Force description
Publish: 2021-04-17 04:45:38
1.
computing power is a measure of bitcoin network processing power. That is, the speed at which the computer calculates the output of the hash function. Bitcoin networks must perform intensive mathematical and encryption related operations for security purposes. For example, when the network reaches a hash rate of 10th / s, it can perform 10 trillion calculations per second
in the process of getting bitcoin through "mining", we need to find its corresponding solution M. for any 64 bit hash value, there is no fixed algorithm to find its solution M. we can only rely on computer random hash collisions. How many hash collisions can a mining machine do per second is the representative of its "computing power", and the unit is written as hash / s, This is called workload proof mechanism pow
computing power provides a solid foundation for the development of big data, and the explosive growth of big data poses a huge challenge to the existing computing power. With the rapid accumulation of big data in the Internet era and the geometric growth of global data, the existing computing power can no longer meet the demand. According to IDC, 90% of the global information data is generated in recent years. And by 2020, about 40% of the information will be stored by cloud computing service providers, of which 1 / 3 of the data has value
therefore, the development of computing power is imminent, otherwise it will greatly restrict the development and application of artificial intelligence. There is a big gap between China and the advanced level of the world in terms of computing power and algorithm. The core of computing power is the chip. Therefore, it is necessary to increase R & D investment in the field of computing power to narrow or even catch up with the gap with the developed countries in the world
unit of force
1 KH / S = 1000 hashes per second
1 MH / S = 1000000 hashes per second
1 GH / S = 1000000000 hashes per second
1 th / S = 100000000000 hashes per second
1 pH / S = 100000000000 hashes per second
1 eh / S = 100000000000 hashes per second
2. After reading your description, how to improve the math calculation ability of the lower grade of primary school? The problem is that in order to improve the ability of mathematics calculation in the lower grades of primary school, mathematics teachers should clearly explain the importance and necessity of mathematics to primary school students, so that primary school students can improve their enthusiasm for learning mathematics. Good examples can be used to encourage primary school students to talk about sports and algorithms, and stimulate their enthusiasm for learning mathematics calculation, Will form everyone love mathematics atmosphere, graally improve the ability of mathematical calculation, good luck!
3. Hello, you should be talking about the so-called computing power of some blockchain platforms. Now, the algorithms of these platforms are uneven. The real blockchain platform in China is actually zero. This computing power is calculated according to the user's activity and some other statistical rates.
4. 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.
5. Walk 1.5km from mining machinery garden to CCB bus station, take No.3 or No.2 bus, and walk 25m to the terminal people's hospital. Or take a taxi
6. It's not as the title says,
in short,
quantum computer is to replace the original ordinary bits with quantum bits
from the physical level, quantum computers are not based on ordinary transistors, but use spin direction controlled particles (such as proton nuclear magnetic resonance) or polarization direction controlled photons (mostly used in school experiments) as carriers. Of course, in theory, any multi-level system can be used as the carrier of qubits
from the perspective of calculation principle, the input state of quantum computer can be either discrete eigenstate (like traditional computer) or superposition state (probability superposition of several different states). The operation of information is extended from traditional logic operations such as "and", "or", "and" to any unitary transformation, and the output can also be superposition state or an eigenstate. So quantum computer will be more flexible and can realize parallel computing< If you want to explain the details, it's a bit troublesome. I'll give you some key words to look up:
1. Quantum state
2. Quantum superposition
3, qubit
4, unitary transformation
5, quantum logic
6, quantum gate (corresponding to traditional logic gate, In fact, it is some special positive transformation)
7, quantum algorithm, quantum algorithm (of course, quantum computer can also realize the traditional algorithm)
8, and then on how to realize from the physical level, it is best to start with quantum optics, because polarized photons are the simplest
in depth:
ordinary digital computers run on binary systems of 0 and 1, which are called "bits". But quantum computers are far more powerful. They can operate on qubits and can compute values between 0 and 1. Suppose an atom placed in a magnetic field rotates like a top, so its axis of rotation can point up or down. Common sense tells us that the rotation of atoms can be up or down, but not all at the same time. But in the strange world of quantum, the atom is described as the sum of two states, an upward turning atom and a downward turning atom. In the wonderful world of quantum, every object is described by the sum of all the incredible states
imagine a string of atoms arranged in a magnetic field and rotating in the same way. If a laser beam is shining on the top of the atoms, it will jump down the group of atoms and quickly flip the rotation axis of some atoms. By measuring the difference between the incoming and outgoing laser beams, we have completed a complex quantum "calculation", involving a lot of rapid spin movement
from the perspective of mathematical abstraction, quantum computer performs the calculation with set as the basic operation unit, while ordinary computer performs the calculation with element as the basic operation unit (if there is only one element in the set, quantum calculation is no different from classical calculation)
take the function y = f (x), X ∈ a as an example. The input parameter of quantum computation is the domain a, and the output domain B is obtained in one step, that is, B = f (a); The input parameter of classical calculation is x, and the output value y is obtained. The range B can only be obtained by multiple calculations, that is, y = f (x), X ∈ a, y ∈ B
quantum computer has a problem to be solved, that is, the output range B can only randomly take out a valid value y. Although the number of elements in output set B is much less than that in input set a by directing the unwanted output to an empty set, it still needs to be calculated many times when all the valid values need to be taken out.
in short,
quantum computer is to replace the original ordinary bits with quantum bits
from the physical level, quantum computers are not based on ordinary transistors, but use spin direction controlled particles (such as proton nuclear magnetic resonance) or polarization direction controlled photons (mostly used in school experiments) as carriers. Of course, in theory, any multi-level system can be used as the carrier of qubits
from the perspective of calculation principle, the input state of quantum computer can be either discrete eigenstate (like traditional computer) or superposition state (probability superposition of several different states). The operation of information is extended from traditional logic operations such as "and", "or", "and" to any unitary transformation, and the output can also be superposition state or an eigenstate. So quantum computer will be more flexible and can realize parallel computing< If you want to explain the details, it's a bit troublesome. I'll give you some key words to look up:
1. Quantum state
2. Quantum superposition
3, qubit
4, unitary transformation
5, quantum logic
6, quantum gate (corresponding to traditional logic gate, In fact, it is some special positive transformation)
7, quantum algorithm, quantum algorithm (of course, quantum computer can also realize the traditional algorithm)
8, and then on how to realize from the physical level, it is best to start with quantum optics, because polarized photons are the simplest
in depth:
ordinary digital computers run on binary systems of 0 and 1, which are called "bits". But quantum computers are far more powerful. They can operate on qubits and can compute values between 0 and 1. Suppose an atom placed in a magnetic field rotates like a top, so its axis of rotation can point up or down. Common sense tells us that the rotation of atoms can be up or down, but not all at the same time. But in the strange world of quantum, the atom is described as the sum of two states, an upward turning atom and a downward turning atom. In the wonderful world of quantum, every object is described by the sum of all the incredible states
imagine a string of atoms arranged in a magnetic field and rotating in the same way. If a laser beam is shining on the top of the atoms, it will jump down the group of atoms and quickly flip the rotation axis of some atoms. By measuring the difference between the incoming and outgoing laser beams, we have completed a complex quantum "calculation", involving a lot of rapid spin movement
from the perspective of mathematical abstraction, quantum computer performs the calculation with set as the basic operation unit, while ordinary computer performs the calculation with element as the basic operation unit (if there is only one element in the set, quantum calculation is no different from classical calculation)
take the function y = f (x), X ∈ a as an example. The input parameter of quantum computation is the domain a, and the output domain B is obtained in one step, that is, B = f (a); The input parameter of classical calculation is x, and the output value y is obtained. The range B can only be obtained by multiple calculations, that is, y = f (x), X ∈ a, y ∈ B
quantum computer has a problem to be solved, that is, the output range B can only randomly take out a valid value y. Although the number of elements in output set B is much less than that in input set a by directing the unwanted output to an empty set, it still needs to be calculated many times when all the valid values need to be taken out.
7.
Generally speaking, the computing power is affected not only by the processor, but also by the chipset, memory and hard disk
from the perspective of parameters, performance
processor: model, core, main frequency, front-end bus, cache
chipset: type
memory: type and capacity
hard disk: capacity, cache, speed
it can be seen from the configuration of a laptop that the processor, chipset and memory are the key to the performance. For example, the processor model, main frequency, chipset model, memory type, capacity; We can only see the size of the capacity of the hard disk in the configuration, but we can't know the speed and cache size (except for software testing)
the strength of the overall computing performance is closely related to the balance of the configuration of the above four main components. If the processor and hard disk are compared to the two sides of a river, then the memory is the bridge connecting the two sides. For example, the wider the "bridge", the more people will pass at the same time. Therefore, large capacity memory has an absolute advantage over small capacity memory. If the "bridge" is narrow, there will be a bottleneck between the processor and the hard disk, which will affect the computational performance in actual use. Chipsets mainly support al channel memory. At present, almost all the chipsets used in commercial laptops support al channel memory, so we won't give a detailed description here
e to different batches of laptops with the same model and configuration, there will be some differences in the configuration of hard disks. These differences are shown in the speed of the hard disk, cache. The higher the speed of the hard disk and the larger the capacity of the single chip, the more data can be read per unit time
8. That's a magic operator.
we think Froude is so powerful
we think Froude is so powerful
9. Operational ability is a series of psychological and behavioral characteristics of indivials in the process of dealing with the relationship between number and quantity. It is one of the important manifestations of mathematics ability. Operational ability is composed of related elements, which reflects certain level differences in the development process. In order to improve the operational teaching practice in primary and secondary schools and optimize the operational teaching evaluation, we should refine the evaluation index of operational ability, Try to use the explicit, concrete and observable operation behavior of students to describe the index content
10. Computing is closely related to everyone's life and proction, and plays an irreplaceable role in reality. If thinking is the heart of mathematics, then calculation is the aorta of mathematics. Therefore, the teaching efficiency of computing teaching will affect students' potential for mathematics learning
computing is a simple thing for teachers, but computing teaching is a profound art. Therefore, we can't treat calculation teaching with our own calculation standard. Every computing class should be fully pre-set from the perspective of learning, including class objectives, key and difficult points, driving classroom questioning, classroom situation, teaching links, etc. Only in this way can we say that with sufficient presupposition, teaching can be used freely, and easy and effective classroom can be created. Therefore, our teaching should come from the students' learning, and should be guided according to the situation, so as to achieve the teaching goal
then, how to improve students' computing ability
first, cultivate good attention quality
aiming at the three characteristics of primary school students: low attention stability, small distribution span and poor transfer ability. Teachers should try their best to let students finish their homework in class. When students do their homework, in order to ensure that students' attention is consciously focused and kept on the homework, teachers should try their best to keep the classroom quiet. Teachers should not give guidance to the whole class, and indivial guidance should not be too loud. The adverse effects of distraction should be eliminated to the greatest extent. For more abstract and step-by-step calculation, teachers should let students repeatedly perceive and give necessary hints to attract students' attention. Teachers can also change the way to train students to show their calculation ability, such as: the way to show oral arithmetic questions, changing the previous way to look at a question card, and then immediately take back the card, and then let the students report the answers, so as to enhance the training intensity and strengthen the intentional attention. At the same time, in the process of calculation, students should try their best to keep their attention on the homework< Second, improve the ability of memory in calculation. First of all, we need to extract the calculation facts from the long-term memory and put them in the working memory. At the same time, we also need the participation of memory in the calculation process, so that the calculation can be carried out correctly. For example, in daily life, let students take part in some memory games to improve their memory. We also need to make students insist on oral arithmetic. Being proficient in oral arithmetic is the basis of correct written arithmetic. Any four mixed arithmetic problems are synthesized by oral arithmetic problems. Both oral and written arithmetic are inseparable from instantaneous memory, and oral arithmetic is the best form of students' short-term memory. The design of oral arithmetic exercises by teachers should be targeted, from easy to difficult, and graally improve, including some simple calculation problems. Persistent training not only cultivates memory ability, but also forms good thinking quality< Third, strengthen students' serious attitude towards calculation
when students lack purpose in the process of calculation, their attitude is often random, they don't care about the correctness of calculation, they care about when to complete the task. Teachers can give some examples of daily life to guide students. For example, when an engineer designed a bridge, e to the wrong decimal point in the calculation, the completed bridge became a dangerous bridge, which not only wasted the resources of the country, but also seriously endangered the safety of the people. So as to strengthen their will to complete the calculation seriously
at the same time, in the calculation, the errors of primary school students always emerge in an endless stream. Psychologist Thorndike believes that "trial and error are the basic forms of learning". Therefore, in the process of primary school students' learning, mistakes are inevitable. Teachers should not blame students for their mistakes. The key point is that teachers should discuss with students, make clear why they made mistakes and what step they took, help students find out the causes of calculation errors, and guide students to learn from their mistakes< Fourth, strengthen the targeted practice
in primary school mathematics, there are many calculations that are related and different. Teachers can put together the concepts, rules, theorems and formulas that are easy to be confused, so that students can fully perceive, distinguish and distinguish them, so that they can make clear the essential characteristics in the discrimination, master the connection and difference between the new and old knowledge, and actively prevent the stereotype of thinking
for example: four mixed operation exercises:
96-3 × thirty-two ÷ 4 96-4 × thirty-two ÷ 4
96-3 × thirty-two ÷ 4 96-4 × thirty-two ÷ 4)
make students distinguish the differences and relations among the same level, different level and operation with brackets, so as to grasp their own essential characteristics< 5. To cultivate good calculation habits of primary school students
good calculation habits of primary school students can not only help them master calculation theory and cultivate their interest in mathematics learning, but also help them overcome the psychological factors causing calculation errors, which is the guarantee of improving their calculation ability. Therefore, it is very necessary to cultivate the calculation habit of primary school students. There are three steps for teachers to cultivate pupils' habit of calculation, which are as follows:
1. Correct examination is the prerequisite for pupils' correct calculation, and its four steps are: first reading, second reading, third thinking and fourth calculation“ "Read" is a serious reading topic, "see" is to see the data, operation symbols, operation order in the topic, "think" is to think of the calculation method and order that should be used, "calculate" is to calculate according to the thought. For example, four arithmetic questions "36 + 4" × 10-7.5) "in the calculation process, read the questions first to see which operations (+ ×、-， Think about what to calculate first, and then what to calculate (in language description: first calculate the difference of "10-7.5", then calculate the proct of "4 times the difference", and finally calculate the sum of "36 plus proct"), and then calculate according to the order of thinking, so that the calculation can be carried out in an orderly way, thus recing the calculation errors< Careful writing is a necessary condition for pupils to calculate correctly. Therefore, in the calculation of primary school students, whether it is ing or off type calculation, the teacher strictly requires standard format, neat writing, clean paper surface (even if the draft also requires clear handwriting), every step of writing should be "back" carefully proofread, and then continue the next step of calculation after confirming that their ing and calculation are correct
3. Careful checking
checking is the guarantee of correct calculation. The teacher should strengthen the demonstration in the classroom teaching, improve the students' understanding of the importance of checking calculation, and develop the conscious behavior of checking calculation after the problem. The teacher can also guide the students to create a variety of checking calculation methods, such as heavy algorithm, inverse algorithm, alternative solution, estimation method, transposition method, substitution method, etc., so that the students can not only improve their interest in checking calculation, enhance their checking ability, and graally form the habit of checking calculation, But also cultivate students' thinking ability
it can be seen that computing teaching is a long-term and complex teaching process, and the improvement of students' computing ability is not a matter overnight. As long as we teachers study hard, summarize and improve our work, dig out the ability factors in computing problems seriously, and work together with students, students' computing ability will be improved
applied problem teaching is also a very important part in primary school mathematics teaching. To cultivate students' ability to solve practical problems, we should start from the following aspects
(1) cultivating students' habit of examining questions
careful examination and understanding of the meaning of questions are the prerequisite for solving practical questions accurately. Therefore, in teaching, students can first find out the direct and indirect conditions according to the requirements of solving problems, build the relationship between conditions and problems, and determine the quantitative relationship. In order to analyze the relationship between the known quantity and the unknown quantity in the problem, students can be asked to think while reading the problem, mark the conditions and problems with different symbols, or express the known conditions and problems with line diagram. In order to cultivate children's habit of careful examination, I often put some confusing questions at the same time, let students analyze and calculate. For example: (1) there are 3000 sci-tech books and story books in the library. The number of sci-tech books is two-thirds of that of story books. How many sci-tech books are there
② there are 3000 storybooks in the library, and the number of science and technology books is 2 / 3 of the storybooks. How many science and technology books are there
there are several 3000 volumes in question 1, and 3000 volumes in question 2 are one, so the calculation method is different. If you do this kind of exercises often, you can easily form the habit of examining questions carefully
(2) teach students the common reasoning methods of analyzing practical problems
in the process of solving problems, students are often used to imitate the solutions of teachers and examples, and complete them mechanically. Therefore, it is very important to teach students the reasoning method of analyzing practical problems and help students to understand the way of solving problems. Analysis method and synthesis method are commonly used analysis methods. The so-called analytical method is to analyze the problems from the application problems, first consider what conditions are needed to solve the problems, and which of these conditions are known and which are unknown, until the unknown conditions can be found in the problems. For example: car a transports 300 kg of coal at a time, car B transports 50 kg more than car a, and how many kg of coal do two cars transport at a time
instruct students to dictate how many kilos of coal are required to be transported by two vehicles at a time? Which two conditions must be known according to the meaning of the question? Which of the conditions listed in the question is known (by car a), which is unknown (by car B), and what should be sought first (300 + 50 = 350 by car B)? Then what do you ask (how many kilos of coal are used for two cars, 300 + 350 = 650)
the synthesis method is based on the known conditions of application problems, and deces the required problems through analysis. For example, to guide students to think like this: knowing that car a carries 300 kg of coal, car B uses 50 kg more than car a, we can find out the weight of coal carried by car B (300 + 50 = 350). With this condition, we can find out how many kg of coal the two cars carry in total 300+350=650 From the two solutions of the above problems, we can see that whether we use the analytical method or the comprehensive method, we should combine the known conditions of the application problems with the problems we seek. The problems we seek are the direction of thinking, and the known conditions are the basis for solving the problems
(3) comparative analysis of easily confused problems
some related and easily confused practical problems can guide students to make comparative analysis, for example: how much is the fraction of a number and the known fraction of a number, and the practical problems of solving this number are often easily confused by students. First, they can't tell whether to use multiplication or division; Secondly, it is not necessary to add brackets when the calculation is not clear. Therefore, the following group of questions can be arranged for comparative teaching
① there are 240 pear trees in the orchard, and apple trees account for 1 / 3 of pear trees. How many apple trees are there
② there are 240 pear trees in the orchard, accounting for 1 / 3 of the apple trees. How many apple trees are there
③ there are 240 pear trees in the orchard, one third less apple trees than pear trees. How many apple trees are there< (4) there are 240 pear trees in the orchard, one third less than apple trees. How many apple trees are there
⑤ there are 240 pear trees in the orchard, one third more apple trees than pear trees. How many apples are there< There are 240 pear trees in the orchard, one third more than apple trees. How many apple trees are there
when comparing two numbers, the following number is the standard number and the preceding number is the comparison number, that is, who is compared with is the standard number (usually set the standard number as 1). Given a number, find it
computing is a simple thing for teachers, but computing teaching is a profound art. Therefore, we can't treat calculation teaching with our own calculation standard. Every computing class should be fully pre-set from the perspective of learning, including class objectives, key and difficult points, driving classroom questioning, classroom situation, teaching links, etc. Only in this way can we say that with sufficient presupposition, teaching can be used freely, and easy and effective classroom can be created. Therefore, our teaching should come from the students' learning, and should be guided according to the situation, so as to achieve the teaching goal
then, how to improve students' computing ability
first, cultivate good attention quality
aiming at the three characteristics of primary school students: low attention stability, small distribution span and poor transfer ability. Teachers should try their best to let students finish their homework in class. When students do their homework, in order to ensure that students' attention is consciously focused and kept on the homework, teachers should try their best to keep the classroom quiet. Teachers should not give guidance to the whole class, and indivial guidance should not be too loud. The adverse effects of distraction should be eliminated to the greatest extent. For more abstract and step-by-step calculation, teachers should let students repeatedly perceive and give necessary hints to attract students' attention. Teachers can also change the way to train students to show their calculation ability, such as: the way to show oral arithmetic questions, changing the previous way to look at a question card, and then immediately take back the card, and then let the students report the answers, so as to enhance the training intensity and strengthen the intentional attention. At the same time, in the process of calculation, students should try their best to keep their attention on the homework< Second, improve the ability of memory in calculation. First of all, we need to extract the calculation facts from the long-term memory and put them in the working memory. At the same time, we also need the participation of memory in the calculation process, so that the calculation can be carried out correctly. For example, in daily life, let students take part in some memory games to improve their memory. We also need to make students insist on oral arithmetic. Being proficient in oral arithmetic is the basis of correct written arithmetic. Any four mixed arithmetic problems are synthesized by oral arithmetic problems. Both oral and written arithmetic are inseparable from instantaneous memory, and oral arithmetic is the best form of students' short-term memory. The design of oral arithmetic exercises by teachers should be targeted, from easy to difficult, and graally improve, including some simple calculation problems. Persistent training not only cultivates memory ability, but also forms good thinking quality< Third, strengthen students' serious attitude towards calculation
when students lack purpose in the process of calculation, their attitude is often random, they don't care about the correctness of calculation, they care about when to complete the task. Teachers can give some examples of daily life to guide students. For example, when an engineer designed a bridge, e to the wrong decimal point in the calculation, the completed bridge became a dangerous bridge, which not only wasted the resources of the country, but also seriously endangered the safety of the people. So as to strengthen their will to complete the calculation seriously
at the same time, in the calculation, the errors of primary school students always emerge in an endless stream. Psychologist Thorndike believes that "trial and error are the basic forms of learning". Therefore, in the process of primary school students' learning, mistakes are inevitable. Teachers should not blame students for their mistakes. The key point is that teachers should discuss with students, make clear why they made mistakes and what step they took, help students find out the causes of calculation errors, and guide students to learn from their mistakes< Fourth, strengthen the targeted practice
in primary school mathematics, there are many calculations that are related and different. Teachers can put together the concepts, rules, theorems and formulas that are easy to be confused, so that students can fully perceive, distinguish and distinguish them, so that they can make clear the essential characteristics in the discrimination, master the connection and difference between the new and old knowledge, and actively prevent the stereotype of thinking
for example: four mixed operation exercises:
96-3 × thirty-two ÷ 4 96-4 × thirty-two ÷ 4
96-3 × thirty-two ÷ 4 96-4 × thirty-two ÷ 4)
make students distinguish the differences and relations among the same level, different level and operation with brackets, so as to grasp their own essential characteristics< 5. To cultivate good calculation habits of primary school students
good calculation habits of primary school students can not only help them master calculation theory and cultivate their interest in mathematics learning, but also help them overcome the psychological factors causing calculation errors, which is the guarantee of improving their calculation ability. Therefore, it is very necessary to cultivate the calculation habit of primary school students. There are three steps for teachers to cultivate pupils' habit of calculation, which are as follows:
1. Correct examination is the prerequisite for pupils' correct calculation, and its four steps are: first reading, second reading, third thinking and fourth calculation“ "Read" is a serious reading topic, "see" is to see the data, operation symbols, operation order in the topic, "think" is to think of the calculation method and order that should be used, "calculate" is to calculate according to the thought. For example, four arithmetic questions "36 + 4" × 10-7.5) "in the calculation process, read the questions first to see which operations (+ ×、-， Think about what to calculate first, and then what to calculate (in language description: first calculate the difference of "10-7.5", then calculate the proct of "4 times the difference", and finally calculate the sum of "36 plus proct"), and then calculate according to the order of thinking, so that the calculation can be carried out in an orderly way, thus recing the calculation errors< Careful writing is a necessary condition for pupils to calculate correctly. Therefore, in the calculation of primary school students, whether it is ing or off type calculation, the teacher strictly requires standard format, neat writing, clean paper surface (even if the draft also requires clear handwriting), every step of writing should be "back" carefully proofread, and then continue the next step of calculation after confirming that their ing and calculation are correct
3. Careful checking
checking is the guarantee of correct calculation. The teacher should strengthen the demonstration in the classroom teaching, improve the students' understanding of the importance of checking calculation, and develop the conscious behavior of checking calculation after the problem. The teacher can also guide the students to create a variety of checking calculation methods, such as heavy algorithm, inverse algorithm, alternative solution, estimation method, transposition method, substitution method, etc., so that the students can not only improve their interest in checking calculation, enhance their checking ability, and graally form the habit of checking calculation, But also cultivate students' thinking ability
it can be seen that computing teaching is a long-term and complex teaching process, and the improvement of students' computing ability is not a matter overnight. As long as we teachers study hard, summarize and improve our work, dig out the ability factors in computing problems seriously, and work together with students, students' computing ability will be improved
applied problem teaching is also a very important part in primary school mathematics teaching. To cultivate students' ability to solve practical problems, we should start from the following aspects
(1) cultivating students' habit of examining questions
careful examination and understanding of the meaning of questions are the prerequisite for solving practical questions accurately. Therefore, in teaching, students can first find out the direct and indirect conditions according to the requirements of solving problems, build the relationship between conditions and problems, and determine the quantitative relationship. In order to analyze the relationship between the known quantity and the unknown quantity in the problem, students can be asked to think while reading the problem, mark the conditions and problems with different symbols, or express the known conditions and problems with line diagram. In order to cultivate children's habit of careful examination, I often put some confusing questions at the same time, let students analyze and calculate. For example: (1) there are 3000 sci-tech books and story books in the library. The number of sci-tech books is two-thirds of that of story books. How many sci-tech books are there
② there are 3000 storybooks in the library, and the number of science and technology books is 2 / 3 of the storybooks. How many science and technology books are there
there are several 3000 volumes in question 1, and 3000 volumes in question 2 are one, so the calculation method is different. If you do this kind of exercises often, you can easily form the habit of examining questions carefully
(2) teach students the common reasoning methods of analyzing practical problems
in the process of solving problems, students are often used to imitate the solutions of teachers and examples, and complete them mechanically. Therefore, it is very important to teach students the reasoning method of analyzing practical problems and help students to understand the way of solving problems. Analysis method and synthesis method are commonly used analysis methods. The so-called analytical method is to analyze the problems from the application problems, first consider what conditions are needed to solve the problems, and which of these conditions are known and which are unknown, until the unknown conditions can be found in the problems. For example: car a transports 300 kg of coal at a time, car B transports 50 kg more than car a, and how many kg of coal do two cars transport at a time
instruct students to dictate how many kilos of coal are required to be transported by two vehicles at a time? Which two conditions must be known according to the meaning of the question? Which of the conditions listed in the question is known (by car a), which is unknown (by car B), and what should be sought first (300 + 50 = 350 by car B)? Then what do you ask (how many kilos of coal are used for two cars, 300 + 350 = 650)
the synthesis method is based on the known conditions of application problems, and deces the required problems through analysis. For example, to guide students to think like this: knowing that car a carries 300 kg of coal, car B uses 50 kg more than car a, we can find out the weight of coal carried by car B (300 + 50 = 350). With this condition, we can find out how many kg of coal the two cars carry in total 300+350=650 From the two solutions of the above problems, we can see that whether we use the analytical method or the comprehensive method, we should combine the known conditions of the application problems with the problems we seek. The problems we seek are the direction of thinking, and the known conditions are the basis for solving the problems
(3) comparative analysis of easily confused problems
some related and easily confused practical problems can guide students to make comparative analysis, for example: how much is the fraction of a number and the known fraction of a number, and the practical problems of solving this number are often easily confused by students. First, they can't tell whether to use multiplication or division; Secondly, it is not necessary to add brackets when the calculation is not clear. Therefore, the following group of questions can be arranged for comparative teaching
① there are 240 pear trees in the orchard, and apple trees account for 1 / 3 of pear trees. How many apple trees are there
② there are 240 pear trees in the orchard, accounting for 1 / 3 of the apple trees. How many apple trees are there
③ there are 240 pear trees in the orchard, one third less apple trees than pear trees. How many apple trees are there< (4) there are 240 pear trees in the orchard, one third less than apple trees. How many apple trees are there
⑤ there are 240 pear trees in the orchard, one third more apple trees than pear trees. How many apples are there< There are 240 pear trees in the orchard, one third more than apple trees. How many apple trees are there
when comparing two numbers, the following number is the standard number and the preceding number is the comparison number, that is, who is compared with is the standard number (usually set the standard number as 1). Given a number, find it
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