Computing power exchange
Publish: 2021-04-14 04:31:56
1. First of all, understand and firmly grasp the basic knowledge. That is, the basic knowledge related to computing power, mainly refers to mathematical concepts, operation laws, operation properties, operation rules and calculation formulas. It is difficult for students to understand some calculation rules. In teaching, teachers should not be in a hurry for success, but should help students to master basic knowledge as a breakthrough, disperse and break through difficulties. For example, when teaching the addition and subtraction method of different denominator fractions, first of all, let students understand that the denominator is different, that is, the units of fractions are different. If the units of fractions are different, they can't add and subtract directly. When they understand this truth, they can guide students to use the knowledge of general score to change the different denominator fractions into the same denominator fractions, so the problem turns into the addition and subtraction of the same denominator fractions that they have learned
Second, strengthen the practice and basic skills training. In the calculation practice, strengthening the basic skills training is an important step to improve the calculation ability. In addition, in the calculation practice, we should help students summarize some regular things, so that they can skillfully use the basic knowledge to calculate, and constantly improve their calculation ability. In addition, the forms of calculation exercises should be diversified, and the forms should serve the content. However, we should pay attention to the quantity of exercises. We can't do the opposite as long as we don't pay attention to the quantity and quality. Some students lack the spirit of diligent learning, and the calculation itself is boring and lack of plot. When students encounter a large number of questions, they are easy to resist and unwilling to calculate, which can seriously affect students' interest in learning mathematics. In teaching, as teachers, we should simplify the topic selection, Try to find some simple calculation problems to guide students to do abstruse calculation problems
thirdly, cultivate students' good study habits. Good learning habits are the guarantee to improve the accuracy of calculation. First of all, students are required to carefully review the calculation, and do not blindly simplify the calculation without reviewing the operation order, such as 15 + 5 × 5), the students mistakenly calculated it as 20 × Secondly, the calculation process should be strictly standardized. When solving problems, students are required to have standard calculation format, neat writing, clean homework and paper surface. Even the draft should be written neatly and clearly. When students make mistakes in calculation, students should not only check the calculation process, but also find out whether there are errors in the draft. For example; The alignment of digits, whether the carry is added or not. Let the students form the habit of self checking in calculation< Fourth, strengthen the cultivation of the ability of oral calculation.
calculation is the basis of estimation and written calculation. Any four item mixed calculation problem is synthesized by the oral calculation problem of the main road. The correctness and rapidity of oral calculation directly affect the improvement of the calculation ability. When designing oral calculation exercises, we should be targeted, from easy to difficult, and graally improve them, including some simple calculation problems, It is helpful to train students' thinking flexibility to do oral arithmetic exercises frequently.
Second, strengthen the practice and basic skills training. In the calculation practice, strengthening the basic skills training is an important step to improve the calculation ability. In addition, in the calculation practice, we should help students summarize some regular things, so that they can skillfully use the basic knowledge to calculate, and constantly improve their calculation ability. In addition, the forms of calculation exercises should be diversified, and the forms should serve the content. However, we should pay attention to the quantity of exercises. We can't do the opposite as long as we don't pay attention to the quantity and quality. Some students lack the spirit of diligent learning, and the calculation itself is boring and lack of plot. When students encounter a large number of questions, they are easy to resist and unwilling to calculate, which can seriously affect students' interest in learning mathematics. In teaching, as teachers, we should simplify the topic selection, Try to find some simple calculation problems to guide students to do abstruse calculation problems
thirdly, cultivate students' good study habits. Good learning habits are the guarantee to improve the accuracy of calculation. First of all, students are required to carefully review the calculation, and do not blindly simplify the calculation without reviewing the operation order, such as 15 + 5 × 5), the students mistakenly calculated it as 20 × Secondly, the calculation process should be strictly standardized. When solving problems, students are required to have standard calculation format, neat writing, clean homework and paper surface. Even the draft should be written neatly and clearly. When students make mistakes in calculation, students should not only check the calculation process, but also find out whether there are errors in the draft. For example; The alignment of digits, whether the carry is added or not. Let the students form the habit of self checking in calculation< Fourth, strengthen the cultivation of the ability of oral calculation.
calculation is the basis of estimation and written calculation. Any four item mixed calculation problem is synthesized by the oral calculation problem of the main road. The correctness and rapidity of oral calculation directly affect the improvement of the calculation ability. When designing oral calculation exercises, we should be targeted, from easy to difficult, and graally improve them, including some simple calculation problems, It is helpful to train students' thinking flexibility to do oral arithmetic exercises frequently.
2. I hope the following answers can help you:
1. Strengthen the teaching of basic knowledge and basic skills, and improve the accuracy of calculation.
the basic knowledge in mathematics is the basis of calculation, which has guiding significance for calculation. The basic knowledge is confused, fuzzy, and the basic knowledge is not solid. In the past, it is the root cause of calculation errors, Therefore, to strengthen and implement the double base teaching is a very practical problem to improve the operation ability, which requires students to do:
(1) memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correct memory formulas and rules are the premise of accurate operation. Among the mathematical concepts, formulas, rules and properties, some are the basis of operation, explaining the reasons for "why it can be done like this", and some are the methods and steps of operation. It gives the proceres of how to do, that is, algorithms. Students learn the relevant concepts, properties and formulas, and memorize, rules and steps on the basis of understanding, Then, through a series of operation activities (i.e. practice), some kind of operation skills are graally formed
(2) correctly understand the concepts and definitions, and master the derivation of formulas. Only by understanding the derivation of some concepts and formulas, can we achieve the positive, reverse and flexible use of formulas, so as to improve the computing ability. The reason of incorrect operation in mathematics learning is often the result of fuzzy concept, formula, rule forgetting, confusion or rigid application
2. Strengthen the reasoning training of scientific system to improve the rapidity of operation
the poor operation ability is often caused by the weak thinking ability. In teaching, we should strengthen the reasoning training on the basis of students' mastering the basic knowledge. In normal practice, we should make sure that there is a basis step by step, there are sufficient reasons, and pay attention to the sequence of operation. Generally, we should pay attention to the following aspects:
1) training must be orderly. Practice must be planned and carried out step by step. In mathematics teaching, practice can be divided into three stages: first, imitation practice stage. This is an exercise carried out under the example demonstration of the teacher after learning the new knowledge. The difficulty of the selected exercises is not high and the change is not big. Students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to put forward the speed requirements; Second, the mastery stage. This is a study organized on the basis of students' preliminary mastery of knowledge and skills. The difficulty of the exercises is appropriately increased, and the forms of the exercises are changed. Students are not only required to operate correctly, but also required to summarize and summarize the process, basis and methods of operation after obtaining the correct answers, so as to promote the operation mode to the theoretical level; Third, comprehensive application stage. At this time, we can choose some difficult comprehensive questions to train students' ability to determine the direction of operation and flexibly use the rules
(2) carry out variant exercises. In order to make students skillful, we must organize variant exercises. The so-called variant practice is the change of concepts and rules under the condition that other effective learning conditions remain unchanged. For mathematical operations, it is to change the non essential characteristics of the problem and keep its structural components unchanged. The concrete ways include the change of expression of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc
(3) understand the effect of practice in time and correct the mistakes in practice in time. In ability practice, it is an effective way to let students know the effect of practice in time. Psychological research shows that if the following feedback information is provided to the students who are carrying out the ability training: ① know the score of each exercise; ② encourage and urge them continuously in the process of practice; ③ analyze the mistakes in practice, then the practice effect will be significantly improved. This is because, on the one hand, students know the problem according to the feedback information, so as to adjust the learning activities and make the practice more effective; On the other hand, it also increases learning motivation to strive for better results or avoid making similar mistakes again
3. The training of thinking flexibility in the process of operation
because mathematical operation is an intelligent operation with clear direction and in line with certain rules, after a certain amount of practice, this kind of operation experience will form a fixed reaction mode and play a tendentious role in the selection of operation direction in subsequent learning, This is the "set" phenomenon in learning. When the formed inertial thinking is consistent with the way to solve new problems, it can quickly respond and get the correct answer. The phenomenon of "shrinking" and "skipping" appears in the process of calculation. This is the positive role of the fixed trend, and also the sign of students mastering knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of using formula method and factorization method to solve quadratic equation of one variable. In the later study of quadratic function, when they encounter the operations related to quadratic equation of one variable, they will quickly make the correct response. When the conventional way of thinking is not completely consistent with or contrary to the solution of new problems, it can not be solved in a simple and flexible way, and the operation process is tedious and tedious, which leads to the wrong solution of the problem. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative effect of "stereotype" and cultivate the flexibility of students' calculation
4. Pay attention to cultivate students' ability of operation rationality
reasonable calculation is to make full use of operation law, proct invariance and quotient invariance, change the data and order of operation, and make the operation as simple, fast and correct as possible. The cultivation of students' simple operation ability is not only the improvement of operation ability, because in the process of cultivation, it must involve the cultivation of observation ability, inctive ability and other abilities, so the cultivation of simple operation ability is actually the cultivation of comprehensive ability. At the same time, it is necessary to cultivate students' overall view of mathematical operation. Before calculation, students should have an overall view of the overall situation. They should grasp the steps of operation, what should be calculated first and then, what are the characteristics of the numbers in the title, and what contains information, etc.
1. Strengthen the teaching of basic knowledge and basic skills, and improve the accuracy of calculation.
the basic knowledge in mathematics is the basis of calculation, which has guiding significance for calculation. The basic knowledge is confused, fuzzy, and the basic knowledge is not solid. In the past, it is the root cause of calculation errors, Therefore, to strengthen and implement the double base teaching is a very practical problem to improve the operation ability, which requires students to do:
(1) memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correct memory formulas and rules are the premise of accurate operation. Among the mathematical concepts, formulas, rules and properties, some are the basis of operation, explaining the reasons for "why it can be done like this", and some are the methods and steps of operation. It gives the proceres of how to do, that is, algorithms. Students learn the relevant concepts, properties and formulas, and memorize, rules and steps on the basis of understanding, Then, through a series of operation activities (i.e. practice), some kind of operation skills are graally formed
(2) correctly understand the concepts and definitions, and master the derivation of formulas. Only by understanding the derivation of some concepts and formulas, can we achieve the positive, reverse and flexible use of formulas, so as to improve the computing ability. The reason of incorrect operation in mathematics learning is often the result of fuzzy concept, formula, rule forgetting, confusion or rigid application
2. Strengthen the reasoning training of scientific system to improve the rapidity of operation
the poor operation ability is often caused by the weak thinking ability. In teaching, we should strengthen the reasoning training on the basis of students' mastering the basic knowledge. In normal practice, we should make sure that there is a basis step by step, there are sufficient reasons, and pay attention to the sequence of operation. Generally, we should pay attention to the following aspects:
1) training must be orderly. Practice must be planned and carried out step by step. In mathematics teaching, practice can be divided into three stages: first, imitation practice stage. This is an exercise carried out under the example demonstration of the teacher after learning the new knowledge. The difficulty of the selected exercises is not high and the change is not big. Students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to put forward the speed requirements; Second, the mastery stage. This is a study organized on the basis of students' preliminary mastery of knowledge and skills. The difficulty of the exercises is appropriately increased, and the forms of the exercises are changed. Students are not only required to operate correctly, but also required to summarize and summarize the process, basis and methods of operation after obtaining the correct answers, so as to promote the operation mode to the theoretical level; Third, comprehensive application stage. At this time, we can choose some difficult comprehensive questions to train students' ability to determine the direction of operation and flexibly use the rules
(2) carry out variant exercises. In order to make students skillful, we must organize variant exercises. The so-called variant practice is the change of concepts and rules under the condition that other effective learning conditions remain unchanged. For mathematical operations, it is to change the non essential characteristics of the problem and keep its structural components unchanged. The concrete ways include the change of expression of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc
(3) understand the effect of practice in time and correct the mistakes in practice in time. In ability practice, it is an effective way to let students know the effect of practice in time. Psychological research shows that if the following feedback information is provided to the students who are carrying out the ability training: ① know the score of each exercise; ② encourage and urge them continuously in the process of practice; ③ analyze the mistakes in practice, then the practice effect will be significantly improved. This is because, on the one hand, students know the problem according to the feedback information, so as to adjust the learning activities and make the practice more effective; On the other hand, it also increases learning motivation to strive for better results or avoid making similar mistakes again
3. The training of thinking flexibility in the process of operation
because mathematical operation is an intelligent operation with clear direction and in line with certain rules, after a certain amount of practice, this kind of operation experience will form a fixed reaction mode and play a tendentious role in the selection of operation direction in subsequent learning, This is the "set" phenomenon in learning. When the formed inertial thinking is consistent with the way to solve new problems, it can quickly respond and get the correct answer. The phenomenon of "shrinking" and "skipping" appears in the process of calculation. This is the positive role of the fixed trend, and also the sign of students mastering knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of using formula method and factorization method to solve quadratic equation of one variable. In the later study of quadratic function, when they encounter the operations related to quadratic equation of one variable, they will quickly make the correct response. When the conventional way of thinking is not completely consistent with or contrary to the solution of new problems, it can not be solved in a simple and flexible way, and the operation process is tedious and tedious, which leads to the wrong solution of the problem. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative effect of "stereotype" and cultivate the flexibility of students' calculation
4. Pay attention to cultivate students' ability of operation rationality
reasonable calculation is to make full use of operation law, proct invariance and quotient invariance, change the data and order of operation, and make the operation as simple, fast and correct as possible. The cultivation of students' simple operation ability is not only the improvement of operation ability, because in the process of cultivation, it must involve the cultivation of observation ability, inctive ability and other abilities, so the cultivation of simple operation ability is actually the cultivation of comprehensive ability. At the same time, it is necessary to cultivate students' overall view of mathematical operation. Before calculation, students should have an overall view of the overall situation. They should grasp the steps of operation, what should be calculated first and then, what are the characteristics of the numbers in the title, and what contains information, etc.
3. Pressure unit:
PA = 1n / M & # 178;, kPa=1000Pa，MPa=1000kPa
atmospheric pressure:
1standard atmospheric pressure = 101325 n / M & 178= 101325 Pascal (PA)
height of mercury column:
1 standard atmospheric pressure = 760 mm, height of mercury column = 101325 Pascal (PA)
PA = 1n / M & # 178;, kPa=1000Pa，MPa=1000kPa
atmospheric pressure:
1standard atmospheric pressure = 101325 n / M & 178= 101325 Pascal (PA)
height of mercury column:
1 standard atmospheric pressure = 760 mm, height of mercury column = 101325 Pascal (PA)
4. 1、 Question raised:
mathematics does not have an external reality, but a kind of relationship, a kind of knowledge of logical thinking, which shows some abstraction. Children live in the real world and have some experience of various things and phenomena in real life. On the other hand, children's thinking is still in the stage of concrete image thinking, They lack the basic concept of understanding the abstract relationship of things. Children in our class mainly rely on memory and proficiency to carry out calculation activities, which lack flexibility; In the process of observation, most of the children are not able to operate actively and are not interested in the experimental results<
2. Research objects:
48 children in class 2 of Da Da Da class
3. Experimental time:
March 2004 - July 2004
4. Experimental objectives:
1. Guide children to develop the habit of exploring surrounding things, thinking, asking questions, and actively answering questions, and be careful and attentive in the process of observation, And express their views with an objective attitude
2. In daily life or games, guide children to observe carefully and attentively, observe from different angles or continuously observe an object for a period of time, find out the reasons for the change of things, and learn simple reasoning
3. Guide children to classify and learn objects from different angles in games and daily life, and classify objects according to two dimensions at the same time. They have preliminary generalization ability< 5. Experimental steps:
(1) observation record form of children's basic situation in this class
ecational goal
reaching the standard
1. Learning ordinal number, odd and even number, adjacent number and other knowledge within 10, learning following number and inverted number<
significant: 38 people
not significant: 10 people
2. Learn the decomposition and composition of numbers within 10, experience the inclusion relationship between total number and part number, and the complementary relationship and exchange relationship between part number and part number
significant: 45 people
not significant: 3 people
3, Help children understand the meaning of addition and subtraction, master the calculation skills of addition and subtraction within 10, and experience the inverse relationship between addition and subtraction
significant: 40 people
not significant: 8 people
4. Be able to listen to the rules of some operation activities, carry out activities according to the rules, check the process and results of activities according to the rules, and tell the process and results of operation activities clearly. And can participate in more group activities
significant: 26 people
not significant: 22 people
5. With the help of teachers, they can summarize relevant mathematical experience, learn to observe and think about problems from different angles and aspects, and solve simple mathematical problems through observation, comparison, analogy and transfer<
significant: 18 people
not significant: 30 people
6. Learn to put and organize activity materials in an orderly way<
significant: 44 people
not significant: 4 people
7. They can play math games friendly with their peers and negotiate with their peers by taking turns, waiting appropriately and negotiating
significant: 10
not significant: 38
mathematics does not have an external reality, but a kind of relationship, a kind of knowledge of logical thinking, which shows some abstraction. Children live in the real world and have some experience of various things and phenomena in real life. On the other hand, children's thinking is still in the stage of concrete image thinking, They lack the basic concept of understanding the abstract relationship of things. Children in our class mainly rely on memory and proficiency to carry out calculation activities, which lack flexibility; In the process of observation, most of the children are not able to operate actively and are not interested in the experimental results<
2. Research objects:
48 children in class 2 of Da Da Da class
3. Experimental time:
March 2004 - July 2004
4. Experimental objectives:
1. Guide children to develop the habit of exploring surrounding things, thinking, asking questions, and actively answering questions, and be careful and attentive in the process of observation, And express their views with an objective attitude
2. In daily life or games, guide children to observe carefully and attentively, observe from different angles or continuously observe an object for a period of time, find out the reasons for the change of things, and learn simple reasoning
3. Guide children to classify and learn objects from different angles in games and daily life, and classify objects according to two dimensions at the same time. They have preliminary generalization ability< 5. Experimental steps:
(1) observation record form of children's basic situation in this class
ecational goal
reaching the standard
1. Learning ordinal number, odd and even number, adjacent number and other knowledge within 10, learning following number and inverted number<
significant: 38 people
not significant: 10 people
2. Learn the decomposition and composition of numbers within 10, experience the inclusion relationship between total number and part number, and the complementary relationship and exchange relationship between part number and part number
significant: 45 people
not significant: 3 people
3, Help children understand the meaning of addition and subtraction, master the calculation skills of addition and subtraction within 10, and experience the inverse relationship between addition and subtraction
significant: 40 people
not significant: 8 people
4. Be able to listen to the rules of some operation activities, carry out activities according to the rules, check the process and results of activities according to the rules, and tell the process and results of operation activities clearly. And can participate in more group activities
significant: 26 people
not significant: 22 people
5. With the help of teachers, they can summarize relevant mathematical experience, learn to observe and think about problems from different angles and aspects, and solve simple mathematical problems through observation, comparison, analogy and transfer<
significant: 18 people
not significant: 30 people
6. Learn to put and organize activity materials in an orderly way<
significant: 44 people
not significant: 4 people
7. They can play math games friendly with their peers and negotiate with their peers by taking turns, waiting appropriately and negotiating
significant: 10
not significant: 38
5. The founder of this company is tan. The company has no employees and everyone is a shareholder. This company has been running for more than 2 years and has been moving forward steadily with great development potential!
6. Calculation ability is a basic quality that everyone must have. It is an important foundation for pupils to further study mathematics and other subjects. To cultivate students' interest in learning mathematics, reasonable guidance, reasonable training, pay attention to the improvement and exercise of students' thinking. It's not a matter of one day to improve students' computing ability. It's a cumulative process. Only with the joint efforts of our teachers and students can we improve students' mathematical computing ability
key words: create situation, train reasonably, train thinking and calculate ability
mathematics cannot do without calculation. Calculation ability is a basic quality that everyone must have. It is an important foundation for pupils to further study mathematics and other subjects. Therefore, to cultivate students' correct, rapid, reasonable and flexible computing ability is one of the important tasks of primary school mathematics teaching. How to effectively improve students' computing ability? Based on my years of teaching practice, I would like to talk about some of my own experience:
first, create problem situations to improve students' interest
"interest is the best teacher." I think teachers should create a certain teaching situation, let students explore new knowledge with a strong thirst for knowledge, make the dry calculation teaching lively and interesting, establish students' self-confidence, let students be willing to learn and do, and explain typical examples of Chinese and foreign mathematicians or short stories related to classroom teaching content to stimulate students' interest. For example: in teaching "the area of a circle", I created a scene - brain swerve, the purpose is to stimulate students' interest in learning. First show the picture, the picture is a piece of green grass, there is a big tree in the middle of the grass, under the big tree, the lamb is eating grass leisurely, and then look carefully, there is a rope between the tree trunk and the lamb, excuse me: what is the range of the lamb eating grass? In this way, not only create a good learning situation for students, but also stimulate their interest in learning mathematics, so that students unconsciously have the idea that the range of sheep eating grass is a circle. Thus, students' imagination has been fully developed. And flexible use of the relevant laws, rules, find out the law of problem solving, enhance the interest in learning. At the same time, according to the characteristics of pupils' inattention, instability, easy to be affected by external and some internal factors, the time and quantity of practice should be reasonably arranged, and the method of "short time, small amount and many times" should be adopted to avoid students' fatigue and boredom, so that students' attention can be stably focused on the practice object, so as to ensure the accuracy of calculation< (1) let students fully "speak" and combine operation with language. In the past, the teaching of calculation is the method of students' calculation, so that students can fully "say" their own thinking process, and give appropriate guidance to give students a good way of thinking. At the same time, teachers and students should attach importance to the role of demonstration operation, combine operation with language, strengthen students' intuitive understanding, and effectively develop students' thinking. For example, when teaching the volume of three-dimensional graphics cylinder and cone, I encourage students to fully "speak", while "speak", think while operating, and realize that the volume of two three-dimensional graphics is equal. For example: the bottom radius of a cylindrical iron block is 10 cm and the height is 5 cm. How many cm should the height of the cone be when it is fused into a conical iron block with a bottom area of 28.26 square cm? In this problem, the volume of cylindrical iron is the volume of conical iron. Through the process of analyzing the meaning of the question, hands-on operation and thinking, the students finally realize that the volume of the two three-dimensional graphics has not changed
(2) promote estimation to make students' intuitive thinking active, so as to improve their computing ability. For example, when teaching proportional application questions, we should first understand the meaning of each sentence. For example: a house with 3 decimeters of brick floor, need 96, now use 2 decimeters of brick floor, how many brick? After observation, the students found that the side length of 3 decimeters is greater than that of 2 decimeters, which means that if the side length of 3 decimeters is large, the number of bricks will be less, and if the side length of 2 decimeters is small, the number of bricks will be more. After intuitive thinking, it is estimated that after changing the side length, the number of bricks will definitely be more than that in front
(3) reasonable training: the calculation of indivial items should be focused on according to the situation that students master, and the points that students are difficult to master should be highlighted. There are many forms of practice. Contrast exercises. In teaching, we should put the easily confused and easily wrong topics together, let the students distinguish and compare, and correct the mistakes through purposeful practice, so as to improve the students' discrimination ability. And timely evaluation of students' homework, correct mistakes< Thirdly, we should combine various ways to train students' thinking.
to improve students' computing ability, one of the important aspects is to pay attention to the improvement and exercise of students' thinking. This requires a combination of methods. On the one hand, improve students' ability of oral arithmetic, which can improve students' thinking agility. For example, the oral calculation of addition and subtraction within 20, some commonly used greatest common factor, least common multiple, commonly used conversion unit exchange, and so on. On the other hand, we should pay attention to the combination of various algorithms, so as to improve the agility of thinking, such as the application of decomposition method: 25 × 14 can be replaced by 25 × 10+25 × 4, or 10 × 25+4 × 25 This can not only exercise students' different ways of thinking, but also quickly and accurately calculate the answer. At the same time, it can also enhance students' thinking motivation and deep understanding of the algorithm. In addition, the presentation of representation can be used to guide students to carry out the process of inction, so as to improve students' ability of abstract thinking. For example, for the teaching of abdication subtraction, students can use sticks or projections to demonstrate. Through the students' intuitive observation of "abdication, one action, ten actions", the teachers' in-depth guidance will make students understand the algorithm more clearly, and exercise their abstract thinking ability at the same time. In addition, for the training and cultivation of students' intuitive thinking, it is necessary to use the estimation method in calculation. This method is appropriate to introce some mathematical problems encountered in real life into teaching examples, so as to integrate students' actual experience and mathematical knowledge more closely, and enhance their ability to use mathematical knowledge to solve practical problems, It can also raise students' awareness of using mathematical methods to solve problems< Fourth, we should re teach the process of calculation theory and rule, and improve the calculation skills.
calculation theory and rule are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, first guide the students to talk about the calculation theory and summarize the rules. For example, when talking about fraction addition with the same denominator, it can be carried out in this way: first use the graph to show it, and then ask what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). Let students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators< (1) pay attention to the training of oral arithmetic and lay a solid foundation of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation. In teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
(2) strengthen the training of simple calculation to improve the efficiency of calculation. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. And simple operation is mostly used in multiplication distribution law, so in the teaching process, we should strengthen the practice in this aspect. When calculating, let students form the habit of seeing, thinking, calculating and acting. The so-called "one look, two think, three calculate, four act" refers to: first, to see the numbers and symbols in the title; Second, think about what method to use or whether there is a simple method and what should be paid attention to when calculating, what should be calculated first and then what should be calculated; The third step is to calculate; The fourth step is to calculate, find problems and correct them in time< Good learning habits are the driving force for students' sustainable development, and an important guarantee for students to learn to learn, form learning ability, and improve their computing ability. In the calculation, we should focus on students to develop some good habits< (1) the habit of careful examination. Careful examination is the premise of correct and rapid calculation< (2) the habit of proofreading in time< (3) the habit of careful calculation. When calculating, the format should be standard, the method should be reasonable, and the calculation process should be carefully checked< (4) the habit of self-examination. In the calculation, we should develop the habit of self-conscious inspection, and correct mistakes in time when they are found
(5) the habit of standardized writing. Scribble writing, disordered format, carelessness and carelessness are the main causes of calculation errors. To ensure the correctness of the calculation, we must develop a good habit of neat writing and standard format
in a word, improving students' computing ability is not a matter overnight, it is a cumulative process, only our teachers and students work together to improve students' mathematical computing ability.
key words: create situation, train reasonably, train thinking and calculate ability
mathematics cannot do without calculation. Calculation ability is a basic quality that everyone must have. It is an important foundation for pupils to further study mathematics and other subjects. Therefore, to cultivate students' correct, rapid, reasonable and flexible computing ability is one of the important tasks of primary school mathematics teaching. How to effectively improve students' computing ability? Based on my years of teaching practice, I would like to talk about some of my own experience:
first, create problem situations to improve students' interest
"interest is the best teacher." I think teachers should create a certain teaching situation, let students explore new knowledge with a strong thirst for knowledge, make the dry calculation teaching lively and interesting, establish students' self-confidence, let students be willing to learn and do, and explain typical examples of Chinese and foreign mathematicians or short stories related to classroom teaching content to stimulate students' interest. For example: in teaching "the area of a circle", I created a scene - brain swerve, the purpose is to stimulate students' interest in learning. First show the picture, the picture is a piece of green grass, there is a big tree in the middle of the grass, under the big tree, the lamb is eating grass leisurely, and then look carefully, there is a rope between the tree trunk and the lamb, excuse me: what is the range of the lamb eating grass? In this way, not only create a good learning situation for students, but also stimulate their interest in learning mathematics, so that students unconsciously have the idea that the range of sheep eating grass is a circle. Thus, students' imagination has been fully developed. And flexible use of the relevant laws, rules, find out the law of problem solving, enhance the interest in learning. At the same time, according to the characteristics of pupils' inattention, instability, easy to be affected by external and some internal factors, the time and quantity of practice should be reasonably arranged, and the method of "short time, small amount and many times" should be adopted to avoid students' fatigue and boredom, so that students' attention can be stably focused on the practice object, so as to ensure the accuracy of calculation< (1) let students fully "speak" and combine operation with language. In the past, the teaching of calculation is the method of students' calculation, so that students can fully "say" their own thinking process, and give appropriate guidance to give students a good way of thinking. At the same time, teachers and students should attach importance to the role of demonstration operation, combine operation with language, strengthen students' intuitive understanding, and effectively develop students' thinking. For example, when teaching the volume of three-dimensional graphics cylinder and cone, I encourage students to fully "speak", while "speak", think while operating, and realize that the volume of two three-dimensional graphics is equal. For example: the bottom radius of a cylindrical iron block is 10 cm and the height is 5 cm. How many cm should the height of the cone be when it is fused into a conical iron block with a bottom area of 28.26 square cm? In this problem, the volume of cylindrical iron is the volume of conical iron. Through the process of analyzing the meaning of the question, hands-on operation and thinking, the students finally realize that the volume of the two three-dimensional graphics has not changed
(2) promote estimation to make students' intuitive thinking active, so as to improve their computing ability. For example, when teaching proportional application questions, we should first understand the meaning of each sentence. For example: a house with 3 decimeters of brick floor, need 96, now use 2 decimeters of brick floor, how many brick? After observation, the students found that the side length of 3 decimeters is greater than that of 2 decimeters, which means that if the side length of 3 decimeters is large, the number of bricks will be less, and if the side length of 2 decimeters is small, the number of bricks will be more. After intuitive thinking, it is estimated that after changing the side length, the number of bricks will definitely be more than that in front
(3) reasonable training: the calculation of indivial items should be focused on according to the situation that students master, and the points that students are difficult to master should be highlighted. There are many forms of practice. Contrast exercises. In teaching, we should put the easily confused and easily wrong topics together, let the students distinguish and compare, and correct the mistakes through purposeful practice, so as to improve the students' discrimination ability. And timely evaluation of students' homework, correct mistakes< Thirdly, we should combine various ways to train students' thinking.
to improve students' computing ability, one of the important aspects is to pay attention to the improvement and exercise of students' thinking. This requires a combination of methods. On the one hand, improve students' ability of oral arithmetic, which can improve students' thinking agility. For example, the oral calculation of addition and subtraction within 20, some commonly used greatest common factor, least common multiple, commonly used conversion unit exchange, and so on. On the other hand, we should pay attention to the combination of various algorithms, so as to improve the agility of thinking, such as the application of decomposition method: 25 × 14 can be replaced by 25 × 10+25 × 4, or 10 × 25+4 × 25 This can not only exercise students' different ways of thinking, but also quickly and accurately calculate the answer. At the same time, it can also enhance students' thinking motivation and deep understanding of the algorithm. In addition, the presentation of representation can be used to guide students to carry out the process of inction, so as to improve students' ability of abstract thinking. For example, for the teaching of abdication subtraction, students can use sticks or projections to demonstrate. Through the students' intuitive observation of "abdication, one action, ten actions", the teachers' in-depth guidance will make students understand the algorithm more clearly, and exercise their abstract thinking ability at the same time. In addition, for the training and cultivation of students' intuitive thinking, it is necessary to use the estimation method in calculation. This method is appropriate to introce some mathematical problems encountered in real life into teaching examples, so as to integrate students' actual experience and mathematical knowledge more closely, and enhance their ability to use mathematical knowledge to solve practical problems, It can also raise students' awareness of using mathematical methods to solve problems< Fourth, we should re teach the process of calculation theory and rule, and improve the calculation skills.
calculation theory and rule are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, first guide the students to talk about the calculation theory and summarize the rules. For example, when talking about fraction addition with the same denominator, it can be carried out in this way: first use the graph to show it, and then ask what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). Let students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators< (1) pay attention to the training of oral arithmetic and lay a solid foundation of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation. In teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
(2) strengthen the training of simple calculation to improve the efficiency of calculation. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. And simple operation is mostly used in multiplication distribution law, so in the teaching process, we should strengthen the practice in this aspect. When calculating, let students form the habit of seeing, thinking, calculating and acting. The so-called "one look, two think, three calculate, four act" refers to: first, to see the numbers and symbols in the title; Second, think about what method to use or whether there is a simple method and what should be paid attention to when calculating, what should be calculated first and then what should be calculated; The third step is to calculate; The fourth step is to calculate, find problems and correct them in time< Good learning habits are the driving force for students' sustainable development, and an important guarantee for students to learn to learn, form learning ability, and improve their computing ability. In the calculation, we should focus on students to develop some good habits< (1) the habit of careful examination. Careful examination is the premise of correct and rapid calculation< (2) the habit of proofreading in time< (3) the habit of careful calculation. When calculating, the format should be standard, the method should be reasonable, and the calculation process should be carefully checked< (4) the habit of self-examination. In the calculation, we should develop the habit of self-conscious inspection, and correct mistakes in time when they are found
(5) the habit of standardized writing. Scribble writing, disordered format, carelessness and carelessness are the main causes of calculation errors. To ensure the correctness of the calculation, we must develop a good habit of neat writing and standard format
in a word, improving students' computing ability is not a matter overnight, it is a cumulative process, only our teachers and students work together to improve students' mathematical computing ability.
7. The cultivation of students' operation ability should pay attention to the following aspects: 1. Strengthen the teaching of basic knowledge and basic skills, and improve the accuracy of operation. The basic knowledge in mathematics is the basis of calculation theory, which has guiding significance for operation. The confusion and fuzziness of basic knowledge and weak basic knowledge are often the root causes of operation errors, Therefore, to strengthen and implement the double base teaching is a very practical problem to improve the ability of operation, which requires students to: (1) memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correct memory formulas and rules are the premise of accurate operation. Among the mathematical concepts, formulas, rules and properties, some are the basis of operation, explaining the reasons for "why it can be done like this", and some are the methods and steps of operation. It gives the proceres of how to do, that is, algorithms. Students learn the relevant concepts, properties and formulas, and memorize, rules and steps on the basis of understanding, Then, through a series of operation activities (i.e. practice), some kind of operation skills are graally formed 2) Only by understanding the derivation of some concepts and formulas, can we achieve the positive, reverse and flexible use of formulas, so as to improve the computing ability. The reason of incorrect operation in mathematics learning is often the result of fuzzy concept, formula, rule forgetting, confusion or rigid application. 2. Strengthen the reasoning training of scientific system, improve the rapidity of operation, poor operation ability is often caused by weak thinking ability. In teaching, it is necessary to strengthen the reasoning training on the basis of students' basic knowledge. In normal practice, it is required to be step by step based, with sufficient reasons, and pay attention to the sequence of operation. In general, we should pay attention to the following aspects: (1) training must be orderly. Practice must be planned and carried out step by step. In mathematics teaching, practice can be divided into three stages: first, imitation practice stage. This is an exercise carried out under the example demonstration of the teacher after learning the new knowledge. The difficulty of the selected exercises is not high and the change is not big. Students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to put forward the speed requirements; Second, the mastery stage. This is a study organized on the basis of students' preliminary mastery of knowledge and skills. The difficulty of the exercises is appropriately increased, and the forms of the exercises are changed. Students are not only required to operate correctly, but also required to summarize and summarize the process, basis and methods of operation after obtaining the correct answers, so as to promote the operation mode to the theoretical level; Third, comprehensive application stage. At this time, we can choose some difficult comprehensive questions to train students' ability to determine the direction of operation and flexibly use the rules 2) Carry out variant exercises. In order to make students skillful, we must organize variant exercises. The so-called variant practice is the change of concepts and rules under the condition that other effective learning conditions remain unchanged. For mathematical operations, it is to change the non essential characteristics of the problem and keep its structural components unchanged. The concrete ways include the change of expression of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc 3) Understand the practice effect in time and correct the contact errors in time. In ability practice, it is an effective way to let students know the effect of practice in time. Psychological research shows that if the following feedback information is provided to the students who are carrying out the ability training: ① know the score of each exercise; ② encourage and urge them continuously in the process of practice; ③ analyze the mistakes in practice, then the practice effect will be significantly improved. This is because, on the one hand, students learn the problems according to the feedback information, so as to adjust their learning activities, which is more effective; On the other hand, it also increases learning motivation to strive for better grades or avoid making mistakes again. 3. In the training of thinking flexibility in the process of operation, mathematical operation is an intelligent operation with clear direction and in line with certain rules. Therefore, after a certain amount of practice, this kind of operation experience will form a fixed reaction mode and play a tendentious role in the selection of operation direction in subsequent learning. This is the "set trend" phenomenon in learning. When the formed inertial thinking is consistent with the way to solve new problems, it can quickly respond and get the correct answer. The phenomenon of "shrinking" and "skipping" appears in the process of operation. At this time, the positive role of stereotype is also a sign of students' mastery of knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of using formula method and factorization method to solve quadratic equation of one variable. In the later study of quadratic function, when they encounter the operations related to quadratic equation of one variable, they will quickly make the correct response. When the conventional way of thinking is not completely consistent with or contrary to the solution of new problems, it can not be solved in a simple and flexible way, and the operation process is tedious and tedious, which leads to the wrong solution of the problem. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative effect of "stereotype" and cultivate the flexibility of students' calculation. 4. Pay attention to cultivate students' ability of operation rationality, reasonable calculation is to make full use of operation law, proct invariance and quotient invariance, change the data and operation order of operation, and make the operation as simple, fast and correct as possible. The cultivation of students' simple operation ability is not only the improvement of operation ability, because in the process of cultivation, it must involve the cultivation of observation ability, inctive ability and other abilities, so the cultivation of simple operation ability is actually the cultivation of comprehensive ability. At the same time, it is necessary to cultivate students' overall view of mathematical operation. Before calculation, students should have an overall view of the overall situation. They should grasp the steps of operation, what should be calculated first and then, what are the characteristics of the numbers in the title, what information is contained, and so on. 5. Teaching classroom is an important place to cultivate students' computing ability, and computing problem has always been the bottleneck to improve mathematics performance. In recent years, it has become outstanding after the use of new textbooks! In my opinion, the exemplary role of teachers can not be ignored. When writing on the blackboard, teachers should guide students how to calculate, teach them methods, and give them some exercises to train their calculation ability. They are required to do less mental calculation and more written calculation, and even the draft should be neat. To cultivate students' computing ability, we should pay special attention to classroom training. Secondly, changing teaching methods is also one of the main means to improve students' computing ability. In view of the existing problems of students, I have tried in these aspects: (1) intuitive teaching, deepen understanding. Through teaching aids and modern teaching means, the internal connection can be demonstrated intuitively, so that the abstract can be changed into the image, and the "nothingness" can be changed into the concrete, so as to deepen students' understanding of knowledge and find the method of solving problems. (2) the combination of number and shape makes it easy. If we use pure algebra or pure geometry method to solve mathematical problems, sometimes the process will be complicated, and it is easier for students with poor operation ability to make mistakes. If we integrate some other knowledge and implement the combination of number and shape, we can simplify the complex and turn the difficult into the easy. (3) learn to think and enhance memory. Only by guiding students to be good at thinking, finding characteristics, essence and connection can they enhance their memory. (4) cultivate students to develop the habit of checking calculation, master the checking method, and check the process and result of calculation in the process or at the end of solving the problem, so as to correct the errors in the process or result of calculation in time. In a word, it is necessary to strengthen the operation practice to cultivate the operation ability of middle school students. In order to effectively improve students' computing ability, we must strengthen the practice, especially the practice should be purposeful, systematic and typical. Through changing, changing, solving and using one question, we can cultivate the proficiency, accuracy, rapidity, flexibility and rationality of calculation. Teachers should also grasp the positive role of mathematics classroom in the cultivation of students' operation ability, train students' thinking profundity in the process of operation in the form of question group training after class, and pay attention to the reasonable arrangement of the difficulty coefficient of questions, so that students can not lose interest in learning mathematics while improving their operation ability.
8. Qube exchange answers for you:
the problem of legal currency is that when the financial crisis occurs, the legal currency depreciates and the social wealth shrinks. When the old legal currency collapses, people will rush to bitcoin and take bitcoin as a new haven for assets - "the 21st century version of gold", so Nakamoto and these people realize this through technical means
first, to be a digital currency, we must have a digital account book. But if the database is in the hands of Zhongben Cong, it is easy to be tampered with. He thinks that everyone can participate in bookkeeping and obtain the account book. This is a very important distributed account book in the blockchain, and anyone can download this account book. In this way, the account book is not in one person's hands, ensuring its security and feasibility.
Second, even if the account book is not in the same person's hands, "it's very easy to modify it". Why can bitcoin be permanent, irreversible, open and transparent? It's reasonable that all blockchain based applications can do this, but at present only bitcoin can. There are four reasons:
1
because bitcoin is a record based on time stream, time can not be reversed, so bitcoin transaction record is irreversible. At the same time, bitcoin is a double entry ledger, and the hash value of the last ten minutes' transaction record is recorded in the next ten minutes' block. Therefore, the modification of any previous transaction record will lead to the change of all subsequent transaction records, so as to ensure its traceability. Secondly, every transaction is made public on the whole network. Everyone can see "a 100 bitcoin transaction from address a to address B" and verify that there is no repeated payment for this transaction. Only legitimate transactions can be included in the block, and then all people can view it again. Therefore, the whole network is open and transparent
2. Computing power is decentralized and huge
in the first place, Nakamoto g his own mine for one year. In the next seven years, tens of millions of miners all over the world participated in the process of mining. Therefore, if you want to modify the transaction records, only 51% of the computing power of the whole network can be achieved, which is almost impossible
3. Transaction record storage is decentralized
a block is generated every ten minutes, and the bookkeeping right may be snatched by people anywhere in the world. Bitcoin calculates a value through the algorithm, which is the number of hash collisions. If the "value" is calculated, it will be given the bookkeeping right to obtain bitcoin. There is a consensus that whoever calculates the value first will be charged, Avoiding the right to keep accounts is always in the hands of one person. This is called mining, so transaction records may be stored around the world, rather than a central organization, such as Alipay.
4. Decentralization of rule making
anyone can propose the modification or change of bitcoin protocol and write the corresponding code, but whether it is adopted or not depends on whether it can have more than 51% of the computing power of the whole network
the above four points ensure that bitcoin is permanent, irreversible and transparent to the whole network.
the problem of legal currency is that when the financial crisis occurs, the legal currency depreciates and the social wealth shrinks. When the old legal currency collapses, people will rush to bitcoin and take bitcoin as a new haven for assets - "the 21st century version of gold", so Nakamoto and these people realize this through technical means
first, to be a digital currency, we must have a digital account book. But if the database is in the hands of Zhongben Cong, it is easy to be tampered with. He thinks that everyone can participate in bookkeeping and obtain the account book. This is a very important distributed account book in the blockchain, and anyone can download this account book. In this way, the account book is not in one person's hands, ensuring its security and feasibility.
Second, even if the account book is not in the same person's hands, "it's very easy to modify it". Why can bitcoin be permanent, irreversible, open and transparent? It's reasonable that all blockchain based applications can do this, but at present only bitcoin can. There are four reasons:
1
because bitcoin is a record based on time stream, time can not be reversed, so bitcoin transaction record is irreversible. At the same time, bitcoin is a double entry ledger, and the hash value of the last ten minutes' transaction record is recorded in the next ten minutes' block. Therefore, the modification of any previous transaction record will lead to the change of all subsequent transaction records, so as to ensure its traceability. Secondly, every transaction is made public on the whole network. Everyone can see "a 100 bitcoin transaction from address a to address B" and verify that there is no repeated payment for this transaction. Only legitimate transactions can be included in the block, and then all people can view it again. Therefore, the whole network is open and transparent
2. Computing power is decentralized and huge
in the first place, Nakamoto g his own mine for one year. In the next seven years, tens of millions of miners all over the world participated in the process of mining. Therefore, if you want to modify the transaction records, only 51% of the computing power of the whole network can be achieved, which is almost impossible
3. Transaction record storage is decentralized
a block is generated every ten minutes, and the bookkeeping right may be snatched by people anywhere in the world. Bitcoin calculates a value through the algorithm, which is the number of hash collisions. If the "value" is calculated, it will be given the bookkeeping right to obtain bitcoin. There is a consensus that whoever calculates the value first will be charged, Avoiding the right to keep accounts is always in the hands of one person. This is called mining, so transaction records may be stored around the world, rather than a central organization, such as Alipay.
4. Decentralization of rule making
anyone can propose the modification or change of bitcoin protocol and write the corresponding code, but whether it is adopted or not depends on whether it can have more than 51% of the computing power of the whole network
the above four points ensure that bitcoin is permanent, irreversible and transparent to the whole network.
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