Analytical calculation of force
Publish: 2021-04-20 23:08:02
1. There are two reasons why calculation always makes mistakes. One is technical, that is, the principle is not clear and the concept is confused, so it is easy to make mistakes. On the other hand, it is perceptual, e to carelessness. There are two ways to improve the computing ability: one is to strengthen the concept and principle of computing, the other is to focus on the training of the degree of care. Most of the children's calculation errors are caused by carelessness, which can be targeted for intensive training, but this is only a temporary training method. In the long run, it is necessary to cultivate children's carefulness in their daily study and life, do things in a planned way, and only good habits are the root causes
1. Strengthen the teaching of basic knowledge and skills to improve the rationality of operation. In teaching, basic knowledge is the basis of calculation theory, which has guiding significance for calculation. The confusion and fuzziness of basic knowledge and the fact that basic knowledge is too hard are often the root causes of calculation errors. Therefore, strengthening and implementing double base teaching is a very practical problem to improve calculation ability
2. Pay attention to the cultivation of students' practical ability and improve the simplicity of operation. In the normal teaching process, teachers must spare no time for students to practice more. On the basis of understanding theorems, formulas, algorithms, etc., they should also practice more to consolidate their memory and deepen their impression. If necessary, the effect will be better if some knowledge points are subject intensive training. Through the questionnaire survey, 80% of the students think that this kind of special topic examination training effect is very good
3. Pay attention to variant training and improve the proficiency of calculation. When commenting on an examination question, teachers should not only be satisfied with explaining the question thoroughly, but also be good at extending the variant of the question and drawing inferences from one instance. Only in this way can students "see both trees and forests" and get twice the result with half the effort. This requires teachers to be good at knowledge accumulation and summary
4. Pay attention to the standardization of problem solving process and improve the accuracy of calculation. Some teachers pay more attention to the analysis of the law of problem solving, thinking and the internal relationship of knowledge when commenting on test questions, but they do not pay enough attention to the process of problem solving, such as the standardization of writing, the skills and accuracy of calculation, etc., resulting in the situation that students can not get full marks or can not get full marks. This requires teachers to standardize writing and attach importance to their exemplary role
in the process of improving students' mathematical operation ability, we must be patient. In the process of training, in addition to explaining the basic concepts, theorems and rules, we should also cultivate students' memory ability, observation ability, understanding ability, associative ability, expression ability, logical thinking ability and other mathematical abilities in a purposeful, step-by-step and hierarchical way, and conct appropriate exercises, Only in this way can we improve the students' mathematical operation ability, so as to improve their ability of learning mathematics.
1. Strengthen the teaching of basic knowledge and skills to improve the rationality of operation. In teaching, basic knowledge is the basis of calculation theory, which has guiding significance for calculation. The confusion and fuzziness of basic knowledge and the fact that basic knowledge is too hard are often the root causes of calculation errors. Therefore, strengthening and implementing double base teaching is a very practical problem to improve calculation ability
2. Pay attention to the cultivation of students' practical ability and improve the simplicity of operation. In the normal teaching process, teachers must spare no time for students to practice more. On the basis of understanding theorems, formulas, algorithms, etc., they should also practice more to consolidate their memory and deepen their impression. If necessary, the effect will be better if some knowledge points are subject intensive training. Through the questionnaire survey, 80% of the students think that this kind of special topic examination training effect is very good
3. Pay attention to variant training and improve the proficiency of calculation. When commenting on an examination question, teachers should not only be satisfied with explaining the question thoroughly, but also be good at extending the variant of the question and drawing inferences from one instance. Only in this way can students "see both trees and forests" and get twice the result with half the effort. This requires teachers to be good at knowledge accumulation and summary
4. Pay attention to the standardization of problem solving process and improve the accuracy of calculation. Some teachers pay more attention to the analysis of the law of problem solving, thinking and the internal relationship of knowledge when commenting on test questions, but they do not pay enough attention to the process of problem solving, such as the standardization of writing, the skills and accuracy of calculation, etc., resulting in the situation that students can not get full marks or can not get full marks. This requires teachers to standardize writing and attach importance to their exemplary role
in the process of improving students' mathematical operation ability, we must be patient. In the process of training, in addition to explaining the basic concepts, theorems and rules, we should also cultivate students' memory ability, observation ability, understanding ability, associative ability, expression ability, logical thinking ability and other mathematical abilities in a purposeful, step-by-step and hierarchical way, and conct appropriate exercises, Only in this way can we improve the students' mathematical operation ability, so as to improve their ability of learning mathematics.
2. The ratio increasing method and the equal difference increasing method are two methods to calculate the rent in the leasing business. According to its basic formula, we can dece and calculate that if the rent is calculated and paid according to the equal proportion increasing method, the actual rent rate will drop, or even drop by a large margin, resulting in the loss of the interests of the lessor; If the rent is calculated according to the equal difference increasing method, the actual rent rate is always equal to the nominal rent rate, and the calculation is simple. Therefore, the equal difference incremental method is more fair, reasonable and practical than the equal ratio incremental method
with the continuous deepening of China's middle school teaching reform, the Shanghai primary and secondary school mathematics curriculum standard (Trial draft) proposes to vigorously promote the digital mathematics activity (Dima) based on modern information technology, and establish the digital mathematics activity system based on computers and calculators (including scientific calculators Function calculator and graphic calculator) as the support, has intelligent software and rich courseware, connection information network Dima platform. Using this platform, we can improve the processing and presentation of mathematics content, and let students learn independently in the information technology environment, and carry out experiments, exploration and research
today, when we vigorously promote the universal application of information technology in the teaching process and promote the integration of information technology and subject curriculum, our school is also implementing the curriculum reform, and the graphic calculator is also applied to the classroom of mathematics expansion course. For this reason, we designed a teaching case of "using graphic calculator to study several methods of expressing arithmetic and proportional sequence"< Teaching background:
in the chapter of sequence, when explaining the concepts of arithmetic sequence and arithmetic sequence, the content is relatively simple and easy for students to master. It is the basis of learning sequence, which is helpful to cultivate students' observation ability and inction ability. The contents of the equal ratio sequence and the equal difference sequence are completely parallel, including the definition, the nature, the formula of the general term, the equal ratio (difference) median of two numbers, etc
after more than half a year of using graphic calculators, senior one students have a preliminary understanding of using graphic calculators to analyze, construct and explore mathematical problems. They felt that the use of graphic calculator not only changed their way of learning mathematics, but also increased their interest in learning mathematics. They like this "do math" way of learning very much
Graphic Calculator has many functions to use sequence, such as the use of general formula and recursive formula of sequence, sequence image and image tracking function, expression function of sequence operation table, iteration function of sequence, programming function of sequence, etc. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation< The design concept of the lesson is the core of the whole series knowledge learning. Conjecture, inction, recursion, analogy and other mathematical ideas are fully reflected in the learning of these two basic knowledge, which can be described as "although a sparrow is small, it has all five internal organs". However, it is difficult to fully and correctly show these in the traditional sequence teaching. This will lead to students' one-sided understanding of what they have learned, which will have a negative impact on the follow-up study of sequence. The graphic calculator has many functions to use the sequence, such as the use of the general formula and recursive formula, the image and image tracking function, the expression function of the operation table, the iteration function and the programming function of the sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. Therefore, we envisage that students can have a clear understanding of the two conventional series by studying and expressing the series with graphic calculator. At the same time, we also want to cultivate students' initiative and inquiry spirit and improve their mathematics learning ability through this learning process<
Design and Implementation:
the teaching content of the new textbook pays more attention to the integration of function thought and computer technology. From the beginning of this chapter, the textbook puts the number sequence in the context of function and gives the definition: the number sequence is a function with a positive integer set (or its finite subset) as the domain of definition. When the independent variable values in the order from small to large, the corresponding function value is the term of the number sequence. Sequence is a kind of discrete function. In the allocation of exercises, teaching materials are often compared with function teaching. The general term formula, recurrence formula and image of arithmetic sequence and proportional sequence are the main contents of our research in this lesson. We imagine that with the help of graphic calculator, we can make students have a vivid, comprehensive and correct understanding of sequence knowledge by doing mathematics, so as to improve students' mathematical thinking ability and cultivate students' correct mathematical view, Really improve students' interest in mathematics learning
case 1 (1) find the 11th term of the arithmetic sequence - 121, - 110, - 99, - 88,...
2) write the general term formula and recurrence formula of the sequence
for this problem, in fact, according to its basic law, you can calculate the result. But using graphic calculator can make us think about the solution of the problem from many angles, which is concive to students' comprehensive and correct understanding of the characteristics of arithmetic sequence, so as to simplify the calculation
method 1: use the numerical iteration function (as shown in Figure 1):
①
method 2: use the array function of the graphic calculator (as shown in Figure 2):
②
method 3: use the recursive function of the calculator
Figure 3: Use & iquest on the premise of setting the function function function; Key, which is the same as Figure 1< Method 4: guess the recurrence formula and the general term formula of the sequence, check whether the recurrence formula and the general term formula of the sequence are correct through the sequence related function of the calculator, and calculate the 11th term of the sequence:
Figure 4 guesses the recurrence formula of the sequence according to the characteristics of the sequence, Using the function of figure calculator, using Y & # 39; Draw a table
④
Fig. Then, we also use y & # 39; Draw a table< Note: while solving this problem, we can also verify that "the general term formula of arithmetic sequence is a special first-order function" through graphic calculator
as shown in Figure 7, we can get that the image of sequence is a discrete point on a straight line, from which we can see that sequence is a special function< Method 5: because the number sequence is a special function, we use the function of graphic calculator to think about the problem.
figure 8 is under the cognitive condition of "the number sequence is a special function", we use the function of calculator to get the function y = - 121 + 11 (x-1), and use the connection between the function and the number sequence an = - 121 + (n-1) to think about the related problems of the number sequence< Method 6: make full use of the function fitting function of the graphic calculator to get the general term formula of the sequence through the combination of number and shape
Figure 9: use the linear regression function of the graphic calculator to list the table of the sequence first, and then connect the general term formula of the arithmetic sequence with the first-order function according to the data in the table, By using the fitting function of graphic calculator, the function relation is obtained, and the general term formula of sequence is obtained< Method 7: use the programming function of graphic calculator to solve the problem of sequence (as shown in Figure 10)
10
comments: Method 1 and method 2 use the iterative function of calculator, but method 2 shows the corresponding relationship between the serial number and the value of the item in the sequence, from which we initially realize that the sequence is a special function
the fourth method is to guess the recurrence formula and general term formula of the sequence, under the support of the sequence function of the calculator, from the operation table of the sequence or the tracking of the image of the sequence to verify whether your guess is correct, and get the answer to the problem to be solved. This kind of learning method is helpful to cultivate students' ability of analysis, conjecture, demonstration and inction. This is what we lack in our regular learning, and the use of graphic calculator has built us such a learning method platform
method 6 and method 7 are both under the condition that the number sequence is a special function. Supported by the function function of the calculator, we find a way to solve the problem by guessing or fitting the analytic formula of the function, which is helpful for students to learn the knowledge of the number sequence and understand the characteristics of the number sequence, Method 8 adopts the programming function of graphic calculator, which can't be achieved in general mathematics teaching. It reveals the essence of arithmetic sequence from another perspective< (3) is 209 the item in the sequence, and if so, what is it< Method 1, array method 2, table method 3, image method 4, equation solving method the purpose of setting this question is: on the basis of the first question, using the functions of operation, tracking and equation solving of graphic calculator to cultivate students' reverse thinking and improve their mathematical thinking ability
it should be pointed out that the sequence we discussed above is tolerance D & gt; 0, for beginners, they often have certain thinking set, such as: "tolerance D & gt; In order to avoid similar problems, we especially remind students to pay attention to the differences between the following two types of sequence
(1) constant sequence (2) arithmetic sequence with negative tolerance
- 2, - 2,... 3, 1, - 1, - 3, ...
students should have a correct understanding of the dialectical relationship between general and special<
case 2: make up a topic of equal ratio series, and study the related properties of equal ratio series
find out typical problems from students' many problems, and study them together with teachers and students, including the examples in the book
(in real life, such as loan to buy a house, population growth and the change of housing area - pay attention to the hot issues around the people, Pay attention to guide students to apply their knowledge to related subjects, life and proction practice, so that students can develop their thinking ability while acquiring and applying knowledge, so that students can use existing knowledge to communicate, and abstract practical problems into mathematical problems and establish mathematical models.)
such as "a foot of the hammer, half of the day, never exhausted", and asked to say its mathematical model, find out its general formula
(both new and old textbooks and textbooks are being compiled, etc.)
with the continuous deepening of China's middle school teaching reform, the Shanghai primary and secondary school mathematics curriculum standard (Trial draft) proposes to vigorously promote the digital mathematics activity (Dima) based on modern information technology, and establish the digital mathematics activity system based on computers and calculators (including scientific calculators Function calculator and graphic calculator) as the support, has intelligent software and rich courseware, connection information network Dima platform. Using this platform, we can improve the processing and presentation of mathematics content, and let students learn independently in the information technology environment, and carry out experiments, exploration and research
today, when we vigorously promote the universal application of information technology in the teaching process and promote the integration of information technology and subject curriculum, our school is also implementing the curriculum reform, and the graphic calculator is also applied to the classroom of mathematics expansion course. For this reason, we designed a teaching case of "using graphic calculator to study several methods of expressing arithmetic and proportional sequence"< Teaching background:
in the chapter of sequence, when explaining the concepts of arithmetic sequence and arithmetic sequence, the content is relatively simple and easy for students to master. It is the basis of learning sequence, which is helpful to cultivate students' observation ability and inction ability. The contents of the equal ratio sequence and the equal difference sequence are completely parallel, including the definition, the nature, the formula of the general term, the equal ratio (difference) median of two numbers, etc
after more than half a year of using graphic calculators, senior one students have a preliminary understanding of using graphic calculators to analyze, construct and explore mathematical problems. They felt that the use of graphic calculator not only changed their way of learning mathematics, but also increased their interest in learning mathematics. They like this "do math" way of learning very much
Graphic Calculator has many functions to use sequence, such as the use of general formula and recursive formula of sequence, sequence image and image tracking function, expression function of sequence operation table, iteration function of sequence, programming function of sequence, etc. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation< The design concept of the lesson is the core of the whole series knowledge learning. Conjecture, inction, recursion, analogy and other mathematical ideas are fully reflected in the learning of these two basic knowledge, which can be described as "although a sparrow is small, it has all five internal organs". However, it is difficult to fully and correctly show these in the traditional sequence teaching. This will lead to students' one-sided understanding of what they have learned, which will have a negative impact on the follow-up study of sequence. The graphic calculator has many functions to use the sequence, such as the use of the general formula and recursive formula, the image and image tracking function, the expression function of the operation table, the iteration function and the programming function of the sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. Therefore, we envisage that students can have a clear understanding of the two conventional series by studying and expressing the series with graphic calculator. At the same time, we also want to cultivate students' initiative and inquiry spirit and improve their mathematics learning ability through this learning process<
Design and Implementation:
the teaching content of the new textbook pays more attention to the integration of function thought and computer technology. From the beginning of this chapter, the textbook puts the number sequence in the context of function and gives the definition: the number sequence is a function with a positive integer set (or its finite subset) as the domain of definition. When the independent variable values in the order from small to large, the corresponding function value is the term of the number sequence. Sequence is a kind of discrete function. In the allocation of exercises, teaching materials are often compared with function teaching. The general term formula, recurrence formula and image of arithmetic sequence and proportional sequence are the main contents of our research in this lesson. We imagine that with the help of graphic calculator, we can make students have a vivid, comprehensive and correct understanding of sequence knowledge by doing mathematics, so as to improve students' mathematical thinking ability and cultivate students' correct mathematical view, Really improve students' interest in mathematics learning
case 1 (1) find the 11th term of the arithmetic sequence - 121, - 110, - 99, - 88,...
2) write the general term formula and recurrence formula of the sequence
for this problem, in fact, according to its basic law, you can calculate the result. But using graphic calculator can make us think about the solution of the problem from many angles, which is concive to students' comprehensive and correct understanding of the characteristics of arithmetic sequence, so as to simplify the calculation
method 1: use the numerical iteration function (as shown in Figure 1):
①
method 2: use the array function of the graphic calculator (as shown in Figure 2):
②
method 3: use the recursive function of the calculator
Figure 3: Use & iquest on the premise of setting the function function function; Key, which is the same as Figure 1< Method 4: guess the recurrence formula and the general term formula of the sequence, check whether the recurrence formula and the general term formula of the sequence are correct through the sequence related function of the calculator, and calculate the 11th term of the sequence:
Figure 4 guesses the recurrence formula of the sequence according to the characteristics of the sequence, Using the function of figure calculator, using Y & # 39; Draw a table
④
Fig. Then, we also use y & # 39; Draw a table< Note: while solving this problem, we can also verify that "the general term formula of arithmetic sequence is a special first-order function" through graphic calculator
as shown in Figure 7, we can get that the image of sequence is a discrete point on a straight line, from which we can see that sequence is a special function< Method 5: because the number sequence is a special function, we use the function of graphic calculator to think about the problem.
figure 8 is under the cognitive condition of "the number sequence is a special function", we use the function of calculator to get the function y = - 121 + 11 (x-1), and use the connection between the function and the number sequence an = - 121 + (n-1) to think about the related problems of the number sequence< Method 6: make full use of the function fitting function of the graphic calculator to get the general term formula of the sequence through the combination of number and shape
Figure 9: use the linear regression function of the graphic calculator to list the table of the sequence first, and then connect the general term formula of the arithmetic sequence with the first-order function according to the data in the table, By using the fitting function of graphic calculator, the function relation is obtained, and the general term formula of sequence is obtained< Method 7: use the programming function of graphic calculator to solve the problem of sequence (as shown in Figure 10)
10
comments: Method 1 and method 2 use the iterative function of calculator, but method 2 shows the corresponding relationship between the serial number and the value of the item in the sequence, from which we initially realize that the sequence is a special function
the fourth method is to guess the recurrence formula and general term formula of the sequence, under the support of the sequence function of the calculator, from the operation table of the sequence or the tracking of the image of the sequence to verify whether your guess is correct, and get the answer to the problem to be solved. This kind of learning method is helpful to cultivate students' ability of analysis, conjecture, demonstration and inction. This is what we lack in our regular learning, and the use of graphic calculator has built us such a learning method platform
method 6 and method 7 are both under the condition that the number sequence is a special function. Supported by the function function of the calculator, we find a way to solve the problem by guessing or fitting the analytic formula of the function, which is helpful for students to learn the knowledge of the number sequence and understand the characteristics of the number sequence, Method 8 adopts the programming function of graphic calculator, which can't be achieved in general mathematics teaching. It reveals the essence of arithmetic sequence from another perspective< (3) is 209 the item in the sequence, and if so, what is it< Method 1, array method 2, table method 3, image method 4, equation solving method the purpose of setting this question is: on the basis of the first question, using the functions of operation, tracking and equation solving of graphic calculator to cultivate students' reverse thinking and improve their mathematical thinking ability
it should be pointed out that the sequence we discussed above is tolerance D & gt; 0, for beginners, they often have certain thinking set, such as: "tolerance D & gt; In order to avoid similar problems, we especially remind students to pay attention to the differences between the following two types of sequence
(1) constant sequence (2) arithmetic sequence with negative tolerance
- 2, - 2,... 3, 1, - 1, - 3, ...
students should have a correct understanding of the dialectical relationship between general and special<
case 2: make up a topic of equal ratio series, and study the related properties of equal ratio series
find out typical problems from students' many problems, and study them together with teachers and students, including the examples in the book
(in real life, such as loan to buy a house, population growth and the change of housing area - pay attention to the hot issues around the people, Pay attention to guide students to apply their knowledge to related subjects, life and proction practice, so that students can develop their thinking ability while acquiring and applying knowledge, so that students can use existing knowledge to communicate, and abstract practical problems into mathematical problems and establish mathematical models.)
such as "a foot of the hammer, half of the day, never exhausted", and asked to say its mathematical model, find out its general formula
(both new and old textbooks and textbooks are being compiled, etc.)
3. In high school mathematics learning, with the deepening of learning content, the level of operation is also constantly improving, and high school students are exposed to more and more problems in operation. Students do not pay enough attention to the improvement of operation ability, which not only affects the development of students' thinking ability, but also inevitably affects the improvement of teaching quality.
4. Calculation ability is accumulated over a long period of time. If you do more calculation problems, your calculation ability will naturally improve. Practice makes perfect. There is only one way to do more calculation problems.
5.
Normal stress = (2 * 50 * (root 2) / 2-20 * (root 2) / 2 / root 2 = 40 MPa (tensile stress)
shear stress = 20 * (root 2) / 2 / root 2 = 10 MPa
6. 1. Weak basic knowledge
the students with weak basic knowledge in the middle and lower part of their grades are most incisive. The full score of the test paper is 150 points, 145 points, the foundation is certainly no problem; If it's less than 90, you need to take a good look
the basic knowledge is not solid, and the required mathematical concepts, theorems, formulas and some commonly used data are vague, and the formulas and rules are ambiguous<
countermeasures:
decompose the main points, key points, difficulties and knowledge points to form their own knowledge structure system, so as to make them familiar with the heart, and understand the exercises at the back of the textbook
2. Poor basic computing ability
this problem is a legacy of history. If the computing ability is average in junior high school, it will also be affected in senior one; At the same time, it has something to do with habit. As long as it's a calculation problem, some students immediately take out their calculators and crackle the problem out. In the long run, their calculation ability is low<
countermeasures:
if you want to strengthen the calculation ability, you should not immerse yourself in the sea tactics, but find some ingenious problems, do more and summarize more, and master both the problem-solving method and the calculation method, so that practice can make perfect and steady. Remember, use calculators as little as possible
3. Poor logical reasoning ability
after doing the same type of questions over and over again, it won't work if you change the question method or make a change<
countermeasures:
as long as they are willing to summarize the problem-solving skills carefully, start from the foundation, practice more, summarize more, accumulate more, and spend more time to do
4. The answers are not standardized
some students write the answers before they finish reading the questions, and the accuracy can be imagined
for example, the writing of fractional expression is not standardized, the writing of general term and function expression is not standardized,
the writing of analytic expression of function is correct but the definition field is not indicated,
the result written as a set is not required to be represented by a set,
the object attribute description of set is inaccurate<
countermeasures:
be serious and careful when doing questions! In practice, the topic as an exam, after the calculation of scores. In this way, compared with yourself, because of the competitive psychology, you will be forced to be careful and standardized graally
5. The efficiency of doing questions before the exam is low
some students seem to be very diligent, but they can't pass the exam every time. Part of the reason is that the students' qualifications are mediocre, but some of them are really smart. Reason: not good at independent thinking, and wrong questions do not know how to summarize<
countermeasures:
usually form a good habit of summarizing and sorting. In view of the wrong questions, this paper establishes the mathematical wrong questions book, writes down the wrong reason and the correct method as well as the solution to this kind of problem
6. The speed of doing questions is not good
in every exam, some students will say: in fact, I can do all these questions, but I don't have time. The examination is fair, and the time given is reasonable. The examinee does not have time, but delays a lot of time in the front questions. The reason is that the speed of doing the questions is not good<
countermeasures:
in the big review to overcome their own problems, and then repeatedly practice to be able to do the problem speed! Fill in the blank choice and a few simple big questions, if put in the hands of students who do more basic questions, they will save more than ten minutes than other students, and the correct rate is very high, so they have more time to do the next big questions. Practice more to speed up.
the students with weak basic knowledge in the middle and lower part of their grades are most incisive. The full score of the test paper is 150 points, 145 points, the foundation is certainly no problem; If it's less than 90, you need to take a good look
the basic knowledge is not solid, and the required mathematical concepts, theorems, formulas and some commonly used data are vague, and the formulas and rules are ambiguous<
countermeasures:
decompose the main points, key points, difficulties and knowledge points to form their own knowledge structure system, so as to make them familiar with the heart, and understand the exercises at the back of the textbook
2. Poor basic computing ability
this problem is a legacy of history. If the computing ability is average in junior high school, it will also be affected in senior one; At the same time, it has something to do with habit. As long as it's a calculation problem, some students immediately take out their calculators and crackle the problem out. In the long run, their calculation ability is low<
countermeasures:
if you want to strengthen the calculation ability, you should not immerse yourself in the sea tactics, but find some ingenious problems, do more and summarize more, and master both the problem-solving method and the calculation method, so that practice can make perfect and steady. Remember, use calculators as little as possible
3. Poor logical reasoning ability
after doing the same type of questions over and over again, it won't work if you change the question method or make a change<
countermeasures:
as long as they are willing to summarize the problem-solving skills carefully, start from the foundation, practice more, summarize more, accumulate more, and spend more time to do
4. The answers are not standardized
some students write the answers before they finish reading the questions, and the accuracy can be imagined
for example, the writing of fractional expression is not standardized, the writing of general term and function expression is not standardized,
the writing of analytic expression of function is correct but the definition field is not indicated,
the result written as a set is not required to be represented by a set,
the object attribute description of set is inaccurate<
countermeasures:
be serious and careful when doing questions! In practice, the topic as an exam, after the calculation of scores. In this way, compared with yourself, because of the competitive psychology, you will be forced to be careful and standardized graally
5. The efficiency of doing questions before the exam is low
some students seem to be very diligent, but they can't pass the exam every time. Part of the reason is that the students' qualifications are mediocre, but some of them are really smart. Reason: not good at independent thinking, and wrong questions do not know how to summarize<
countermeasures:
usually form a good habit of summarizing and sorting. In view of the wrong questions, this paper establishes the mathematical wrong questions book, writes down the wrong reason and the correct method as well as the solution to this kind of problem
6. The speed of doing questions is not good
in every exam, some students will say: in fact, I can do all these questions, but I don't have time. The examination is fair, and the time given is reasonable. The examinee does not have time, but delays a lot of time in the front questions. The reason is that the speed of doing the questions is not good<
countermeasures:
in the big review to overcome their own problems, and then repeatedly practice to be able to do the problem speed! Fill in the blank choice and a few simple big questions, if put in the hands of students who do more basic questions, they will save more than ten minutes than other students, and the correct rate is very high, so they have more time to do the next big questions. Practice more to speed up.
7. Sudoku has nothing to do with mathematical operation. My suggestion is to do more problems that are a little more difficult to calculate. I'm also a past person. I used to see that the problems that are difficult to calculate are often skipped. I suggest that we should find some time to work out some problems that are a little more complicated, especially for solid geometry and analytic functions, It's very easy to have a strange result because of a calculation error. You should practice more
8. If you are in high school, you should write down your mistakes in a notebook and often take a look at them. You will know that you always make mistakes in those places in the future exam, and you will pay special attention to them. There is also the wrong place to do repeated calculus, until you do it right. Usually, we should pay special attention to these calculation problems. We should not deal with them casually. When we encounter calculation, we should use special draft paper instead of finding a vacant space. This is very inconvenient for later inspection! Of course, when you finish a question, you can estimate whether your answers are obviously different. This is a good skill in high school. Of course, it requires you to have a certain foundation in mathematics. Usually pay more attention to calculation when practicing, sometimes the method will not forget the calculation! Because when the college entrance examination is revised, the teacher attaches great importance to calculation!
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