers' choice and combination of mathematical methods, the first thing to consider is how to maximize the achievement of this goal has been determined
4. The principle of adapting to the teaching content
the teaching task is realized through the teaching of the teaching content. The teaching content here refers to the nature of the subject and the content of a class. The teaching content is an important condition to restrict the teaching method. The teaching method varies with the nature of the subject. For the same subject, the selection of teaching methods is different e to the different contents of teaching materials. The same is to impart new knowledge, such as conceptual content, it is necessary to choose the teaching method; If it is to clarify the characteristics of things and reveal the law of development and change of things, demonstration method can be used. So we should choose the appropriate teaching method according to the teaching content
5. The principle of promoting children's learning
a good teaching method should be a proceral structure that fully stimulates students' learning motivation and actively participates in learning. It should fully consider how students learn and how to learn better. It should fully attract students' attention, and at the same time keep students' attention as much as possible, so that students can always actively participate in the learning process; It should not only pay attention to the rationality and effectiveness of teachers' behavior, but also pay full attention to students' emotional state, the degree of students' participation in learning, the problems or difficulties encountered in the process of students' participation in learning, and the various problems that students may raise; It should help to form and strengthen students' self-confidence in learning mathematics; It should enable students to get the most possible experience in the process of learning, and get some satisfaction of "success" under this experience
teachers should make students clear their learning tasks and goals in various ways; Help students determine their own learning style according to the learning content; Pay attention to children's personality, experience basis, interest orientation and learning style, rather than change their preset ecation and teaching plan; Encourage students to use different strategies and ways to participate in learning; Let the students use various ways to observe the object, foresee the result and test the hypothesis; Integrate the different reactions of students in the learning process into their own teaching methods< First of all, teachers should realize that students of different ages have different cognitive psychological levels and psychological characteristics. For example, students of lower ages are more likely to be attracted by some novel objects, but it is difficult to identify mathematical characteristics for some complex situations, In the process of learning, they rely more on intuition, so they are weak in some logical operations. Therefore, in this age group, more materials can be used for demonstration. Operation experiment and other methods. For the students of a little older age, they have begun to recognize some mathematical characteristics from a more complex situation. Although mathematical thinking still mainly depends on intuition, they have established the preliminary logical operation ability of language and symbols. Therefore, they can use more heuristic conversation, exploratory discovery, exploratory experiments and other methods< Secondly, teachers should realize that different students have different cognitive structures and learning styles. A professional mature teacher knows how to choose flexible, open and diversified adaptive teaching methods according to the characteristics of different students' cognitive structure and learning style. Specific teaching methods are related to specific students' characteristics, so as to meet students' learning needs
finally, teachers should realize that students of different ages have different life experiences. Even students of the same age have different life experiences. The students' existing life experience, accumulated daily experience and established daily concepts are the basis for students to realize the mathematization of practical problems. Therefore, these differences should be taken into account when choosing and combining teaching methods.

10. Summary of 19 kinds of primary school mathematics teaching methods
good methods can make us better use of our talents, while poor methods may hinder the development of our talents. - [English] Bernard
"mathematics provides language, ideas and methods for other sciences", "initially learn to use mathematical thinking to observe and analyze the real society, (primary school mathematics curriculum standard)
there are two kinds of mathematical thinking methods, image thinking method and abstract thinking method.
primary school mathematics should cultivate students' image thinking ability, and on this basis, lay a solid foundation for the development of abstract thinking ability Image thinking method
image thinking method refers to the method that people use image thinking to understand and solve problems. Its thinking basis is specific image, and the thinking process is expanded from specific image.
the main means of image thinking are material objects, graphics, tables and typical image materials. Its cognitive characteristics are that indivial is general, and the indivial is general, Its thinking process is represented by representation, analogy, association and imagination. Its thinking quality is represented by active imagination of intuitive materials, processing and refining of representation to prompt essence, law or object. Its thinking goal is to solve practical problems and improve its own thinking ability in solving problems.
1 Physical demonstration method
uses the physical objects around to demonstrate the conditions and problems of mathematical problems, and the relationship between conditions and conditions, conditions and problems. On this basis, we can analyze and think, and seek solutions to problems.
this method can visualize the mathematical content, and concretize the quantitative relationship. For example, the encounter problem in mathematics can be solved by physical demonstration Another example is the problem of planting trees around a circular (square) pond. If we can carry out a practical operation, the effect will be much better.
in the second grade mathematics textbook, "three children meet and shake hands, and each two shake hands once, a total of several times" and "put three different number cards into two digits, In primary school teaching, it is difficult to achieve the expected teaching goal if the physical demonstration method is used for the knowledge of arrangement and combination.
especially for some mathematical concepts, if there is no physical demonstration, pupils can not really master the area of rectangle, the understanding of cuboid, the volume of cylinder, etc, Therefore, primary school mathematics teachers should make as many mathematics teaching (learning) tools as possible, and these teaching (learning) tools should be well preserved after use, which can be reused. This can effectively improve the efficiency of classroom teaching, and improve students' academic performance.
2, The graphic method is intuitive and reliable, easy to analyze the relationship between number and shape, not limited by logical derivation, and flexible and open-minded. However, the graphic method depends on the reliability of people's image processing. Once the graphic method is inconsistent with the actual situation, it is easy to make the association and imagination based on it fallacious or go into the wrong area, For example, some mathematics teachers like to draw mathematical figures by hand, which will inevitably lead to inaccuracy and misunderstanding.
in classroom teaching, we should use more graphic methods to solve problems; Some questions, the picture is good, the topic meaning student also understood; For some problems, drawing can help to analyze the meaning of the problem, enlighten the thinking, and serve as an auxiliary means for other solutions.
example 1 it takes 24 minutes to saw a piece of wood into three sections, and how many minutes to saw it into six sections The way of thinking is: graphic method.
the direction of thinking is: sawing several times, each time for a few minutes.
the idea is: sawing three sections for several times, each time for a few minutes, sawing six sections for several times, how many minutes it takes.
example 2 judges that in an isosceles triangle, point D is the midpoint of bottom BC, and the area of figure a is larger than that of figure B, The perimeter of figure a is longer than that of figure B. (Figure outline)
method of thinking: graphic method.
direction of thinking: first compare the area, then compare the perimeter.
idea: make an auxiliary line. The area of figure a is larger than that of figure B, so "the area of figure a is larger than that of figure B" is correct, So "the circumference of figure a is longer than that of figure B" is wrong.
3. List method
the method of using list table to analyze, think, find ideas and solve problems is called list method. List method is clear and clear, easy to analyze, compare, prompt rules, and also concive to memory. Its limitation lies in the small scope of solution, narrow application type, Most of them are related to finding rules or displaying rules. For example, the teaching of positive and negative proportion content, data arrangement, multiplication formula, digit order and so on, mostly adopts the "list method". "
use the list method to solve the traditional mathematical problem: chicken and rabbit in the same cage. Make three tables: the first table is the example method one by one. According to the condition that there are 20 chickens and rabbits in total, assume that there is only one chicken, Then there are 19 rabbits and 78 legs in total; The second table lists a few, and then finds the law of the number of legs and the number of legs, so as to rece the number of lists; The third table is listed from the middle, because there are 20 chickens and rabbits, so each takes 10, and then according to the actual data to determine the direction of listing.
4. Exploration method
according to a certain direction, the method of trying to explore the law and explore the idea of solving problems is called exploration method, It's about how to find the formula before there is no formula. "Sukhomlinsky said: in the depths of people's hearts, there is a deep-rooted need, that is, to hope to be a discoverer, researcher and explorer. In children's spiritual world, this need is particularly strong." learning should take inquiry as the core. ", It is one of the basic concepts of the new curriculum. When it is difficult to transform problems into simple, basic, familiar and typical problems, a good method often adopted is to explore and try.
first, the direction of exploration should be accurate, the interest should be high, and random attempts or formalistic exploration should be avoided. For example, when teaching "scale", the teaching method should be simple, basic, familiar and typical, The teacher creates the teaching situation of "the students test the teacher" and asks the teacher, "is it OK for us to test now?" Students listen: very strange, just when the students doubt, the teacher said: "today change the past test method, by you to test the teacher, willing to?" The teacher said, "here is a map. You can measure the distance between the two places with a ruler. I can tell you the actual distance quickly. Do you believe it?" Then the students came on stage to measure and count, and the teachers answered the corresponding actual distance one by one. The students were even more surprised and said with one voice: "teacher, tell us quickly, how do you calculate?" The teacher said, "actually, a good friend is helping the teacher secretly. Do you know who it is? Want to know it? " Then the content to be learned "scale" is drawn out.
Second, directional guess, repeated practice, and looking for rules in continuous analysis and adjustment.
example 3: find rules and fill in numbers.
(1) 1,4,10,13,19
(2) 2, 8, 18, 32, 72.
thirdly, the combination of independent inquiry and cooperative inquiry; In primary school mathematics teaching activities, teachers should try their best to create situations for students to explore, create opportunities for students to explore, and encourage students with the spirit and habit of exploring.
5, The method of incing and discovering the general law of things is called observation; We should learn to observe first, and we can never be a scientist unless we learn to observe.
the content of "observation" in primary school mathematics generally includes: 1) the change law and position characteristics of numbers; ② The relationship between condition and conclusion; ③ The structural characteristics of the title; ④ For example, observe a group of formulas: 25 × 4＝4 × 25,62 × 11＝11 × 62,100 × 6＝6 × 100... Sum up the exchange rate of multiplication: in the multiplication formula, exchange the position of two factors, the proct remains unchanged.
"observation" requirements:
first, observation should be careful and accurate.
example 4 find out where the following problems are wrong, and correct them.
(1) 25 × 16=25 × four × 4=25 × 4 × twenty-five × 4< br />218 × 36+18 × 64=18+18 × (36 + 64)
in case 5, write the number of the following questions directly:
(1) 3.6 + 6.4 (2) 3.6 + 6.04
(3) 125 × fifty-seven × 0.04 (4)(351－37－13) ÷ 5
Second, scientific observation. Scientific observation is permeated with more rational factors. It is to observe the research object purposefully and in a planned way. For example, when teaching the understanding of cuboid, we should observe in order: (1) face shape, number, the relationship between faces 2) Edge -- the formation of edges, the number of edges, and the relationship between edges (the opposite edges are equal; There are four opposite edges; The edges of the cuboid can be divided into three groups 3) Vertex: the formation and number of vertices. One of the important functions of understanding vertices is to lead to the concepts of length, width and height of cuboid.
thirdly, observation must be combined with thinking.
example 6

7
10
6

18
this is a question for thinking in the second semester of grade one Typical method
the method of associating the problem-solving rules of the typical problems that have been solved to find out the solution ideas is called typical method. Typical method is relative to general method. To solve mathematical problems, some need to use general methods, while others need to use special (typical) methods. For example, normalization, multiple ratio and summation algorithm, itinerary, engineering, eliminating similarities and differences, etc It is known that the father is 30 years older than his son. The father's age this year is just seven times that of his son. How old are the father and the son this year? The key points are: the father is 30 years older than his son, and the father is several times older than his son. Typical problems have typical solutions. If you want to really learn mathematics well, you need to understand and master the general ideas and solutions, as well as learn typical solutions.
(2) be familiar with typical materials, and be able to think of applicable typical problems quickly, In order to determine the problem-solving method needed.
example 8 saw "a city has a bus line, 16500 meters long, an average of every 500 meters to set up a station. This line needs to set up how many stations?" This topic should be associated with the typical problem of "how many minutes it takes to saw wood" mentioned above.
(3) typicality is related to skills.
Example 9 there are 82 people in the two engineering teams. If eight people are transferred from team B to team a, the number of people in the two teams is exactly the same. How many people are there in each team? The skill of this problem: the total number of the two teams before and after the transfer has not changed. First calculate the number of each team after the transfer, and then calculate the number of the original teams.
7. Scaling method
the method to solve the problem through the scaling estimation of the research object is called scaling method. Scaling method is flexible and ingenious, but it depends on the ability to expand knowledge and imagination