Clear calculation power
Publish: 2021-04-10 07:33:39
1. According to IDC's "2018-2019 evaluation report on the development of China's artificial intelligence computing power", by 2022, the investment in computing power in the global artificial intelligence market will exceed 17.6 billion US dollars, and the compound growth rate of the market will exceed 30% in the next five years (2018-2022). And computing power will become an important infrastructure in modern society and an important part of China's new infrastructure strategy. Xnmatrix is a new generation of global and decentralized cloud computing platform, and a new infrastructure in the field of digital economy in the Web3.0 intelligent era.
2. First of all, your question is not very clear. If you are talking about the Shanzhai national chain before, it can tell you for sure that it is not reliable. In the world of blockchain, except bitcoin and a few mainstream currencies, everything else is rubbish
if you're talking about nationwide computing power in computing power leasing and mining machinery business, it's reliable. At least you're a member of the mining association. The outside world doesn't know much about this group. Our insiders still know this group of people. Although they are all mud legged (compared with bitcontinent), they are all old people in the mining circle. They are also early believers in bitcoin, and they are quite confident.
if you're talking about nationwide computing power in computing power leasing and mining machinery business, it's reliable. At least you're a member of the mining association. The outside world doesn't know much about this group. Our insiders still know this group of people. Although they are all mud legged (compared with bitcontinent), they are all old people in the mining circle. They are also early believers in bitcoin, and they are quite confident.
3. Operation ability is one of the basic components of mathematical ability, which refers to the ability to use the knowledge about operation to carry out operation and reasoning to obtain the result of operation
operation is actually a dective reasoning process, and operation is reasoning. In the primary mathematics stage, mathematical operation mainly includes four operations: integral, rational, radical, exponential, logarithmic and trigonometric functions. In the higher mathematics stage, there are limit operation, differential and integral operation, vector and matrix operation, data, information processing and probability operation, set, matrix operation, and so on Mathematical operation ability includes all these aspects of operation ability. To cultivate the above operation ability, students should first master the relevant knowledge of all kinds of operation (such as the concept and nature of the operation object, the definition and rules of operation, etc.) With the popularity of calculators, it is no longer necessary to learn four digit mathematical tables and do more training in multi digit numerical calculation in middle schools. However, it is necessary to develop estimation ability and the ability to process a large number of data. Furthermore, e to the use of program calculators and computers, more complex operations can be carried out by programs, At this time, students need to learn programming or algorithmic language to get the ability to use them.
operation is actually a dective reasoning process, and operation is reasoning. In the primary mathematics stage, mathematical operation mainly includes four operations: integral, rational, radical, exponential, logarithmic and trigonometric functions. In the higher mathematics stage, there are limit operation, differential and integral operation, vector and matrix operation, data, information processing and probability operation, set, matrix operation, and so on Mathematical operation ability includes all these aspects of operation ability. To cultivate the above operation ability, students should first master the relevant knowledge of all kinds of operation (such as the concept and nature of the operation object, the definition and rules of operation, etc.) With the popularity of calculators, it is no longer necessary to learn four digit mathematical tables and do more training in multi digit numerical calculation in middle schools. However, it is necessary to develop estimation ability and the ability to process a large number of data. Furthermore, e to the use of program calculators and computers, more complex operations can be carried out by programs, At this time, students need to learn programming or algorithmic language to get the ability to use them.
4. First of all, the computing power needs to be trained repeatedly
5. 1、 Pay attention to the process teaching of calculation theory and rule, and improve the calculation skills
calculation principles and rules are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, I first guide the students to talk about the calculation theory and summarize the rules. For example, when I talk about fraction addition with the same denominator, I can do it like this: first use the graph to show it, and then ask the question: what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). And let the students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators
the calculation method is programmed and regularized, and can be mastered only by mechanical training, but it can not adapt to the ever-changing specific situation, let alone flexible application. Therefore, we must deal with the relationship between theory and algorithm, guide students to follow "theory" into "method", and control "method" with "theory", and promote the formation of computational skills through intellectual activities. If students don't understand the concept of digits, they can't understand the principle of digit alignment in written calculation: if they don't understand the basic properties of decimals, they can't transform the division of decimals into the division of integers; If we don't know the meaning of the four operations, it's difficult to explain the calculation rules. To make students understand the concepts of number and four arithmetic correctly is the premise of mastering the four arithmetic. Therefore, it is necessary to explain the knowledge of number and four arithmetic in teaching. In normal teaching, the meaning of four operations can be graally formed and deepened in the process of solving problems. Calculation rules are the basis for students to carry out four operations correctly. We can pay attention to the steps and methods of calculation through typical examples. The laws and properties of operation are the basis of clarifying the laws of calculation and simple algorithms. Students can be guided to observe, compare, analyze and find out the common characteristics through the calculation of specific formula questions, and then summarize them, so that students can understand the practical significance of the laws and properties. We should pay special attention to make students learn to apply the laws and properties of operation on the basis of students' understanding, and make some simple calculation methods, so as to continuously improve students' calculation ability< Second, strengthen the basic training and cultivate the ability of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation
for example, the decomposition of numbers within 10, the addition and subtraction of numbers within 20, and the multiplication and division method in the table are the key to improve the accuracy of calculation. In addition, according to the learning content of different grades, let students memorize some data with high frequency of use, such as grade 25 × 4=100、125 × 8=1000 Senior grade: the denominator is 2, 4, 5, 8, 20, 25 of the simplest true score of the small value, percentage value, 1 ~ 20 of the square value, so that students form skilled oral skills, to achieve correct, rapid, flexible calculation
2. Strengthen the training of estimation and develop students' thinking. Estimation is the ability to approximate or roughly estimate the operation process or result. Estimation is helpful for students to find out their deviation in solving problems, to rethink and calculate, so as to improve their computing ability. In teaching, teachers should teach students some estimation methods, so that students can form a correct direction of thinking and improve the accuracy of calculation
for example: multiply multiple numbers, master the number of digits and mantissa of the proct; Four decimal calculation, to see the positioning of the decimal point. According to the characteristics of the formula, the estimation result is a common estimation method, such as 25 × 85, because 0. 85 is less than 1, so 25 × 85 is less than 25; one hundred ÷ 0.25, because 0.25 is less than 1, so 100 ÷ The quotient of 0.25 is greater than 100, etc. in this way, once obvious errors are found, they can be corrected in time, which provides a guarantee for the acquisition of correct answers and trains the correctness of students' thinking
in addition, the estimation is also used in the calculation of applied problems, such as average applied problem: there are 10 grannies in the nursing home, with an average age of 80.5 years old, and 12 grandfathers, with an average age of 73.5 years old. The average age of the elderly in the hospital. Before answering the question, ask the students to estimate the average age of the elderly. With the estimation results, we can avoid (80.5 + 73.5) ÷ 10 + 12) ≈ 7 years old
in teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
3. Strengthen the simple calculation training to improve the calculation efficiency. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. In calculation, students are easy to apply and abuse some properties and laws. Let students do some contrast exercises, diagnose mistakes by themselves, reflect on the wrong nodes of calculation, and prevent the same mistakes from happening again. For example: 300-175 + 25300-175-25; one hundred and twenty-five × eight ÷ one hundred and twenty-five × 8，125 × 8 ÷ one hundred and twenty-five × 8…… Let the students distinguish under what circumstances the use of properties and laws can be simple, understand why some can be used, some problems can not be used. In the simple calculation training, we should also let the students carry on the algorithm diversification training, such as 25 × 48, let the students come to different algorithms through discussion and communication, (1) 25 × 48=25 × four × 12 225 × 48=25 × 40+8 325 × 48=5 × 6 × five × 8 425 × 48=25 × 4 × forty-eight ÷ 4) On this basis, let the students summarize some regular things, clarify the context of knowledge, and form a good cognitive structure
thirdly, cultivate good habits and improve computing ability. Good learning habits are the driving force of students' sustainable development and an important guarantee for students to learn to learn, form learning ability and improve computing ability. In the calculation, we should focus on students to develop some good habits. 1. The habit of careful examination. Careful examination is the premise of correct and rapid calculation. 2. The habit of proofreading in time. 3. The habit of calculating carefully. When calculating, the format should be standard, the method should be reasonable, and the calculation process should be carefully checked. 4. The habit of consciously testing. In the calculation, we should develop the habit of self-conscious inspection, and correct mistakes in time. 5. Standardize the habit of writing. Scribble writing, disordered format, carelessness and carelessness are the main causes of calculation errors. To ensure the correctness of the calculation, we must develop a good habit of neat writing and standard format
computing teaching is a long-term and complex teaching process. It is not a matter of a day to improve students' computing ability. It is necessary to be regular, planned and step-by-step, speed in time, density in quantity, flexibility and novelty in form and content. Only when we teachers and students work together and persevere, can we achieve results. The above are my own teaching methods
calculation principles and rules are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, I first guide the students to talk about the calculation theory and summarize the rules. For example, when I talk about fraction addition with the same denominator, I can do it like this: first use the graph to show it, and then ask the question: what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). And let the students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators
the calculation method is programmed and regularized, and can be mastered only by mechanical training, but it can not adapt to the ever-changing specific situation, let alone flexible application. Therefore, we must deal with the relationship between theory and algorithm, guide students to follow "theory" into "method", and control "method" with "theory", and promote the formation of computational skills through intellectual activities. If students don't understand the concept of digits, they can't understand the principle of digit alignment in written calculation: if they don't understand the basic properties of decimals, they can't transform the division of decimals into the division of integers; If we don't know the meaning of the four operations, it's difficult to explain the calculation rules. To make students understand the concepts of number and four arithmetic correctly is the premise of mastering the four arithmetic. Therefore, it is necessary to explain the knowledge of number and four arithmetic in teaching. In normal teaching, the meaning of four operations can be graally formed and deepened in the process of solving problems. Calculation rules are the basis for students to carry out four operations correctly. We can pay attention to the steps and methods of calculation through typical examples. The laws and properties of operation are the basis of clarifying the laws of calculation and simple algorithms. Students can be guided to observe, compare, analyze and find out the common characteristics through the calculation of specific formula questions, and then summarize them, so that students can understand the practical significance of the laws and properties. We should pay special attention to make students learn to apply the laws and properties of operation on the basis of students' understanding, and make some simple calculation methods, so as to continuously improve students' calculation ability< Second, strengthen the basic training and cultivate the ability of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation
for example, the decomposition of numbers within 10, the addition and subtraction of numbers within 20, and the multiplication and division method in the table are the key to improve the accuracy of calculation. In addition, according to the learning content of different grades, let students memorize some data with high frequency of use, such as grade 25 × 4=100、125 × 8=1000 Senior grade: the denominator is 2, 4, 5, 8, 20, 25 of the simplest true score of the small value, percentage value, 1 ~ 20 of the square value, so that students form skilled oral skills, to achieve correct, rapid, flexible calculation
2. Strengthen the training of estimation and develop students' thinking. Estimation is the ability to approximate or roughly estimate the operation process or result. Estimation is helpful for students to find out their deviation in solving problems, to rethink and calculate, so as to improve their computing ability. In teaching, teachers should teach students some estimation methods, so that students can form a correct direction of thinking and improve the accuracy of calculation
for example: multiply multiple numbers, master the number of digits and mantissa of the proct; Four decimal calculation, to see the positioning of the decimal point. According to the characteristics of the formula, the estimation result is a common estimation method, such as 25 × 85, because 0. 85 is less than 1, so 25 × 85 is less than 25; one hundred ÷ 0.25, because 0.25 is less than 1, so 100 ÷ The quotient of 0.25 is greater than 100, etc. in this way, once obvious errors are found, they can be corrected in time, which provides a guarantee for the acquisition of correct answers and trains the correctness of students' thinking
in addition, the estimation is also used in the calculation of applied problems, such as average applied problem: there are 10 grannies in the nursing home, with an average age of 80.5 years old, and 12 grandfathers, with an average age of 73.5 years old. The average age of the elderly in the hospital. Before answering the question, ask the students to estimate the average age of the elderly. With the estimation results, we can avoid (80.5 + 73.5) ÷ 10 + 12) ≈ 7 years old
in teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
3. Strengthen the simple calculation training to improve the calculation efficiency. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. In calculation, students are easy to apply and abuse some properties and laws. Let students do some contrast exercises, diagnose mistakes by themselves, reflect on the wrong nodes of calculation, and prevent the same mistakes from happening again. For example: 300-175 + 25300-175-25; one hundred and twenty-five × eight ÷ one hundred and twenty-five × 8，125 × 8 ÷ one hundred and twenty-five × 8…… Let the students distinguish under what circumstances the use of properties and laws can be simple, understand why some can be used, some problems can not be used. In the simple calculation training, we should also let the students carry on the algorithm diversification training, such as 25 × 48, let the students come to different algorithms through discussion and communication, (1) 25 × 48=25 × four × 12 225 × 48=25 × 40+8 325 × 48=5 × 6 × five × 8 425 × 48=25 × 4 × forty-eight ÷ 4) On this basis, let the students summarize some regular things, clarify the context of knowledge, and form a good cognitive structure
thirdly, cultivate good habits and improve computing ability. Good learning habits are the driving force of students' sustainable development and an important guarantee for students to learn to learn, form learning ability and improve computing ability. In the calculation, we should focus on students to develop some good habits. 1. The habit of careful examination. Careful examination is the premise of correct and rapid calculation. 2. The habit of proofreading in time. 3. The habit of calculating carefully. When calculating, the format should be standard, the method should be reasonable, and the calculation process should be carefully checked. 4. The habit of consciously testing. In the calculation, we should develop the habit of self-conscious inspection, and correct mistakes in time. 5. Standardize the habit of writing. Scribble writing, disordered format, carelessness and carelessness are the main causes of calculation errors. To ensure the correctness of the calculation, we must develop a good habit of neat writing and standard format
computing teaching is a long-term and complex teaching process. It is not a matter of a day to improve students' computing ability. It is necessary to be regular, planned and step-by-step, speed in time, density in quantity, flexibility and novelty in form and content. Only when we teachers and students work together and persevere, can we achieve results. The above are my own teaching methods
6. How to improve the calculation ability of junior one students<
the traditional formulation of mathematical ability includes:
logical thinking ability,
basic operation ability,
space imagination ability,
Application of mathematical knowledge,
ability to analyze and solve practical problems and establish mathematical models< According to the ecational objectives, it can be divided into four aspects:
mathematical knowledge,
citizen consciousness,
social needs and language communication< As we all know,
computational ability is one of the most important abilities in mathematics. It can be said that if a student lacks computational ability,
mathematics is doomed to die
the most wonderful solution depends on calculation< No matter in primary school or middle school or even in the future university,
the level of computational ability determines students' mathematical development< Therefore,
the computational ability of students is very important
to cultivate middle school students' computing ability,
we must do a good job in the first grade of junior high school
when a tall building rises from the ground,
if the foundation of the building is not firm, the consequences can be known as
. The first grade of junior high school is the foundation stage, because it is the foundation, so it is more important< The first is the poor operation skills of primary school mathematics,
most students have formed the habit of doing problems blindly with time and sweat,
although they have done many problems,
they don't really think about it< The second is the inaccurate grasp of the concept of rational number and the key points of
rule< In my teaching practice,
I have focused on the following four aspects:
first, pay attention to the foundation, grasp the key,
"rational number"
as the foundation of algebra,
is arranged at the beginning of junior one
the mastery of knowledge in this unit determines the development of junior high school mathematics. Here, we must do the following points:
1
, pay attention to knowledge generation, based on long-term development: after the number axis, absolute value, opposite number and other related knowledge reserve, enter the rational number addition operation,
we should pay special attention to the discussion of each algorithm,
don't joke like some teachers,
say:
announce the calculation method directly in class,
then start to consolidate the topic
we must fully understand the concept of the new curriculum standard,
thoroughly understand the spirit of the new curriculum,
pay attention to the generation and development of students' knowledge
when exploring the rules, we should set up the appropriate situation around the students,
let the students fully observe, think, classify, discuss and express, and understand the rules with heart. Only in this way can the students accurately
use the rules correctly and flexibly< Compared with primary school mathematics, only because of the introction of "negative number"
, the balance of primary school calculation is completely broken. How many students do wrong calculations because of mistakes in symbols is obvious to all. For example:
calculate the following questions:
(1) - 1 + 3
(2) - 12-2
(3) (- 3) x (- 5)
solution
:
original formula
= - 4
solution
:
original formula
= - 10
solution
:
original formula
= - 15
the above are all caused by "qualitative". Therefore, the author thinks that whether it is rational number addition, subtraction, multiplication Qualitative should be put in the first place in any
operation of division and power! It's a big mistake. Secondly, the operation specification of calculation must be
strictly required,
great attention should be paid from the beginning of calculation
in order to break this qualitative,
when I teach the addition of rational numbers,
I did not strictly follow the standard mathematical language calculation rules,
instead, according to the actual situation, I arranged the popular language which is in line with the students' mind,
rational and interesting,
for example, when two numbers with the same number are added together, they are all negative family, love each other
together. When the two numbers of different signs are added, one goes to the East and the other to the West. The one who is strong will listen to the other and fight, and his strength will be weakened. In this way, students can master it well, and
are very willing to learn. But we must let the students understand that we are all classmates, and we should love each other, be friendly and help each other
3
, pay attention to mixed operation and strengthen operation sequence: mixed operation is an advanced stage of rational number operation, so we should pay special attention to operation sequence and standardize operation procere. In order to avoid detours, teachers require students to read the questions as a whole, observe the mixed
operations, which operations, whether there are brackets, what should be calculated first, what should be calculated later, and what kind of rules should be used for calculation,
teachers' blackboard writing should be neat,
and have the correct mathematical format to demonstrate the calculation process,
students should be ecated step by step,
steadily
timely "friendly reminder" should be given to students where they often make mistakes. Of course, they can fall down first and then turn stone into gold. This kind of memory is more profound
4
, remind students to be patient, careful and take part in the calculation with a certain right attitude. The writing steps are complete, and the key steps
are not omitted, reflecting the order and thinking of calculation<
2. Integral addition and subtraction connect the preceding and the following:
after the end of the rational number unit,
entered the real algebraic stage
"letter represents number"
,
and the
"integral addition and subtraction"
in the letter represents number unit
has become the highlight of calculation
in order to improve the calculation ability of integral addition and subtraction,
we must pay attention to the whole process of teaching, have an overall design on the macro level, and strengthen the standardization of operation process on the micro level<
1
, learn to divide the whole into parts first, and then learn to divide the whole into parts: the essence of addition and subtraction of integral is to merge the same kind of items. Therefore, we must first have a clear understanding of the same
kind of items: the same kind of items must have two conditions:
(1)
contain the same letter
(2)
the index of the same letter is also
the same
these two conditions are indispensable
after correctly identifying the similar items,
through teaching exploration, let the students know that merging similar items is actually
the addition and subtraction of coefficients, while the letters and their indexes remain unchanged. There are two bottlenecks for students to learn the knowledge of removing brackets:
(1)
, symbol error
(2)
, missed multiplication<
for these two thorny problems,
abstract generalization is very important when learning to remove brackets< In practical teaching,
after summarizing the rule of removing brackets,
is condensed into "
'+'
(
) invariant sign
'-
'
(
) to change the sign
"catchy, students have great interest in
and have clear memory< When using the law of multiplication and distribution to remove brackets,
we should pay attention to multiply each item in brackets with a number,
just like
sharing moon cakes with each child in the class,
if we don't give Li Si food,
he will cry,
no one will be happy if he doesn't give it to anyone
therefore, every
child should be given moon cakes
2
, pay attention to the operating proceres, strengthen the calculation details: details determine success or failure, and the calculation problem is one vote veto: one step wrong step by step
wrong. Therefore, in teaching, it is necessary to standardize the steps of problem-solving, make clear which steps the integral addition and subtraction have, and make clear what should be
done in each step. Through examples and students' practice, the steps of integral addition and subtraction are summarized as follows:
1
remove brackets
2
marker
3
exchange
4
merge. In this way, students can operate step by step and rece the blindness of calculation, so as to improve their calculation ability
3
, point out the way to solve the problem, recognize the essence of the problem: in the integral addition and subtraction, there are many types of questions. For example,
students tend to think in a fixed way,
they replace letters with numbers and directly put them into integral expressions for calculation,
they lose their mind and ignore the complexity of algebraic expressions
the teacher must point to the right place,
let the students understand that it is the best policy to simplify the integral before substituting it into the evaluation. Another example is to interpret the problem of "the results of
...
do not contain
x
items, and seek the value of
m
". When learning
students to solve problems, they are blinded and cannot be considered comprehensively. Here, the teacher must point out:
"the result does not contain the
x
term, which means that the coefficient of the
x
term
= 0
after the simplification and combination of this algebraic formula
"in a word, the teacher should let the students think about the new problems in time, try to solve them, and then enlighten the students. No matter what kind of questions, if most of the students have deviation, as
teachers must seriously consider and summarize in time,
only in this way,
can improve the students' calculation ability of integral addition and subtraction to a new level.
the traditional formulation of mathematical ability includes:
logical thinking ability,
basic operation ability,
space imagination ability,
Application of mathematical knowledge,
ability to analyze and solve practical problems and establish mathematical models< According to the ecational objectives, it can be divided into four aspects:
mathematical knowledge,
citizen consciousness,
social needs and language communication< As we all know,
computational ability is one of the most important abilities in mathematics. It can be said that if a student lacks computational ability,
mathematics is doomed to die
the most wonderful solution depends on calculation< No matter in primary school or middle school or even in the future university,
the level of computational ability determines students' mathematical development< Therefore,
the computational ability of students is very important
to cultivate middle school students' computing ability,
we must do a good job in the first grade of junior high school
when a tall building rises from the ground,
if the foundation of the building is not firm, the consequences can be known as
. The first grade of junior high school is the foundation stage, because it is the foundation, so it is more important< The first is the poor operation skills of primary school mathematics,
most students have formed the habit of doing problems blindly with time and sweat,
although they have done many problems,
they don't really think about it< The second is the inaccurate grasp of the concept of rational number and the key points of
rule< In my teaching practice,
I have focused on the following four aspects:
first, pay attention to the foundation, grasp the key,
"rational number"
as the foundation of algebra,
is arranged at the beginning of junior one
the mastery of knowledge in this unit determines the development of junior high school mathematics. Here, we must do the following points:
1
, pay attention to knowledge generation, based on long-term development: after the number axis, absolute value, opposite number and other related knowledge reserve, enter the rational number addition operation,
we should pay special attention to the discussion of each algorithm,
don't joke like some teachers,
say:
announce the calculation method directly in class,
then start to consolidate the topic
we must fully understand the concept of the new curriculum standard,
thoroughly understand the spirit of the new curriculum,
pay attention to the generation and development of students' knowledge
when exploring the rules, we should set up the appropriate situation around the students,
let the students fully observe, think, classify, discuss and express, and understand the rules with heart. Only in this way can the students accurately
use the rules correctly and flexibly< Compared with primary school mathematics, only because of the introction of "negative number"
, the balance of primary school calculation is completely broken. How many students do wrong calculations because of mistakes in symbols is obvious to all. For example:
calculate the following questions:
(1) - 1 + 3
(2) - 12-2
(3) (- 3) x (- 5)
solution
:
original formula
= - 4
solution
:
original formula
= - 10
solution
:
original formula
= - 15
the above are all caused by "qualitative". Therefore, the author thinks that whether it is rational number addition, subtraction, multiplication Qualitative should be put in the first place in any
operation of division and power! It's a big mistake. Secondly, the operation specification of calculation must be
strictly required,
great attention should be paid from the beginning of calculation
in order to break this qualitative,
when I teach the addition of rational numbers,
I did not strictly follow the standard mathematical language calculation rules,
instead, according to the actual situation, I arranged the popular language which is in line with the students' mind,
rational and interesting,
for example, when two numbers with the same number are added together, they are all negative family, love each other
together. When the two numbers of different signs are added, one goes to the East and the other to the West. The one who is strong will listen to the other and fight, and his strength will be weakened. In this way, students can master it well, and
are very willing to learn. But we must let the students understand that we are all classmates, and we should love each other, be friendly and help each other
3
, pay attention to mixed operation and strengthen operation sequence: mixed operation is an advanced stage of rational number operation, so we should pay special attention to operation sequence and standardize operation procere. In order to avoid detours, teachers require students to read the questions as a whole, observe the mixed
operations, which operations, whether there are brackets, what should be calculated first, what should be calculated later, and what kind of rules should be used for calculation,
teachers' blackboard writing should be neat,
and have the correct mathematical format to demonstrate the calculation process,
students should be ecated step by step,
steadily
timely "friendly reminder" should be given to students where they often make mistakes. Of course, they can fall down first and then turn stone into gold. This kind of memory is more profound
4
, remind students to be patient, careful and take part in the calculation with a certain right attitude. The writing steps are complete, and the key steps
are not omitted, reflecting the order and thinking of calculation<
2. Integral addition and subtraction connect the preceding and the following:
after the end of the rational number unit,
entered the real algebraic stage
"letter represents number"
,
and the
"integral addition and subtraction"
in the letter represents number unit
has become the highlight of calculation
in order to improve the calculation ability of integral addition and subtraction,
we must pay attention to the whole process of teaching, have an overall design on the macro level, and strengthen the standardization of operation process on the micro level<
1
, learn to divide the whole into parts first, and then learn to divide the whole into parts: the essence of addition and subtraction of integral is to merge the same kind of items. Therefore, we must first have a clear understanding of the same
kind of items: the same kind of items must have two conditions:
(1)
contain the same letter
(2)
the index of the same letter is also
the same
these two conditions are indispensable
after correctly identifying the similar items,
through teaching exploration, let the students know that merging similar items is actually
the addition and subtraction of coefficients, while the letters and their indexes remain unchanged. There are two bottlenecks for students to learn the knowledge of removing brackets:
(1)
, symbol error
(2)
, missed multiplication<
for these two thorny problems,
abstract generalization is very important when learning to remove brackets< In practical teaching,
after summarizing the rule of removing brackets,
is condensed into "
'+'
(
) invariant sign
'-
'
(
) to change the sign
"catchy, students have great interest in
and have clear memory< When using the law of multiplication and distribution to remove brackets,
we should pay attention to multiply each item in brackets with a number,
just like
sharing moon cakes with each child in the class,
if we don't give Li Si food,
he will cry,
no one will be happy if he doesn't give it to anyone
therefore, every
child should be given moon cakes
2
, pay attention to the operating proceres, strengthen the calculation details: details determine success or failure, and the calculation problem is one vote veto: one step wrong step by step
wrong. Therefore, in teaching, it is necessary to standardize the steps of problem-solving, make clear which steps the integral addition and subtraction have, and make clear what should be
done in each step. Through examples and students' practice, the steps of integral addition and subtraction are summarized as follows:
1
remove brackets
2
marker
3
exchange
4
merge. In this way, students can operate step by step and rece the blindness of calculation, so as to improve their calculation ability
3
, point out the way to solve the problem, recognize the essence of the problem: in the integral addition and subtraction, there are many types of questions. For example,
students tend to think in a fixed way,
they replace letters with numbers and directly put them into integral expressions for calculation,
they lose their mind and ignore the complexity of algebraic expressions
the teacher must point to the right place,
let the students understand that it is the best policy to simplify the integral before substituting it into the evaluation. Another example is to interpret the problem of "the results of
...
do not contain
x
items, and seek the value of
m
". When learning
students to solve problems, they are blinded and cannot be considered comprehensively. Here, the teacher must point out:
"the result does not contain the
x
term, which means that the coefficient of the
x
term
= 0
after the simplification and combination of this algebraic formula
"in a word, the teacher should let the students think about the new problems in time, try to solve them, and then enlighten the students. No matter what kind of questions, if most of the students have deviation, as
teachers must seriously consider and summarize in time,
only in this way,
can improve the students' calculation ability of integral addition and subtraction to a new level.
7. 1、 Pay attention to the process teaching of calculation theory and rule, and improve the calculation skills
calculation principles and rules are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, I first guide the students to talk about the calculation theory and summarize the rules. For example, when I talk about fraction addition with the same denominator, I can do it like this: first use the graph to show it, and then ask the question: what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). And let the students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators
the calculation method is programmed and regularized, and can be mastered only by mechanical training, but it can not adapt to the ever-changing specific situation, let alone flexible application. Therefore, we must deal with the relationship between theory and algorithm, guide students to follow "theory" into "method", and control "method" with "theory", and promote the formation of computational skills through intellectual activities. If students don't understand the concept of digits, they can't understand the principle of digit alignment in written calculation: if they don't understand the basic properties of decimals, they can't transform the division of decimals into the division of integers; If we don't know the meaning of the four operations, it's difficult to explain the calculation rules. To make students understand the concepts of number and four arithmetic correctly is the premise of mastering the four arithmetic. Therefore, it is necessary to explain the knowledge of number and four arithmetic in teaching. In normal teaching, the meaning of four operations can be graally formed and deepened in the process of solving problems. Calculation rules are the basis for students to carry out four operations correctly. We can pay attention to the steps and methods of calculation through typical examples. The laws and properties of operation are the basis of clarifying the laws of calculation and simple algorithms. Students can be guided to observe, compare, analyze and find out the common characteristics through the calculation of specific formula questions, and then summarize them, so that students can understand the practical significance of the laws and properties. We should pay special attention to make students learn to apply the laws and properties of operation on the basis of students' understanding, and make some simple calculation methods, so as to continuously improve students' calculation ability< Second, strengthen the basic training and cultivate the ability of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation
for example, the decomposition of numbers within 10, the addition and subtraction of numbers within 20, and the multiplication and division method in the table are the key to improve the accuracy of calculation. In addition, according to the learning content of different grades, let students memorize some data with high frequency of use, such as grade 25 × 4=100、125 × 8=1000 Senior grade: the denominator is 2, 4, 5, 8, 20, 25 of the simplest true score of the small value, percentage value, 1 ~ 20 of the square value, so that students form skilled oral skills, to achieve correct, rapid, flexible calculation
2. Strengthen the training of estimation and develop students' thinking. Estimation is the ability to approximate or roughly estimate the operation process or result. Estimation is helpful for students to find out their deviation in solving problems, to rethink and calculate, so as to improve their computing ability. In teaching, teachers should teach students some estimation methods, so that students can form a correct direction of thinking and improve the accuracy of calculation
for example: multiply multiple numbers, master the number of digits and mantissa of the proct; Four decimal calculation, to see the positioning of the decimal point. According to the characteristics of the formula, the estimation result is a common estimation method, such as 25 × 85, because 0. 85 is less than 1, so 25 × 85 is less than 25; one hundred ÷ 0.25, because 0.25 is less than 1, so 100 ÷ The quotient of 0.25 is greater than 100, etc. in this way, once obvious errors are found, they can be corrected in time, which provides a guarantee for the acquisition of correct answers and trains the correctness of students' thinking
in addition, the estimation is also used in the calculation of applied problems, such as average applied problem: there are 10 grannies in the nursing home, with an average age of 80.5 years old, and 12 grandfathers, with an average age of 73.5 years old. The average age of the elderly in the hospital. Before answering the question, ask the students to estimate the average age of the elderly. With the estimation results, we can avoid (80.5 + 73.5) ÷ 10 + 12) ≈ 7 years old
in teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
3. Strengthen the simple calculation training to improve the calculation efficiency. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. In calculation, students are easy to apply and abuse some properties and laws. Let students do some contrast exercises, diagnose mistakes by themselves, reflect on the wrong nodes of calculation, and prevent the same mistakes from happening again. For example: 300-175 + 25300-1
calculation principles and rules are the basis of calculation. The correct operation must be based on a thorough understanding of the calculation principle. The calculation principle in the students' mind is clear and the rules are firmly remembered. When they do four calculation problems, they can proceed in an orderly way. How to clarify the calculation? For example, in the teaching of fraction addition, I first guide the students to talk about the calculation theory and summarize the rules. For example, when I talk about fraction addition with the same denominator, I can do it like this: first use the graph to show it, and then ask the question: what are the fractional units of the two fractions? How many units are there? How much is one plus two? By calculating this problem, can you summarize the rules of adding fractions with the same denominator Guide the students to narrate in their own language. At this time, the students' narration may be incomplete). And let the students think again: how to calculate? And explain the reasons. On this basis, the conclusion is: add and subtract fractions with the same denominator, add and subtract molecules, and the denominator remains unchanged. In this way, the students not only have a clear understanding of the calculation theory, but also have a good command of the rules, which lays a foundation for learning the addition and subtraction method of different denominators
the calculation method is programmed and regularized, and can be mastered only by mechanical training, but it can not adapt to the ever-changing specific situation, let alone flexible application. Therefore, we must deal with the relationship between theory and algorithm, guide students to follow "theory" into "method", and control "method" with "theory", and promote the formation of computational skills through intellectual activities. If students don't understand the concept of digits, they can't understand the principle of digit alignment in written calculation: if they don't understand the basic properties of decimals, they can't transform the division of decimals into the division of integers; If we don't know the meaning of the four operations, it's difficult to explain the calculation rules. To make students understand the concepts of number and four arithmetic correctly is the premise of mastering the four arithmetic. Therefore, it is necessary to explain the knowledge of number and four arithmetic in teaching. In normal teaching, the meaning of four operations can be graally formed and deepened in the process of solving problems. Calculation rules are the basis for students to carry out four operations correctly. We can pay attention to the steps and methods of calculation through typical examples. The laws and properties of operation are the basis of clarifying the laws of calculation and simple algorithms. Students can be guided to observe, compare, analyze and find out the common characteristics through the calculation of specific formula questions, and then summarize them, so that students can understand the practical significance of the laws and properties. We should pay special attention to make students learn to apply the laws and properties of operation on the basis of students' understanding, and make some simple calculation methods, so as to continuously improve students' calculation ability< Second, strengthen the basic training and cultivate the ability of calculation. Oral arithmetic is a basic skill that students must master. It is one of the most basic and important skills in mathematics learning. Oral arithmetic is related to learning and mastering a series of contents, such as addition and subtraction of multiple digits, multiplication and division, and four calculation of decimal and fraction In the first and second paragraph of mathematics curriculum standard, it is emphasized to pay attention to oral arithmetic. Therefore, primary school calculation teaching should pay special attention to the training of oral calculation
for example, the decomposition of numbers within 10, the addition and subtraction of numbers within 20, and the multiplication and division method in the table are the key to improve the accuracy of calculation. In addition, according to the learning content of different grades, let students memorize some data with high frequency of use, such as grade 25 × 4=100、125 × 8=1000 Senior grade: the denominator is 2, 4, 5, 8, 20, 25 of the simplest true score of the small value, percentage value, 1 ~ 20 of the square value, so that students form skilled oral skills, to achieve correct, rapid, flexible calculation
2. Strengthen the training of estimation and develop students' thinking. Estimation is the ability to approximate or roughly estimate the operation process or result. Estimation is helpful for students to find out their deviation in solving problems, to rethink and calculate, so as to improve their computing ability. In teaching, teachers should teach students some estimation methods, so that students can form a correct direction of thinking and improve the accuracy of calculation
for example: multiply multiple numbers, master the number of digits and mantissa of the proct; Four decimal calculation, to see the positioning of the decimal point. According to the characteristics of the formula, the estimation result is a common estimation method, such as 25 × 85, because 0. 85 is less than 1, so 25 × 85 is less than 25; one hundred ÷ 0.25, because 0.25 is less than 1, so 100 ÷ The quotient of 0.25 is greater than 100, etc. in this way, once obvious errors are found, they can be corrected in time, which provides a guarantee for the acquisition of correct answers and trains the correctness of students' thinking
in addition, the estimation is also used in the calculation of applied problems, such as average applied problem: there are 10 grannies in the nursing home, with an average age of 80.5 years old, and 12 grandfathers, with an average age of 73.5 years old. The average age of the elderly in the hospital. Before answering the question, ask the students to estimate the average age of the elderly. With the estimation results, we can avoid (80.5 + 73.5) ÷ 10 + 12) ≈ 7 years old
in teaching, let students estimate, and combine calculation teaching with estimation teaching organically, so that students' calculation ability and estimation ability will be improved, killing two birds with one stone. It is very helpful to improve students' calculation quality and train good thinking to carry out estimation training at any time, deepen students' understanding of calculation theory and methods, clarify the range of answers and rece errors
3. Strengthen the simple calculation training to improve the calculation efficiency. Simple calculation is an important part of primary school calculation teaching. It requires students to make full use of the learned operation laws, properties and formulas, reasonably change the operation data and operation order, make the calculation as simple and fast as possible, and improve the calculation efficiency. Therefore, in teaching, we must strengthen the training of simple calculation, graally enhance the consciousness of simple calculation and improve the ability of simple calculation. In calculation, students are easy to apply and abuse some properties and laws. Let students do some contrast exercises, diagnose mistakes by themselves, reflect on the wrong nodes of calculation, and prevent the same mistakes from happening again. For example: 300-175 + 25300-1
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