Computing power depends on
Publish: 2021-03-24 18:05:51
1. A good habit of calculation is a catalyst for success, which benefits people for life. The advantages and disadvantages of students' computing habits directly affect the formation and improvement of their computing ability. Therefore, in order to improve students' computing ability, we should first cultivate students' good habit of examining questions, writing and checking
the habit of examining questions. A good habit of examining questions is the key factor to improve the calculation ability, and the accuracy of calculation largely depends on the correctness of examining questions. Examination is the key first step in the process of calculation. Examination can overcome the influence of thinking set and eliminate the interference of thinking caused by strong information concentration. For example, when calculating 18-7 + 3, many students calculate 18-7 + 3 = 18 e to the strong information of "rounding". As soon as the students see the topic, they do it. They don't examine the topic carefully, and they don't think about what counts first and then what counts. As a result, such a simple calculation problem is wrong. Therefore, it is urgent to strengthen the cultivation of good examination habits
writing habits. Good writing habits can help students rece unnecessary mistakes. Nonstandard writing is also a common reason for calculation errors. When students are calculating, they sometimes look at it by mistake because of the illegible handwriting, such as 6 and 0, 3 and 8; Some write, write, erase, and blur; Some vertical writing is not standard, the number is not aligned and so on, may cause the calculation error. Therefore, in teaching, it is necessary to require students to write neat, standard format, to urge students to write numbers correctly and clearly
the habit of checking calculation. Checking and checking calculation is not only an effective measure to ensure correct calculation, but also a means to promote students' understanding of calculation process and calculation skills. Students can further understand the inverse operation relationship between addition and subtraction through checking calculation. But because of their weak willpower, primary school students are often unable to consciously check and calculate. Therefore, in the teaching of calculation, we should pay attention to teach students the methods of checking calculation, such as: requiring students to do "four checks": one check whether the number is copied correctly; Second, check whether the symbols are accurate; Third, check whether the operation sequence is correct; 4. Check whether the results are correct and write them down. The cultivation of students' good habits is not a day's work, it needs us to persevere in our efforts. This is a good thing beneficial to students all their lives, and we must do a good job.
the habit of examining questions. A good habit of examining questions is the key factor to improve the calculation ability, and the accuracy of calculation largely depends on the correctness of examining questions. Examination is the key first step in the process of calculation. Examination can overcome the influence of thinking set and eliminate the interference of thinking caused by strong information concentration. For example, when calculating 18-7 + 3, many students calculate 18-7 + 3 = 18 e to the strong information of "rounding". As soon as the students see the topic, they do it. They don't examine the topic carefully, and they don't think about what counts first and then what counts. As a result, such a simple calculation problem is wrong. Therefore, it is urgent to strengthen the cultivation of good examination habits
writing habits. Good writing habits can help students rece unnecessary mistakes. Nonstandard writing is also a common reason for calculation errors. When students are calculating, they sometimes look at it by mistake because of the illegible handwriting, such as 6 and 0, 3 and 8; Some write, write, erase, and blur; Some vertical writing is not standard, the number is not aligned and so on, may cause the calculation error. Therefore, in teaching, it is necessary to require students to write neat, standard format, to urge students to write numbers correctly and clearly
the habit of checking calculation. Checking and checking calculation is not only an effective measure to ensure correct calculation, but also a means to promote students' understanding of calculation process and calculation skills. Students can further understand the inverse operation relationship between addition and subtraction through checking calculation. But because of their weak willpower, primary school students are often unable to consciously check and calculate. Therefore, in the teaching of calculation, we should pay attention to teach students the methods of checking calculation, such as: requiring students to do "four checks": one check whether the number is copied correctly; Second, check whether the symbols are accurate; Third, check whether the operation sequence is correct; 4. Check whether the results are correct and write them down. The cultivation of students' good habits is not a day's work, it needs us to persevere in our efforts. This is a good thing beneficial to students all their lives, and we must do a good job.
2. In terms of personal PC, the price of procts with different configurations will also vary, which mainly depends on the differences of CPU, graphics card and memory carried by procts with different configurations. High configuration PC has higher computing power, can play games with higher configuration requirements, and can run 3D and audio-visual software that eat more memory. Low configuration PC computing power is not enough, it can only play ordinary games, run ordinary office software
also playing online games, mobile phones with higher computing power are more fluent, and those with less computing power will get stuck
if you want a mobile phone to have higher computing power and play games without jamming, you need not only more core and higher frequency CPU, but also more memory and more stable and fast network
therefore, network, storage and computing power are the three main factors that determine the computing power of mobile phones. You can go to the tenth power computing platform to learn more about computing power and get free computing power.
also playing online games, mobile phones with higher computing power are more fluent, and those with less computing power will get stuck
if you want a mobile phone to have higher computing power and play games without jamming, you need not only more core and higher frequency CPU, but also more memory and more stable and fast network
therefore, network, storage and computing power are the three main factors that determine the computing power of mobile phones. You can go to the tenth power computing platform to learn more about computing power and get free computing power.
3. 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.
4. [how to improve pupils' computational ability]
students' computational ability is an important task of primary school mathematics teaching and an important foundation for students to learn mathematics in the future. So, as a junior mathematics teacher, how to cultivate pupils' computing ability? I start from the following aspects:
first, stimulate the interest in learning computing“ Interest is the best teacher. Interesting computing ability is a basic ability that everyone must have. Cultivating drama and vivid stories will make the relatively simple and boring learning of computing lively and interesting. It will make students interested in learning and get twice the result with half the effort
the game is exciting. For example: the division and combination of teaching numbers can adopt the mathematical game of "clapping hands" and take the division and combination of 10 as an example. The teacher patted his hand and asked: Liao Xiaohe, I ask you, what's my 4 beats? This game can be adjusted according to the change of learning content at any time. According to the students' proficiency, the rhythm can be adjusted at any time; It can change the form at any time, such as collective answer, group answer, indivial student answer, teacher ask student answer, student ask student answer and so on
the story is exciting. To stimulate interest with typical examples of Chinese and foreign mathematicians or short stories related to the classroom content. In teaching, we should timely list the typical examples of Chinese and foreign mathematicians. For example, Chen Jingrun, a famous mathematician in our country, constantly calculates in order to conquer "Goldbach conjecture", and the draft paper calculates in several sacks. Through such vivid and typical examples, we can stimulate students' will and arouse their interest in calculation; Or use the stories that students like to hear and see to activate the classroom atmosphere and attract students' attention. For example, in the two digit plus one digit carry addition, there are some mistakes that often appear when "little careless" is doing the problem. Let the students point out the mistakes first, and then look at the mistakes they have made. It not only arouses students' attention, but also stimulates students' interest in mathematics learning, so that students can concentrate on calculation and improve the learning effect in class
Second, cultivate good computing habits
a good habit of computing is a catalyst for success, which benefits people for life. The advantages and disadvantages of students' computing habits directly affect the formation and improvement of their computing ability. Therefore, in order to improve students' computing ability, we should first cultivate students' good habit of examining questions, writing and checking
the habit of examining questions. A good habit of examining questions is the key factor to improve the calculation ability, and the accuracy of calculation largely depends on the correctness of examining questions. Examination is the key first step in the process of calculation. Examination can overcome the influence of thinking set and eliminate the interference of thinking caused by strong information concentration. For example, when calculating 18-7 + 3, many students calculate 18-7 + 3 = 18 e to the strong information of "rounding". As soon as the students see the topic, they do it. They don't examine the topic carefully, and they don't think about what counts first and then what counts. As a result, such a simple calculation problem is wrong. Therefore, it is urgent to strengthen the cultivation of good examination habits
writing habits. Good writing habits can help students rece unnecessary mistakes. Nonstandard writing is also a common reason for calculation errors. When students are calculating, they sometimes look at it by mistake because of the illegible handwriting, such as 6 and 0, 3 and 8; Some write, write, erase, and blur; Some vertical writing is not standard, the number is not aligned and so on, may cause the calculation error. Therefore, in teaching, it is necessary to require students to write neat, standard format, to urge students to write numbers correctly and clearly
the habit of checking calculation. Checking and checking calculation is not only an effective measure to ensure correct calculation, but also a means to promote students' understanding of calculation process and calculation skills. Students can further understand the inverse operation relationship between addition and subtraction through checking calculation. But because of their weak willpower, primary school students are often unable to consciously check and calculate. Therefore, in the teaching of calculation, we should pay attention to teach students the methods of checking calculation, such as: requiring students to do "four checks": one check whether the number is copied correctly; Second, check whether the symbols are accurate; Third, check whether the operation sequence is correct; 4. Check whether the results are correct and write them down. The cultivation of students' good habits is not a day's work, it needs us to persevere in our efforts. This is a good thing beneficial to students all their lives, and we must do a good job
Third, understand the calculation principle and optimize the algorithm in hands-on operation
calculation is the premise and basis of correct operation. In the students' mind, the examples are clear, and the calculation is orderly. It is a difficult point to explore the arithmetic of carry addition within 20. When learning carry addition within 20, students can put it into practice, experience the process of "making up ten", and understand the method of "making up ten". For example:. At the beginning of class, students list the corresponding formula: 8 + 5 through situations and questions. Some students immediately reported the answer: teacher, 8 + 5 = 13. I said: you are so smart! How many children know the result? If you know, try to verify whether your results are correct; Children who don't know can use learning aids to help us calculate. Under my guidance, students use learning aids to represent 8 and 5 respectively, and operate according to their own different ideas. In the process of operation, students can understand the arithmetic of addition and carry. In the report, I try my best to let the students narrate, supplement, collect all kinds of information, and show a variety of algorithms. On this basis, I guide the students to find that these algorithms are interlinked. They all achieve the purpose of oral calculation by rounding up 10, so that the students can understand this kind of problem. Through the method of "looking at the large number, dividing the decimal, first rounding up 10, then adding a few", they can "optimize" the "diversification" in time, Seek a simple and fast method, so as to improve students' computing ability< Fourth, pay attention to the training of oral arithmetic in the teaching of calculation
in order to make the students have higher computing ability in primary school, we must pay attention to oral arithmetic and strengthen the training of oral arithmetic. Because oral arithmetic is an important part of calculation ability, and it is also the basis of written arithmetic, abacus and estimation. It is widely used in daily life and study. Therefore, in mathematics teaching, I attach great importance to strengthening students' oral arithmetic training. Before each mathematics class, I will use 3 to 5 minutes to carry out various forms of oral arithmetic training for students. For example: (1) oral arithmetic competition, let students write the number directly after the oral arithmetic exercises in the book, and organize proofreading and evaluation after the competition. And let the students who can calculate quickly and correctly talk about their own tricks 2) Read the cards and write the numbers directly. You can write the numbers on the cards. Students can write the numbers one by one. At last, students can show the numbers to organize proofreading and evaluation 3) Look at the problem and answer it by mouth. Let the students do it by themselves and then answer it by name 4) Listen and count, the teacher read the problem, let the students write the problem directly, show the problem after listening and count, organize the students to proofread and evaluate the result 5) Find a friend: let the students take the mental arithmetic card to find the number, etc. This tense and orderly training form can not only pay attention to every student, but also arouse students' great interest, and greatly improve the quality of group students' oral arithmetic practice< 5. Carefully design the calculation exercises
practice is an important way for students to consolidate knowledge and form skills. When designing exercises, we should pay attention to the following points: 1. We can design some exercises that can reflect the basis of calculation theory and the formation of algorithm for students to practice, such as the calculation process of 9 + 5 =. In this way, students not only understand the calculation theory, but also master the calculation method, playing a multiplier effect with half the effort. 2. Practice with easy to confuse contrast. In order to improve the students' identification ability and accuracy of calculation, we put the confusing questions together and let them distinguish and compare. 3. Often make mistakes and practice over and over again. The students use the new algorithm to calculate some of the typical errors on the blackboard, let the students find out the mistakes, correct them, can clear the obstacles for the students algorithm. 4. The practice should be taught according to the person, and the practice goal should be put forward in different levels. For the students with strong computing ability, the requirements can be improved; For students with slow thinking, the requirements are lower; For poor students, let them do the most basic exercises, give help and encouragement in practice, let them overcome inferiority, build up confidence, and really mobilize their learning enthusiasm< Sixth, strengthen the collation and analysis of wrong questions
we should pay attention to the collection and collation of students' mistakes, and analyze the ideological roots of their mistakes. In my usual homework, I prepare a notebook to classify and record the errors in students' calculation, find out the common errors and find out the typical errors, so as to "suit the remedy to the case" in teaching, especially find out the typical errors with unclear calculation and wrong methods, organize students to analyze the root causes, find out the "cause", and then design a certain number of targeted exercises, Purposeful "living therapy". At the same time, each student is required to prepare a wrong problem book, and the students are required to "sort out the wrong problems", record the mistakes in their homework book, exercise book and test paper in the wrong problem book in time, find out the reasons for the mistakes, and correct and classify them in time
it's a long and hard process to cultivate students' computing ability. Let's all math teachers join hands and make unremitting efforts to improve students' computing ability
students' computational ability is an important task of primary school mathematics teaching and an important foundation for students to learn mathematics in the future. So, as a junior mathematics teacher, how to cultivate pupils' computing ability? I start from the following aspects:
first, stimulate the interest in learning computing“ Interest is the best teacher. Interesting computing ability is a basic ability that everyone must have. Cultivating drama and vivid stories will make the relatively simple and boring learning of computing lively and interesting. It will make students interested in learning and get twice the result with half the effort
the game is exciting. For example: the division and combination of teaching numbers can adopt the mathematical game of "clapping hands" and take the division and combination of 10 as an example. The teacher patted his hand and asked: Liao Xiaohe, I ask you, what's my 4 beats? This game can be adjusted according to the change of learning content at any time. According to the students' proficiency, the rhythm can be adjusted at any time; It can change the form at any time, such as collective answer, group answer, indivial student answer, teacher ask student answer, student ask student answer and so on
the story is exciting. To stimulate interest with typical examples of Chinese and foreign mathematicians or short stories related to the classroom content. In teaching, we should timely list the typical examples of Chinese and foreign mathematicians. For example, Chen Jingrun, a famous mathematician in our country, constantly calculates in order to conquer "Goldbach conjecture", and the draft paper calculates in several sacks. Through such vivid and typical examples, we can stimulate students' will and arouse their interest in calculation; Or use the stories that students like to hear and see to activate the classroom atmosphere and attract students' attention. For example, in the two digit plus one digit carry addition, there are some mistakes that often appear when "little careless" is doing the problem. Let the students point out the mistakes first, and then look at the mistakes they have made. It not only arouses students' attention, but also stimulates students' interest in mathematics learning, so that students can concentrate on calculation and improve the learning effect in class
Second, cultivate good computing habits
a good habit of computing is a catalyst for success, which benefits people for life. The advantages and disadvantages of students' computing habits directly affect the formation and improvement of their computing ability. Therefore, in order to improve students' computing ability, we should first cultivate students' good habit of examining questions, writing and checking
the habit of examining questions. A good habit of examining questions is the key factor to improve the calculation ability, and the accuracy of calculation largely depends on the correctness of examining questions. Examination is the key first step in the process of calculation. Examination can overcome the influence of thinking set and eliminate the interference of thinking caused by strong information concentration. For example, when calculating 18-7 + 3, many students calculate 18-7 + 3 = 18 e to the strong information of "rounding". As soon as the students see the topic, they do it. They don't examine the topic carefully, and they don't think about what counts first and then what counts. As a result, such a simple calculation problem is wrong. Therefore, it is urgent to strengthen the cultivation of good examination habits
writing habits. Good writing habits can help students rece unnecessary mistakes. Nonstandard writing is also a common reason for calculation errors. When students are calculating, they sometimes look at it by mistake because of the illegible handwriting, such as 6 and 0, 3 and 8; Some write, write, erase, and blur; Some vertical writing is not standard, the number is not aligned and so on, may cause the calculation error. Therefore, in teaching, it is necessary to require students to write neat, standard format, to urge students to write numbers correctly and clearly
the habit of checking calculation. Checking and checking calculation is not only an effective measure to ensure correct calculation, but also a means to promote students' understanding of calculation process and calculation skills. Students can further understand the inverse operation relationship between addition and subtraction through checking calculation. But because of their weak willpower, primary school students are often unable to consciously check and calculate. Therefore, in the teaching of calculation, we should pay attention to teach students the methods of checking calculation, such as: requiring students to do "four checks": one check whether the number is copied correctly; Second, check whether the symbols are accurate; Third, check whether the operation sequence is correct; 4. Check whether the results are correct and write them down. The cultivation of students' good habits is not a day's work, it needs us to persevere in our efforts. This is a good thing beneficial to students all their lives, and we must do a good job
Third, understand the calculation principle and optimize the algorithm in hands-on operation
calculation is the premise and basis of correct operation. In the students' mind, the examples are clear, and the calculation is orderly. It is a difficult point to explore the arithmetic of carry addition within 20. When learning carry addition within 20, students can put it into practice, experience the process of "making up ten", and understand the method of "making up ten". For example:. At the beginning of class, students list the corresponding formula: 8 + 5 through situations and questions. Some students immediately reported the answer: teacher, 8 + 5 = 13. I said: you are so smart! How many children know the result? If you know, try to verify whether your results are correct; Children who don't know can use learning aids to help us calculate. Under my guidance, students use learning aids to represent 8 and 5 respectively, and operate according to their own different ideas. In the process of operation, students can understand the arithmetic of addition and carry. In the report, I try my best to let the students narrate, supplement, collect all kinds of information, and show a variety of algorithms. On this basis, I guide the students to find that these algorithms are interlinked. They all achieve the purpose of oral calculation by rounding up 10, so that the students can understand this kind of problem. Through the method of "looking at the large number, dividing the decimal, first rounding up 10, then adding a few", they can "optimize" the "diversification" in time, Seek a simple and fast method, so as to improve students' computing ability< Fourth, pay attention to the training of oral arithmetic in the teaching of calculation
in order to make the students have higher computing ability in primary school, we must pay attention to oral arithmetic and strengthen the training of oral arithmetic. Because oral arithmetic is an important part of calculation ability, and it is also the basis of written arithmetic, abacus and estimation. It is widely used in daily life and study. Therefore, in mathematics teaching, I attach great importance to strengthening students' oral arithmetic training. Before each mathematics class, I will use 3 to 5 minutes to carry out various forms of oral arithmetic training for students. For example: (1) oral arithmetic competition, let students write the number directly after the oral arithmetic exercises in the book, and organize proofreading and evaluation after the competition. And let the students who can calculate quickly and correctly talk about their own tricks 2) Read the cards and write the numbers directly. You can write the numbers on the cards. Students can write the numbers one by one. At last, students can show the numbers to organize proofreading and evaluation 3) Look at the problem and answer it by mouth. Let the students do it by themselves and then answer it by name 4) Listen and count, the teacher read the problem, let the students write the problem directly, show the problem after listening and count, organize the students to proofread and evaluate the result 5) Find a friend: let the students take the mental arithmetic card to find the number, etc. This tense and orderly training form can not only pay attention to every student, but also arouse students' great interest, and greatly improve the quality of group students' oral arithmetic practice< 5. Carefully design the calculation exercises
practice is an important way for students to consolidate knowledge and form skills. When designing exercises, we should pay attention to the following points: 1. We can design some exercises that can reflect the basis of calculation theory and the formation of algorithm for students to practice, such as the calculation process of 9 + 5 =. In this way, students not only understand the calculation theory, but also master the calculation method, playing a multiplier effect with half the effort. 2. Practice with easy to confuse contrast. In order to improve the students' identification ability and accuracy of calculation, we put the confusing questions together and let them distinguish and compare. 3. Often make mistakes and practice over and over again. The students use the new algorithm to calculate some of the typical errors on the blackboard, let the students find out the mistakes, correct them, can clear the obstacles for the students algorithm. 4. The practice should be taught according to the person, and the practice goal should be put forward in different levels. For the students with strong computing ability, the requirements can be improved; For students with slow thinking, the requirements are lower; For poor students, let them do the most basic exercises, give help and encouragement in practice, let them overcome inferiority, build up confidence, and really mobilize their learning enthusiasm< Sixth, strengthen the collation and analysis of wrong questions
we should pay attention to the collection and collation of students' mistakes, and analyze the ideological roots of their mistakes. In my usual homework, I prepare a notebook to classify and record the errors in students' calculation, find out the common errors and find out the typical errors, so as to "suit the remedy to the case" in teaching, especially find out the typical errors with unclear calculation and wrong methods, organize students to analyze the root causes, find out the "cause", and then design a certain number of targeted exercises, Purposeful "living therapy". At the same time, each student is required to prepare a wrong problem book, and the students are required to "sort out the wrong problems", record the mistakes in their homework book, exercise book and test paper in the wrong problem book in time, find out the reasons for the mistakes, and correct and classify them in time
it's a long and hard process to cultivate students' computing ability. Let's all math teachers join hands and make unremitting efforts to improve students' computing ability
5. Players only need to participate in the game and get computing power through different behaviors. Computing power will proce PXB as a reward; The greater the contribution of the game, the more rewards you get
6. The history of computer
the birth and development of modern computer before the advent of modern computer, the development of computer has gone through three stages: mechanical computer, electromechanical computer and electronic computer
as early as the 17th century, a group of European mathematicians began to design and manufacture digital computers that perform basic operations in digital form. In 1642, Pascal, a French mathematician, made the earliest decimal adder by using a gear transmission similar to clocks and watches. In 1678, Leibniz, a German mathematician, developed a computer to further solve the multiplication and division of decimal numbers
British mathematician Babbage put forward an idea when he made the model of difference machine in 1822. One arithmetic operation at a time will develop into a certain complete operation process automatically. In 1884, Babbage designed a program-controlled universal analyzer. Although this analyzer has described the rudiment of the program control computer, it can not be realized e to the technical conditions at that time< During the more than 100 years since Babbage's idea was put forward, great progress has been made in electromagnetics, electrotechnics and electronics, and vacuum diodes and vacuum triodes have been successively invented in components and devices; In terms of system technology, wireless telegraph, television and radar were invented one after another. All these achievements have prepared technical and material conditions for the development of modern computer< At the same time, mathematics and physics are developing rapidly. In the 1930s, all fields of physics experienced the stage of quantification. The mathematical equations describing various physical processes, some of which were difficult to solve by classical analysis methods. As a result, numerical analysis has been paid attention to, and various numerical integration, numerical differentiation, and numerical solutions of differential equations have been developed. The calculation process has been reced to a huge amount of basic operations, thus laying the foundation of modern computer numerical algorithm
the urgent need for advanced computing tools in society is the fundamental driving force for the birth of modern computers. Since the 20th century, there have been a lot of computational difficulties in various fields of science and technology, which has hindered the further development of the discipline. Especially before and after the outbreak of the Second World War, the need for high-speed computing tools in military science and technology is particularly urgent. During this period, Germany, the United States and the United Kingdom started the research of electromechanical computer and electronic computer almost at the same time<
Giuseppe in Germany was the first to use electrical components to make computers. The fully automatic relay computer Z-3, which he made in 1941, has the characteristics of modern computer, such as floating-point counting, binary operation, instruction form of digital storage address and so on. In the United States, the relay computers mark-1, mark-2, model-1, model-5 and so on were made successively from 1940 to 1947. However, the switching speed of the relay is about one hundredth of a second, which greatly limits the computing speed of the computer
the development process of electronic computer has experienced the evolution from making components to whole machine, from special machine to general machine, from "external program" to "stored program". In 1938, the Bulgarian American scholar atanasov first made the computing unit of the electronic computer. In 1943, the communications office of the British Foreign Office made the "giant" computer. This is a special cryptanalysis machine, which was used in the Second World War< In February 1946, ENIAC, a large-scale electronic digital integrator computer, was developed by Moore College of the University of Pennsylvania in the United States. At first, ENIAC was also specially used for artillery trajectory calculation. Later, it was improved many times and became a general-purpose computer capable of various scientific calculations. This computer, which uses electronic circuit to perform arithmetic operation, logic operation and information storage, is 1000 times faster than relay computer. This is the first electronic computer in the world. However, the program of this kind of computer is still external, the storage capacity is too small, and it has not fully possessed the main characteristics of modern computer
the new breakthrough was completed by a design team led by mathematician von Neumann. In March 1945, they published a new general electronic computer scheme of stored program - electronic discrete variable automatic computer (EDVAC). Then in June 1946, von Neumann and others put forward a more perfect design report "preliminary study on the logical structure of electronic computer devices". From July to August of the same year, they taught a special course "theory and technology of electronic computer design" for experts from more than 20 institutions in the United States and Britain at Moore college, which promoted the design and manufacture of stored program computers< In 1949, the Mathematics Laboratory of Cambridge University in England took the lead in making EDSAC; The United States made the eastern standard automatic computer (SFAC) in 1950. At this point, the embryonic period of the development of electronic computer came to an end, and the development period of modern computer began
at the same time of creating digital computer, we also developed another kind of important computing tool analog computer. When physicists summarize the laws of nature, they often use mathematical equations to describe a process; On the contrary, the process of solving mathematical equations may also adopt the physical process simulation method. After the invention of logarithm, the slide rule made in 1620 has changed multiplication and division into addition and subtraction for calculation. Maxwell skillfully transformed the calculation of integral (area) into the measurement of length, and made the integrator in 1855< Fourier analysis, another great achievement of mathematical physics in the 19th century, played a direct role in promoting the development of simulators. In the late 19th century and the early 20th century, a variety of analytical machines for calculating Fourier coefficients and differential equations were developed. However, when trying to popularize the differential analysis machine to solve partial differential equations and use the simulator to solve general scientific calculation problems, people graally realize the limitations of the simulator in the aspects of universality and accuracy, and turn their main energy to the digital computer
after the advent of electronic digital computer, analog computer still continues to develop, and hybrid computer is proced by combining with digital computer. Simulators and mixers have become special varieties of modern computers, that is, efficient information processing tools or simulation tools used in specific fields
since the middle of the 20th century, the computer has been in a period of high-speed development. The computer has developed from a hardware only system to a computer system which includes three subsystems: hardware, software and firmware. The performance price ratio of computer system is increased by two orders of magnitude every 10 years. The types of computers have been divided into microcomputers, minicomputers, general-purpose computers (including giant, large and medium-sized computers), and various special computers (such as various control computers and analog-to-digital hybrid computers)
computer devices, from electron tubes to transistors, from discrete components to integrated circuits to microprocessors, have made three leaps in the development of computers< In the period of electron tube computer (1946-1959), computers were mainly used for scientific calculation. Main memory is the main factor that determines the appearance of computer technology. At that time, the main memory included mercury delay line memory, cathode ray oscilloscope electrostatic memory, magnetic drum and magnetic core memory, which were usually used to classify computers.
the birth and development of modern computer before the advent of modern computer, the development of computer has gone through three stages: mechanical computer, electromechanical computer and electronic computer
as early as the 17th century, a group of European mathematicians began to design and manufacture digital computers that perform basic operations in digital form. In 1642, Pascal, a French mathematician, made the earliest decimal adder by using a gear transmission similar to clocks and watches. In 1678, Leibniz, a German mathematician, developed a computer to further solve the multiplication and division of decimal numbers
British mathematician Babbage put forward an idea when he made the model of difference machine in 1822. One arithmetic operation at a time will develop into a certain complete operation process automatically. In 1884, Babbage designed a program-controlled universal analyzer. Although this analyzer has described the rudiment of the program control computer, it can not be realized e to the technical conditions at that time< During the more than 100 years since Babbage's idea was put forward, great progress has been made in electromagnetics, electrotechnics and electronics, and vacuum diodes and vacuum triodes have been successively invented in components and devices; In terms of system technology, wireless telegraph, television and radar were invented one after another. All these achievements have prepared technical and material conditions for the development of modern computer< At the same time, mathematics and physics are developing rapidly. In the 1930s, all fields of physics experienced the stage of quantification. The mathematical equations describing various physical processes, some of which were difficult to solve by classical analysis methods. As a result, numerical analysis has been paid attention to, and various numerical integration, numerical differentiation, and numerical solutions of differential equations have been developed. The calculation process has been reced to a huge amount of basic operations, thus laying the foundation of modern computer numerical algorithm
the urgent need for advanced computing tools in society is the fundamental driving force for the birth of modern computers. Since the 20th century, there have been a lot of computational difficulties in various fields of science and technology, which has hindered the further development of the discipline. Especially before and after the outbreak of the Second World War, the need for high-speed computing tools in military science and technology is particularly urgent. During this period, Germany, the United States and the United Kingdom started the research of electromechanical computer and electronic computer almost at the same time<
Giuseppe in Germany was the first to use electrical components to make computers. The fully automatic relay computer Z-3, which he made in 1941, has the characteristics of modern computer, such as floating-point counting, binary operation, instruction form of digital storage address and so on. In the United States, the relay computers mark-1, mark-2, model-1, model-5 and so on were made successively from 1940 to 1947. However, the switching speed of the relay is about one hundredth of a second, which greatly limits the computing speed of the computer
the development process of electronic computer has experienced the evolution from making components to whole machine, from special machine to general machine, from "external program" to "stored program". In 1938, the Bulgarian American scholar atanasov first made the computing unit of the electronic computer. In 1943, the communications office of the British Foreign Office made the "giant" computer. This is a special cryptanalysis machine, which was used in the Second World War< In February 1946, ENIAC, a large-scale electronic digital integrator computer, was developed by Moore College of the University of Pennsylvania in the United States. At first, ENIAC was also specially used for artillery trajectory calculation. Later, it was improved many times and became a general-purpose computer capable of various scientific calculations. This computer, which uses electronic circuit to perform arithmetic operation, logic operation and information storage, is 1000 times faster than relay computer. This is the first electronic computer in the world. However, the program of this kind of computer is still external, the storage capacity is too small, and it has not fully possessed the main characteristics of modern computer
the new breakthrough was completed by a design team led by mathematician von Neumann. In March 1945, they published a new general electronic computer scheme of stored program - electronic discrete variable automatic computer (EDVAC). Then in June 1946, von Neumann and others put forward a more perfect design report "preliminary study on the logical structure of electronic computer devices". From July to August of the same year, they taught a special course "theory and technology of electronic computer design" for experts from more than 20 institutions in the United States and Britain at Moore college, which promoted the design and manufacture of stored program computers< In 1949, the Mathematics Laboratory of Cambridge University in England took the lead in making EDSAC; The United States made the eastern standard automatic computer (SFAC) in 1950. At this point, the embryonic period of the development of electronic computer came to an end, and the development period of modern computer began
at the same time of creating digital computer, we also developed another kind of important computing tool analog computer. When physicists summarize the laws of nature, they often use mathematical equations to describe a process; On the contrary, the process of solving mathematical equations may also adopt the physical process simulation method. After the invention of logarithm, the slide rule made in 1620 has changed multiplication and division into addition and subtraction for calculation. Maxwell skillfully transformed the calculation of integral (area) into the measurement of length, and made the integrator in 1855< Fourier analysis, another great achievement of mathematical physics in the 19th century, played a direct role in promoting the development of simulators. In the late 19th century and the early 20th century, a variety of analytical machines for calculating Fourier coefficients and differential equations were developed. However, when trying to popularize the differential analysis machine to solve partial differential equations and use the simulator to solve general scientific calculation problems, people graally realize the limitations of the simulator in the aspects of universality and accuracy, and turn their main energy to the digital computer
after the advent of electronic digital computer, analog computer still continues to develop, and hybrid computer is proced by combining with digital computer. Simulators and mixers have become special varieties of modern computers, that is, efficient information processing tools or simulation tools used in specific fields
since the middle of the 20th century, the computer has been in a period of high-speed development. The computer has developed from a hardware only system to a computer system which includes three subsystems: hardware, software and firmware. The performance price ratio of computer system is increased by two orders of magnitude every 10 years. The types of computers have been divided into microcomputers, minicomputers, general-purpose computers (including giant, large and medium-sized computers), and various special computers (such as various control computers and analog-to-digital hybrid computers)
computer devices, from electron tubes to transistors, from discrete components to integrated circuits to microprocessors, have made three leaps in the development of computers< In the period of electron tube computer (1946-1959), computers were mainly used for scientific calculation. Main memory is the main factor that determines the appearance of computer technology. At that time, the main memory included mercury delay line memory, cathode ray oscilloscope electrostatic memory, magnetic drum and magnetic core memory, which were usually used to classify computers.
7. There are two reasons why calculation always makes mistakes. One is technical, that is, the principle is not clear and the concept is confused, so it is easy to make mistakes. On the other hand, it is perceptual, e to carelessness. There are two ways to improve the computing ability: one is to strengthen the concept and principle of computing, the other is to focus on the training of the degree of care. Most of the children's calculation errors are caused by carelessness, which can be targeted for intensive training, but this is only a temporary training method. In the long run, it is necessary to cultivate children's carefulness in their daily study and life, do things in a planned way, and only good habits are the root causes
1. Strengthen the teaching of basic knowledge and skills to improve the rationality of operation. In teaching, basic knowledge is the basis of calculation theory, which has guiding significance for calculation. The confusion and fuzziness of basic knowledge and the fact that basic knowledge is too hard are often the root causes of calculation errors. Therefore, strengthening and implementing double base teaching is a very practical problem to improve calculation ability
2. Pay attention to the cultivation of students' practical ability and improve the simplicity of operation. In the normal teaching process, teachers must spare no time for students to practice more. On the basis of understanding theorems, formulas, algorithms, etc., they should also practice more to consolidate their memory and deepen their impression. If necessary, the effect will be better if some knowledge points are subject intensive training. Through the questionnaire survey, 80% of the students think that this kind of special topic examination training effect is very good
3. Pay attention to variant training and improve the proficiency of calculation. When commenting on an examination question, teachers should not only be satisfied with explaining the question thoroughly, but also be good at extending the variant of the question and drawing inferences from one instance. Only in this way can students "see both trees and forests" and get twice the result with half the effort. This requires teachers to be good at knowledge accumulation and summary
4. Pay attention to the standardization of problem solving process and improve the accuracy of calculation. Some teachers pay more attention to the analysis of the law of problem solving, thinking and the internal relationship of knowledge when commenting on test questions, but they do not pay enough attention to the process of problem solving, such as the standardization of writing, the skills and accuracy of calculation, etc., resulting in the situation that students can not get full marks or can not get full marks. This requires teachers to standardize writing and attach importance to their exemplary role
in the process of improving students' mathematical operation ability, we must be patient. In the process of training, in addition to explaining the basic concepts, theorems and rules, we should also cultivate students' memory ability, observation ability, understanding ability, associative ability, expression ability, logical thinking ability and other mathematical abilities in a purposeful, step-by-step and hierarchical way, and conct appropriate exercises, Only in this way can we improve the students' mathematical operation ability, so as to improve their ability of learning mathematics.
1. Strengthen the teaching of basic knowledge and skills to improve the rationality of operation. In teaching, basic knowledge is the basis of calculation theory, which has guiding significance for calculation. The confusion and fuzziness of basic knowledge and the fact that basic knowledge is too hard are often the root causes of calculation errors. Therefore, strengthening and implementing double base teaching is a very practical problem to improve calculation ability
2. Pay attention to the cultivation of students' practical ability and improve the simplicity of operation. In the normal teaching process, teachers must spare no time for students to practice more. On the basis of understanding theorems, formulas, algorithms, etc., they should also practice more to consolidate their memory and deepen their impression. If necessary, the effect will be better if some knowledge points are subject intensive training. Through the questionnaire survey, 80% of the students think that this kind of special topic examination training effect is very good
3. Pay attention to variant training and improve the proficiency of calculation. When commenting on an examination question, teachers should not only be satisfied with explaining the question thoroughly, but also be good at extending the variant of the question and drawing inferences from one instance. Only in this way can students "see both trees and forests" and get twice the result with half the effort. This requires teachers to be good at knowledge accumulation and summary
4. Pay attention to the standardization of problem solving process and improve the accuracy of calculation. Some teachers pay more attention to the analysis of the law of problem solving, thinking and the internal relationship of knowledge when commenting on test questions, but they do not pay enough attention to the process of problem solving, such as the standardization of writing, the skills and accuracy of calculation, etc., resulting in the situation that students can not get full marks or can not get full marks. This requires teachers to standardize writing and attach importance to their exemplary role
in the process of improving students' mathematical operation ability, we must be patient. In the process of training, in addition to explaining the basic concepts, theorems and rules, we should also cultivate students' memory ability, observation ability, understanding ability, associative ability, expression ability, logical thinking ability and other mathematical abilities in a purposeful, step-by-step and hierarchical way, and conct appropriate exercises, Only in this way can we improve the students' mathematical operation ability, so as to improve their ability of learning mathematics.
8. It depends on which components of the force triangle are decomposed along which axis. It can be used flexibly.
9. In brief, I hope to help you with the four elements of operation ability: accuracy, reasonableness, brevity, speed. The cultivation ways of operation ability are as follows: 1. Accurately understand and firmly grasp the concepts, properties, formulas, rules and some commonly used data required by various operations; 2; The deep understanding of concepts, properties, formulas and rules directly affects the choice of methods and the speed of operation. The concept is fuzzy, the formula and the rule are ambiguous, which will certainly affect the accuracy of the operation. In order to improve the speed of operation, it is necessary to memorize some commonly used data. For example, the square of natural number within 20, simple Pythagorean number, special trigonometric function value,,,,, LG2, Lg3, e accurate to approximate value of 0.001, etc. 2、 Master the general methods and rules of operation, and flexibly use concepts, properties, formulas and rules for operation. Teachers can combine the content of teaching materials, compile and collect some flexible exercises, cultivate the flexibility of students' calculation, and guide students to collect, summarize and accumulate experience to form skilled skills, so as to improve the simplicity and rapidity of calculation. 3、 Pay attention to the typical demonstration of teachers and examples in learning, and make clear the goal of solving problems, the steps of calculation and their basis. Through the typical demonstration, the transition from understanding knowledge to application knowledge is relatively smooth, thus forming the computing ability. 4、 To improve the reasoning ability in operation, the essence of mathematical operation is to dece the result from the known data and formula according to the definition and nature of operation, which is also a process of reasoning. Whether the operation is correct or not depends on whether the reasoning is correct. If the reasoning is not correct, the operation will be wrong. We should pay special attention to the equivalent transformation in operational reasoning. 5、 Pay attention to the training of the ability of identity transformation of numbers and expressions. 1. Symbol transformation, for example, symbol transformation when removing brackets and adding brackets. 2. Reciprocal transformation, such as addition and subtraction, multiplication and division, power and root, differentiation and integration, etc. 3. Formula change. For example, A2 + B2 = (a + b) 2-2ab, etc. 4. Decomposition transformation, for example, given X-Y = 3, Y-Z = 5, finding x-z, we can decompose x-z = (X-Y) + (Y-Z). 5. Substitution transformation, such as introcing auxiliary elements, constructing auxiliary functions, adding auxiliary lines, adding parameters, etc. 6、 To strengthen the operation practice, any ability is formed and developed in certain practical activities. In order to effectively improve the students' operation ability, we must strengthen the practice, and the practice should be purposeful, systematic and typical. Through changing, changing, solving and using one question, we can cultivate the proficiency, accuracy, flexibility and organization of calculation. In the form of question group training, students' thinking profundity in the process of operation is cultivated, and their operation ability is improved. 7、 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 the calculation, so as to correct the errors in the process or result of calculation in time, and master the checking method. For example, to solve an equation, the solution can be substituted into the original equation test. For solving fractional equation, irrational equation, logarithmic equation and exponential equation, the value range of unknowns can also be tested. The test methods usually include: rection method, substitution method, valuation method, inverse operation, etc
10. Transfer coefficient, 0.5
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