Divergence of computing power
Publish: 2021-04-21 11:18:46
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3. The first grade of junior high school is the initial grade of junior high school. Some students are used to the oral arithmetic of primary school. When they get to junior high school, they also follow the method of primary school completely. There is no process of calculation, and the error rate is very high. Some students always think that the calculation problem is much easier than the analytical application problem. They always think that the calculation is an easy thing, so they are too confident or unable to concentrate in the calculation, and the results are full of mistakes. For junior high school students, it is a very important aspect of junior high school mathematics teaching to strengthen calculation teaching, cultivate good calculation habits and effectively improve the accuracy of calculation. Next, I will analyze the reasons for the low calculation accuracy and how to improve the calculation ability< First, the reasons for the low accuracy rate of calculation
1. Bad learning habits: many junior high school students have been to Olympiad Mathematics in primary school, and they are used to using fixed formulas to calculate, so many simple calculations come to the answer in one step, without any calculation process, so many calculation children don't understand the whole process, they just pay attention to the answer, There is no emphasis on the generation of knowledge
2. Unreasonable use of thinking mode: compared with primary school, junior high school mathematics has a leap in the depth, breadth and ability of knowledge, such as the introction of negative numbers, the use of letters to express numbers, the formation of spatial concepts, and the knowledge of functions, which are obviously different from the old knowledge. Some students' thinking still stays in the way of primary school thinking, and can not carry out divergent thinking Abstract thinking, etc
3. Unreasonable learning methods: many junior high school students have not mastered good learning methods, but only attach importance to the results, despise the process, be eager for success, be careless, have little knowledge of concepts, rules, formulas and theorems, mechanically imitate and memorize them by rote. The application of knowledge points is not in place
therefore, the problem of improving computing power is a comprehensive problem. To improve students' computing ability, I think we should start from the following aspects:
Second, we should pay attention to students' Ideological Ecation and form good habits.
many junior high school students who have just entered middle school live in school for the first time, live without their parents for the first time, and depend on themselves for the first time. Children are in an important turning point. On the one hand, they have strong curiosity, love to talk, love to move, and are competitive. The motivation of learning comes from interest and passion, and the harvest comes from "unintentional". On the other hand, they have poor self-consciousness, weak self-control, great emotional fluctuation, and unstable motivation and effect. Strong interest is the premise of learning mathematics well< The introction of negative sign and sign rule is an important starting point of algebra operation. In addition to understanding, we should pay special attention to its application points. For example, when learning rational number operation, grade one students in junior high school should emphasize that "first determine the symbol, then calculate, observe the characteristics, and then start", that is, first determine the symbol of each operation or result, and then calculate its absolute value; When calculating, first observe the characteristics of the topic, choose the appropriate method, in order to calculate simple and fast. At the beginning, some students can't flexibly use the multiplication algorithm to solve the problem according to the characteristics of the problem. Instead, they use the algorithm of the same level to change the score into a decimal (or decimal into a fraction) and then calculate it from left to right. We can let children use different calculation methods, and then let them feel for themselves which kind of calculation is simple and fast
2. The main obstacle for students to perceive letters is that they are easily influenced by the fixed pattern of primary school arithmetic. For example, students think a is a positive number and always think - a must be a negative number. If we compare the size of 4A and 2a, students are more susceptible to 4 & gt; 2, while ignoring the essential attribute that a can be positive, negative and zero, the wrong judgment is 4A & gt; 2a, ignoring 4A = 2A (when
A = 0); Or 4A & lt; 2A (when a & lt
0). Therefore, we should highlight what rational number a is in teaching, and try our best to let children give examples in teaching, so that their understanding can develop from the outside to the inside, from the concrete to the abstract.
Fourth, we should strengthen the teaching of basic knowledge
the combination of calculation ability and thinking ability, including analyzing operation conditions, exploring operation direction, and selecting operation formula, A series of processes such as determining a reasonable operation method, etc. Middle school mathematics is to cultivate students' computing ability, rather than just mechanically applying formulas. If there is an error in calculation, we often hear students blame themselves for "carelessness, not seeing the title clearly, ing wrong numbers, etc." of course, we can't rule out the error caused by carelessness in indivial cases, but solving problems often "carelessness", which is not just "carelessness". At the same time, it reflects the confusion and fuzziness of basic knowledge. Basic knowledge is not hard, which is often the root cause of calculation errors, so strengthening basic teaching is a very practical problem to improve calculation ability:
1. Correctly understand the concept. Memorizing some important formulas, rules and theorems accurately is the basic requirement of operation, and memorizing them correctly is the premise of accurate calculation. And can grasp the formula derivation, only understand some concepts and formula derivation, in order to achieve the positive use, reverse use and flexible use of the formula, so as to improve the operation ability
2. Students are required to see each data and operation symbol clearly, determine the correct operation order, and choose a reasonable calculation method. In order to do a calculation problem correctly, we must first read the problem carefully, observe from multiple angles, think comprehensively, and pass the examination
3. At ordinary times, we should strengthen the training of students' mathematical thinking methods. Mathematical thought is the basic viewpoint of mathematics, the most essential and the highest level thing in mathematics. It is the source of the basic strategy to solve the rationality of operation and the soul of mathematical operation
4. Strengthen the calculation practice. In order to improve students' computing ability, it is necessary to carry out strict training. The students are required to form the habit of standard writing, writing neat, correct format, correct handwriting, do not scribble, do not alter, keep the homework neat and beautiful. We should be confident and strive to be right once; Slow down and think clearly before writing; Don't do mental arithmetic, don't jump, and write clearly on the draft paper. It is best to train children to complete a certain number of calculation problems within the specified time, and the accuracy must be guaranteed. This is a process of long-term adherence. Many parents always want their children to practice once or twice to achieve this. Being too eager for success will have the opposite effect
5. Strengthen the cultivation of students' habit of checking calculation questions accurately. Many children are still wrong after checking the calculation, or some directly change the correct one into the wrong one. To correct this bad habit, it is not enough to ask students to be careful, but also to improve their checking ability. The reason why students can't find out their problems is that they just look at one side or do the calculation again, instead of using the learned mathematical knowledge to do the calculation from different angles. The fact shows that this method of recalculation is not of great significance, and the students who can quickly judge the truth of the answers from all aspects will have a profound understanding of the problem and meaningful learning
6. Let the students put the problems that they often make mistakes in their daily life into the wrong problem set. They can often see which problems are easy to make mistakes in their daily life and correct them in the future< Fifth, strengthen reasoning training, pay attention to problem-solving strategies, and improve the simplicity of calculation
in normal teaching, we should strengthen reasoning training on the basis of students' mastery of basic knowledge. In normal practice, we need to be step by step based, with sufficient reasons, and pay attention to the order of calculation. Some students are lack of comparative consciousness, so they often find a way to do it, and think it's OK to do it right. Guide students to use conditions flexibly, improve the simplicity of operation, such as flexible use of concepts and formulas, flexible choice of operation ways, etc. The combination of number and shape can simplify the complex.
1. Bad learning habits: many junior high school students have been to Olympiad Mathematics in primary school, and they are used to using fixed formulas to calculate, so many simple calculations come to the answer in one step, without any calculation process, so many calculation children don't understand the whole process, they just pay attention to the answer, There is no emphasis on the generation of knowledge
2. Unreasonable use of thinking mode: compared with primary school, junior high school mathematics has a leap in the depth, breadth and ability of knowledge, such as the introction of negative numbers, the use of letters to express numbers, the formation of spatial concepts, and the knowledge of functions, which are obviously different from the old knowledge. Some students' thinking still stays in the way of primary school thinking, and can not carry out divergent thinking Abstract thinking, etc
3. Unreasonable learning methods: many junior high school students have not mastered good learning methods, but only attach importance to the results, despise the process, be eager for success, be careless, have little knowledge of concepts, rules, formulas and theorems, mechanically imitate and memorize them by rote. The application of knowledge points is not in place
therefore, the problem of improving computing power is a comprehensive problem. To improve students' computing ability, I think we should start from the following aspects:
Second, we should pay attention to students' Ideological Ecation and form good habits.
many junior high school students who have just entered middle school live in school for the first time, live without their parents for the first time, and depend on themselves for the first time. Children are in an important turning point. On the one hand, they have strong curiosity, love to talk, love to move, and are competitive. The motivation of learning comes from interest and passion, and the harvest comes from "unintentional". On the other hand, they have poor self-consciousness, weak self-control, great emotional fluctuation, and unstable motivation and effect. Strong interest is the premise of learning mathematics well< The introction of negative sign and sign rule is an important starting point of algebra operation. In addition to understanding, we should pay special attention to its application points. For example, when learning rational number operation, grade one students in junior high school should emphasize that "first determine the symbol, then calculate, observe the characteristics, and then start", that is, first determine the symbol of each operation or result, and then calculate its absolute value; When calculating, first observe the characteristics of the topic, choose the appropriate method, in order to calculate simple and fast. At the beginning, some students can't flexibly use the multiplication algorithm to solve the problem according to the characteristics of the problem. Instead, they use the algorithm of the same level to change the score into a decimal (or decimal into a fraction) and then calculate it from left to right. We can let children use different calculation methods, and then let them feel for themselves which kind of calculation is simple and fast
2. The main obstacle for students to perceive letters is that they are easily influenced by the fixed pattern of primary school arithmetic. For example, students think a is a positive number and always think - a must be a negative number. If we compare the size of 4A and 2a, students are more susceptible to 4 & gt; 2, while ignoring the essential attribute that a can be positive, negative and zero, the wrong judgment is 4A & gt; 2a, ignoring 4A = 2A (when
A = 0); Or 4A & lt; 2A (when a & lt
0). Therefore, we should highlight what rational number a is in teaching, and try our best to let children give examples in teaching, so that their understanding can develop from the outside to the inside, from the concrete to the abstract.
Fourth, we should strengthen the teaching of basic knowledge
the combination of calculation ability and thinking ability, including analyzing operation conditions, exploring operation direction, and selecting operation formula, A series of processes such as determining a reasonable operation method, etc. Middle school mathematics is to cultivate students' computing ability, rather than just mechanically applying formulas. If there is an error in calculation, we often hear students blame themselves for "carelessness, not seeing the title clearly, ing wrong numbers, etc." of course, we can't rule out the error caused by carelessness in indivial cases, but solving problems often "carelessness", which is not just "carelessness". At the same time, it reflects the confusion and fuzziness of basic knowledge. Basic knowledge is not hard, which is often the root cause of calculation errors, so strengthening basic teaching is a very practical problem to improve calculation ability:
1. Correctly understand the concept. Memorizing some important formulas, rules and theorems accurately is the basic requirement of operation, and memorizing them correctly is the premise of accurate calculation. And can grasp the formula derivation, only understand some concepts and formula derivation, in order to achieve the positive use, reverse use and flexible use of the formula, so as to improve the operation ability
2. Students are required to see each data and operation symbol clearly, determine the correct operation order, and choose a reasonable calculation method. In order to do a calculation problem correctly, we must first read the problem carefully, observe from multiple angles, think comprehensively, and pass the examination
3. At ordinary times, we should strengthen the training of students' mathematical thinking methods. Mathematical thought is the basic viewpoint of mathematics, the most essential and the highest level thing in mathematics. It is the source of the basic strategy to solve the rationality of operation and the soul of mathematical operation
4. Strengthen the calculation practice. In order to improve students' computing ability, it is necessary to carry out strict training. The students are required to form the habit of standard writing, writing neat, correct format, correct handwriting, do not scribble, do not alter, keep the homework neat and beautiful. We should be confident and strive to be right once; Slow down and think clearly before writing; Don't do mental arithmetic, don't jump, and write clearly on the draft paper. It is best to train children to complete a certain number of calculation problems within the specified time, and the accuracy must be guaranteed. This is a process of long-term adherence. Many parents always want their children to practice once or twice to achieve this. Being too eager for success will have the opposite effect
5. Strengthen the cultivation of students' habit of checking calculation questions accurately. Many children are still wrong after checking the calculation, or some directly change the correct one into the wrong one. To correct this bad habit, it is not enough to ask students to be careful, but also to improve their checking ability. The reason why students can't find out their problems is that they just look at one side or do the calculation again, instead of using the learned mathematical knowledge to do the calculation from different angles. The fact shows that this method of recalculation is not of great significance, and the students who can quickly judge the truth of the answers from all aspects will have a profound understanding of the problem and meaningful learning
6. Let the students put the problems that they often make mistakes in their daily life into the wrong problem set. They can often see which problems are easy to make mistakes in their daily life and correct them in the future< Fifth, strengthen reasoning training, pay attention to problem-solving strategies, and improve the simplicity of calculation
in normal teaching, we should strengthen reasoning training on the basis of students' mastery of basic knowledge. In normal practice, we need to be step by step based, with sufficient reasons, and pay attention to the order of calculation. Some students are lack of comparative consciousness, so they often find a way to do it, and think it's OK to do it right. Guide students to use conditions flexibly, improve the simplicity of operation, such as flexible use of concepts and formulas, flexible choice of operation ways, etc. The combination of number and shape can simplify the complex.
4. The cultivation of primary school students' computational ability runs through the whole primary school mathematics teaching activities, and its importance is beyond doubt. The mastery of calculation methods and skills and the correctness of calculation results depend on continuous practice. A small program that can automatically set questions and score is very important. Wechat app "calculate my best" is a software for training and scoring primary school students' computational ability, covering:
1. Add, subtract, multiply and divide in the table (applicable to grade one and two students)
2. Vertical calculation of addition, subtraction, multiplication and division (applicable to the third and fourth grade students)
3. Simple operation and equation solving (suitable for the fourth and fifth grade students)
4. There are more than ten typical problems in primary school (which can be used in grade 4, 5 and 6)
features: it can score in real time, and you can see the test results immediately after clicking "hand in the paper". If you don't know what your mistake is, you can click the "help" button (you can ask for help only after you hand in the paper) to check the correct answer. The time, item, score and time of each test are saved in the score record
after use, if you think the software is helpful to your students or children's learning, please share it with your colleagues or friends
just search for "calculate my best" in wechat applet, come and have a try!
1. Add, subtract, multiply and divide in the table (applicable to grade one and two students)
2. Vertical calculation of addition, subtraction, multiplication and division (applicable to the third and fourth grade students)
3. Simple operation and equation solving (suitable for the fourth and fifth grade students)
4. There are more than ten typical problems in primary school (which can be used in grade 4, 5 and 6)
features: it can score in real time, and you can see the test results immediately after clicking "hand in the paper". If you don't know what your mistake is, you can click the "help" button (you can ask for help only after you hand in the paper) to check the correct answer. The time, item, score and time of each test are saved in the score record
after use, if you think the software is helpful to your students or children's learning, please share it with your colleagues or friends
just search for "calculate my best" in wechat applet, come and have a try!
5. To a large extent, the inaccuracy of understanding and memorizing concepts, formulas and rules is e to the lack of deep understanding of basic concepts, the lack of thorough grasp of basic formulas and rules, and the lack of proficiency in their application. In teaching, it is essential for students to firmly grasp the concepts, properties, formulas, rules and theorems needed by operation. We should focus on improving students' memory ability, teach them memory methods, and firmly grasp some commonly used data, formulas and rules. We should go through the process from concrete to abstract, from perceptual to rational, naturally form concepts, derive formulas and rules, pay attention to the lack of knowledge reflected in students' operations, and do not simply attribute the causes of solving problems to carelessness, or methods and skills. Only by mastering the relevant knowledge, can we make the direction of operation clear and provide reliable basis for operation, which is the premise of correct operation. Therefore, it is essential for students to learn the basic knowledge of operation< Second, we should strengthen the teaching of the occurrence, development and formation of formulas and theorems. Ignoring the preconditions of formulas and theorems and abusing formulas and theorems are the main reasons for students' low computational ability. There are many factors, but they are not comprehensive enough, or the methods are not right, and they are not in harmony with students' cognitive rules, It has a lot to do with it. Therefore, we should make great efforts in designing problems and organizing contents, let students experience the occurrence, development and formation process of knowledge, make dead knowledge alive, follow students' cognitive rules, and deepen students' knowledge and understanding of knowledge, instead of cramming, so that they will not take out of context. The focus of classroom teaching is not only on the main body of formulas and theorems, but also on the error prone areas such as the conditions of formulas and theorems and special situations< In high school, many mathematical knowledge often use simple numerical operation, but numerical operation is just the weakness of high school students. In fact, as long as our teachers can give proper guidance, flexibly use formulas and draw inferences from one instance, we can improve students' computing ability. In order to enable students to master the correct algorithm, teachers should often infiltrate modern mathematical thinking methods, and carry out some contrast exercises on students' easily confused problems. Encourage students to dare to innovate, strengthen the training of "one problem with multiple solutions" and "simple algorithm". In order to improve students' computing ability, it is necessary for them to master the theory and algorithm. Only by making clear the characteristics, methods and influencing factors of calculation, can they improve their computing ability better. Algorithm research helps to simplify the thinking process, get effective problem-solving strategies, strengthen practice, use various forms, and make students form skills
1. Intensive training, practice makes perfect
an important way to improve the speed of operation is to practice diligently, often and repeatedly. Only through certain intensive training, can students achieve the goal of "practice makes perfect". Therefore, we should carefully organize the training, whether in class or out of class, in addition to the requirements of quantity and quality, we should also have certain requirements for the speed of problem solving. In the classroom, we should arrange some limited time operation training and more hierarchical and targeted problem group training, so that different types of students can complete the appropriate training tasks in a certain period of time, so as to improve the efficiency of classroom teaching and improve the rate of reaching the standard in class< It is not enough to grasp the general rules of mathematical operation, but also to form skilled skills. Without the formation of skilled skills, it is impossible to complete the operation simply and quickly. Therefore, we should consciously discover and summarize some skills and techniques through operation practice. Such as "substitution method", "combination of number and shape", "1" transformation and the choice of coordinate system in analytic geometry, etc. In addition, the following points should be achieved:
first, master the general principles of operation. The general rule of general method is not only beneficial to the operation orientation, but also to improve the speed of operation. Therefore, we should master the transformation of basic number form and form some basic skills. For example, the multiplication formula is used to simplify the number calculation; The root of square is obtained by decomposing the quality factor; Using the rational method of denominator to find the value of root formula. In order to cultivate students' correct and rapid computing ability, it is very necessary for them to master certain skills
Second, be familiar with some methods and skills of mental calculation and quick calculation. Mental arithmetic is a form of calculation. It is a kind of calculation without writing. It is a sign of "familiarity" and can strengthen students' thinking inspiration. In teaching, whether it is to find solutions to problems, or to carry out the operation process, we should strengthen the training of mental calculation, and teach some methods of quick calculation, which is a very effective way to improve the operation speed
thirdly, memorize some common data and important conclusions. Such as the square number of one or two digits, trigonometric function value of special angle, some common mathematical propositions, etc. So as to expand the capacity of knowledge, increase the span of thinking, improve the agility of thinking
3. Tempering thinking and fast operation
infiltrating thinking training into operation training is an effective measure to improve operation speed. Because good thinking quality is a powerful guarantee to improve the computing ability. In teaching, we need to strengthen the training of mathematical methods and thinking methods, such as mastering some common mathematical methods: collocation method, substitution method, undetermined coefficient method, mathematical inction method, parameter method, elimination method, etc; Familiar with some common mathematical logic methods: analysis, synthesis, reverse, inction, dection, etc; Master the common mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, inction and dection, etc; Master common mathematical ideas: function and equation, combination of number and shape, classified discussion, transformation, etc. It is necessary to strengthen the thinking training of students in reverse, divergence, entirety, structure and intuition, so as to provide guarantee for finding a simple and fast way of operation from the aspects of thinking method, problem-solving ideas and problem-solving strategies< The teachers in vocational schools agree that the students in vocational schools are not solid in their junior middle school learning, and they do not have a firm grasp of basic knowledge and methods. They should keep some fixed knowledge and methods in mind and ask them to use them to solve problems. It is true that the fixed way of thinking has a positive side in operation, but it also has a negative impact. When students master a certain kind of knowledge (method), they often use conventional methods to solve problems when they encounter problems. In this way, they will inevitably have the inertia of thinking and lack the consciousness of thinking from multiple directions and angles, which is not concive to the improvement of students' operation speed. What's more, students in vocational schools are active in thinking and just want to find a simpler and faster method of calculation so that they can have more time to do other things. Therefore, the fixed way of thinking will affect the speed of students' operation, make the operation process cumbersome, and thus cause students' aversion to mathematics learning. In my teaching, I often guide students to think about problems from various aspects and angles, and strive to cultivate their observation ability, association ability and comparative consciousness, so as to seek the best way to solve problems< It can not exist alone without specific mathematical knowledge, nor can it develop independently without other abilities. It permeates with memory ability, observation ability, understanding ability, association ability and expression ability, and supports each other with mathematical abilities such as logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the process of teaching, only when we often summarize the rules, constantly guide and graally accumulate, can we really improve the computing ability< It is an important factor to cultivate students' good study habits. Because of its strict characteristics, mathematics does not allow students to be careless and careless. Students' mistakes in calculation are partly caused by their bad study habits. In teaching, teachers should let students form the good habits of careful examination, careful observation and writing standard before doing questions. In the process of learning mathematics, students can be asked not to rely on calculators when they encounter simple calculation problems, so that they can form the judgment of the calculation results in mental calculation, oral calculation and written calculation. Good calculation habit is the guarantee of improving calculation ability. In calculation, students are required to do one look, two think, three calculate and four check. A look: before doing a question, first look at the question completely, see each number and each operation symbol, and make a preliminary perception. Second, on the basis of clearly understanding the topic, we should make clear the relationship between the characteristics of the clearing form and each operation, choose a reasonable method according to the specific situation, and determine the operation steps. Third calculation: after determining the operation steps and methods, calculate carefully. Four checks: we should "look back" in time to check whether the algorithm is reasonable, whether the operation symbol is copied wrong, whether the minus sign is missed, and whether the calculation result is wrong
be patient in calculation, and never give up until you finish a problem. Students are required to write carefully, because only when they write carefully can they concentrate their attention, so the accuracy of calculation is improved. Over time, students will be able to develop good calculation habits< In a word, China's mathematics ecation has a tradition of paying attention to the training of basic knowledge, basic skills and ability training, which should be carried forward in senior high school mathematics curriculum in the new century. Teaching practice shows that it is a complex system engineering and a long-term task to improve students' computing ability. As long as we cherish every training opportunity, carry out long-term infiltration in a planned, targeted and conscious way, and enable students to graally understand the essence of operation ability, it will inevitably promote students to develop the habit of correct, reasonable and fast operation, and finally achieve the purpose of improving students' operation ability.
1. Intensive training, practice makes perfect
an important way to improve the speed of operation is to practice diligently, often and repeatedly. Only through certain intensive training, can students achieve the goal of "practice makes perfect". Therefore, we should carefully organize the training, whether in class or out of class, in addition to the requirements of quantity and quality, we should also have certain requirements for the speed of problem solving. In the classroom, we should arrange some limited time operation training and more hierarchical and targeted problem group training, so that different types of students can complete the appropriate training tasks in a certain period of time, so as to improve the efficiency of classroom teaching and improve the rate of reaching the standard in class< It is not enough to grasp the general rules of mathematical operation, but also to form skilled skills. Without the formation of skilled skills, it is impossible to complete the operation simply and quickly. Therefore, we should consciously discover and summarize some skills and techniques through operation practice. Such as "substitution method", "combination of number and shape", "1" transformation and the choice of coordinate system in analytic geometry, etc. In addition, the following points should be achieved:
first, master the general principles of operation. The general rule of general method is not only beneficial to the operation orientation, but also to improve the speed of operation. Therefore, we should master the transformation of basic number form and form some basic skills. For example, the multiplication formula is used to simplify the number calculation; The root of square is obtained by decomposing the quality factor; Using the rational method of denominator to find the value of root formula. In order to cultivate students' correct and rapid computing ability, it is very necessary for them to master certain skills
Second, be familiar with some methods and skills of mental calculation and quick calculation. Mental arithmetic is a form of calculation. It is a kind of calculation without writing. It is a sign of "familiarity" and can strengthen students' thinking inspiration. In teaching, whether it is to find solutions to problems, or to carry out the operation process, we should strengthen the training of mental calculation, and teach some methods of quick calculation, which is a very effective way to improve the operation speed
thirdly, memorize some common data and important conclusions. Such as the square number of one or two digits, trigonometric function value of special angle, some common mathematical propositions, etc. So as to expand the capacity of knowledge, increase the span of thinking, improve the agility of thinking
3. Tempering thinking and fast operation
infiltrating thinking training into operation training is an effective measure to improve operation speed. Because good thinking quality is a powerful guarantee to improve the computing ability. In teaching, we need to strengthen the training of mathematical methods and thinking methods, such as mastering some common mathematical methods: collocation method, substitution method, undetermined coefficient method, mathematical inction method, parameter method, elimination method, etc; Familiar with some common mathematical logic methods: analysis, synthesis, reverse, inction, dection, etc; Master the common mathematical thinking methods: observation and analysis, generalization and abstraction, analysis and synthesis, special and general, analogy, inction and dection, etc; Master common mathematical ideas: function and equation, combination of number and shape, classified discussion, transformation, etc. It is necessary to strengthen the thinking training of students in reverse, divergence, entirety, structure and intuition, so as to provide guarantee for finding a simple and fast way of operation from the aspects of thinking method, problem-solving ideas and problem-solving strategies< The teachers in vocational schools agree that the students in vocational schools are not solid in their junior middle school learning, and they do not have a firm grasp of basic knowledge and methods. They should keep some fixed knowledge and methods in mind and ask them to use them to solve problems. It is true that the fixed way of thinking has a positive side in operation, but it also has a negative impact. When students master a certain kind of knowledge (method), they often use conventional methods to solve problems when they encounter problems. In this way, they will inevitably have the inertia of thinking and lack the consciousness of thinking from multiple directions and angles, which is not concive to the improvement of students' operation speed. What's more, students in vocational schools are active in thinking and just want to find a simpler and faster method of calculation so that they can have more time to do other things. Therefore, the fixed way of thinking will affect the speed of students' operation, make the operation process cumbersome, and thus cause students' aversion to mathematics learning. In my teaching, I often guide students to think about problems from various aspects and angles, and strive to cultivate their observation ability, association ability and comparative consciousness, so as to seek the best way to solve problems< It can not exist alone without specific mathematical knowledge, nor can it develop independently without other abilities. It permeates with memory ability, observation ability, understanding ability, association ability and expression ability, and supports each other with mathematical abilities such as logical thinking ability. Therefore, the problem of improving computing power is a comprehensive problem. In the process of teaching, only when we often summarize the rules, constantly guide and graally accumulate, can we really improve the computing ability< It is an important factor to cultivate students' good study habits. Because of its strict characteristics, mathematics does not allow students to be careless and careless. Students' mistakes in calculation are partly caused by their bad study habits. In teaching, teachers should let students form the good habits of careful examination, careful observation and writing standard before doing questions. In the process of learning mathematics, students can be asked not to rely on calculators when they encounter simple calculation problems, so that they can form the judgment of the calculation results in mental calculation, oral calculation and written calculation. Good calculation habit is the guarantee of improving calculation ability. In calculation, students are required to do one look, two think, three calculate and four check. A look: before doing a question, first look at the question completely, see each number and each operation symbol, and make a preliminary perception. Second, on the basis of clearly understanding the topic, we should make clear the relationship between the characteristics of the clearing form and each operation, choose a reasonable method according to the specific situation, and determine the operation steps. Third calculation: after determining the operation steps and methods, calculate carefully. Four checks: we should "look back" in time to check whether the algorithm is reasonable, whether the operation symbol is copied wrong, whether the minus sign is missed, and whether the calculation result is wrong
be patient in calculation, and never give up until you finish a problem. Students are required to write carefully, because only when they write carefully can they concentrate their attention, so the accuracy of calculation is improved. Over time, students will be able to develop good calculation habits< In a word, China's mathematics ecation has a tradition of paying attention to the training of basic knowledge, basic skills and ability training, which should be carried forward in senior high school mathematics curriculum in the new century. Teaching practice shows that it is a complex system engineering and a long-term task to improve students' computing ability. As long as we cherish every training opportunity, carry out long-term infiltration in a planned, targeted and conscious way, and enable students to graally understand the essence of operation ability, it will inevitably promote students to develop the habit of correct, reasonable and fast operation, and finally achieve the purpose of improving students' operation ability.
6. In the examination syllabus of the senior high school entrance examination, there are clear requirements for the ability of "operation ability" of Mathematics: "be able to operate correctly, deform and process data according to the rules and formulas; be able to find and design reasonable and simple operation ways according to the conditions of problems; It is specially mentioned that "operation ability is the combination of thinking ability and operation skills. Operation includes the calculation, estimation and approximate calculation of numbers, the combination and decomposition deformation of formulas, the calculation and solution of geometric quantities of geometric figures, etc. operation ability includes the analysis of operation conditions, exploration of operation direction, calculation and calculation of geometric quantities, etc It also includes the ability to adjust the operation when encountering obstacles in the process of operation and the skills of operation and calculation. "
there are at least three reasons for calculation errors: first, writing errors, such as the symbols and coefficients of number and formula operation, sloppy handwriting, reading mistakes and ing mistakes when looking "in a trance", etc; Second, the memory of formula, theorem, definition and rule is not accurate, the understanding is not deep, and the application is not flexible.
for example, the nature of function, the algorithm of quadratic radical, etc In the choice of the diversity of ideas and the evaluation of the amount of computation
in mathematics learning, operation is always accompanied by mathematics learning. In operation, it is not uncommon for students to make mistakes in one step, or waste a lot of time e to tedious calculation. In recent years, in order to cultivate students' computing ability, I have put forward a set of solutions: "independent", "accurate", "fast", etc "Reasonable" and "standard", please self diagnose the type, train in time, and solve the problems in each test paper in a timely and targeted way. First, you should see what mistakes you have made, and then make reasonable plans and solutions according to different situations, so as to achieve a better effect, He negates his computing ability blindly and comprehensively
first, pay attention to the learning process
solid foundation, flexible methods, pay attention to calculation theory, optimize calculation, avoid "making a mountain out of a molehill", neat writing, standardized expression, concise process, learning estimation and checking. Correct errors in time, constantly repeat, persevere and avoid impatience. Quietness proces wisdom< Second, form a problem-solving style.
examine the questions carefully, have a clear goal, answer the questions, calculate in order, grasp the rhythm, think carefully, strengthen checking, pay attention to the choice, strengthen character operation, overall operation, strengthen memory, pay attention to the method, and solve more than one problem< Third, improve operational skills
master some commonly used mathematical operational skills, methods and rules, and be familiar with some common question types and answering methods. Return to teaching materials, integrate knowledge points, strengthen training for weak points of knowledge and methods, rece calculation, and carry out a certain amount of training, so as to make your mind in a good state of adaptation, It is necessary to strengthen the ability training of solving one more problem, solving multiple problems at one time, and divergent deformation. It is necessary to expand the ability of thinking and flexible use of knowledge. For solving operational problems, the more complicated the operation steps are, the more mistakes are likely to occur. Many problems can be considered from multiple angles by various methods. There are many ways of thinking. Because of the different ways of thinking in solving problems, the time spent in solving problems must be different. Often pay attention to select some problems with multiple solutions or relatively large amount of calculation, and use plenty of time to think and do them. Combined with these practical problems, we should flexibly use concepts, appropriately choose formulas, and use the best methods In order to simplify the operation and improve the speed of operation, we should use the method of mathematical thinking reasonably.
there are at least three reasons for calculation errors: first, writing errors, such as the symbols and coefficients of number and formula operation, sloppy handwriting, reading mistakes and ing mistakes when looking "in a trance", etc; Second, the memory of formula, theorem, definition and rule is not accurate, the understanding is not deep, and the application is not flexible.
for example, the nature of function, the algorithm of quadratic radical, etc In the choice of the diversity of ideas and the evaluation of the amount of computation
in mathematics learning, operation is always accompanied by mathematics learning. In operation, it is not uncommon for students to make mistakes in one step, or waste a lot of time e to tedious calculation. In recent years, in order to cultivate students' computing ability, I have put forward a set of solutions: "independent", "accurate", "fast", etc "Reasonable" and "standard", please self diagnose the type, train in time, and solve the problems in each test paper in a timely and targeted way. First, you should see what mistakes you have made, and then make reasonable plans and solutions according to different situations, so as to achieve a better effect, He negates his computing ability blindly and comprehensively
first, pay attention to the learning process
solid foundation, flexible methods, pay attention to calculation theory, optimize calculation, avoid "making a mountain out of a molehill", neat writing, standardized expression, concise process, learning estimation and checking. Correct errors in time, constantly repeat, persevere and avoid impatience. Quietness proces wisdom< Second, form a problem-solving style.
examine the questions carefully, have a clear goal, answer the questions, calculate in order, grasp the rhythm, think carefully, strengthen checking, pay attention to the choice, strengthen character operation, overall operation, strengthen memory, pay attention to the method, and solve more than one problem< Third, improve operational skills
master some commonly used mathematical operational skills, methods and rules, and be familiar with some common question types and answering methods. Return to teaching materials, integrate knowledge points, strengthen training for weak points of knowledge and methods, rece calculation, and carry out a certain amount of training, so as to make your mind in a good state of adaptation, It is necessary to strengthen the ability training of solving one more problem, solving multiple problems at one time, and divergent deformation. It is necessary to expand the ability of thinking and flexible use of knowledge. For solving operational problems, the more complicated the operation steps are, the more mistakes are likely to occur. Many problems can be considered from multiple angles by various methods. There are many ways of thinking. Because of the different ways of thinking in solving problems, the time spent in solving problems must be different. Often pay attention to select some problems with multiple solutions or relatively large amount of calculation, and use plenty of time to think and do them. Combined with these practical problems, we should flexibly use concepts, appropriately choose formulas, and use the best methods In order to simplify the operation and improve the speed of operation, we should use the method of mathematical thinking reasonably.
7. How to improve the mathematical operation ability
there are clear requirements for the "operation ability" of mathematics in the "examination outline" of college entrance examination: "be able to carry out correct operation, deformation and data processing according to the rules and formulas; According to the conditions of the problem, we can find and design a reasonable and simple way of calculation; Be able to estimate and approximate the data according to the requirements. ", In particular, it is mentioned that "operation ability is the combination of thinking ability and operation skills. Operation includes the calculation, estimation and approximate calculation of numbers, the combination and decomposition deformation of formulas, and the calculation and solution of geometric quantities of geometric figures. Operation ability includes the analysis of operation conditions, exploration of operation direction, selection of operation formula, selection of calculation method and calculation method The thinking ability in a series of processes, such as determining the operation program, also includes the ability to adjust the operation when encountering obstacles in the process of operation, and the skills of operation and calculation. "
there are at least three reasons for calculation errors: one is writing errors. For example, the symbols and coefficients of numeral and formula operation, the handwriting is sloppy, and the mistakes of reading and ing when looking "in a trance", etc; Second, the memory of formula, theorem, definition and rule is not accurate, the understanding is not deep, and the application is not flexible. For example, the nature of the function, logarithmic algorithm, trigonometric difference times and a half formula, vector proct and geometric meaning, conic nature, trinomial theorem, several types of probability judgment, derivative algorithm and so on. Third, the thinking training of problem solving is not in place and the process control is not strict. For example, the method of making questions depends on the impression, the lack of solving strategies for multiple-choice questions, fill in the blanks and answer questions, the diversity of thinking and the evaluation of the amount of calculation
in mathematics learning, operation is always accompanied by mathematics learning. In the calculation, it is not uncommon for students to make mistakes in one step, or waste a lot of time e to complicated calculation. In recent years, in order to realize the cultivation of students' computing ability, I have put forward a set of solutions: "independent", "accurate", "rapid", "reasonable" and "standard". Please self diagnose the type and train in time. According to the problems in each test paper, you should solve them in a timely and targeted way. First, you should see what mistakes you have made, and then make reasonable plans and solutions according to different situations, so as to achieve a better effect. Don't think that your computing ability is not good in general, and negate your computing ability blindly and comprehensively< First, pay attention to the learning process. Solid foundation, flexible method, pay attention to calculation, optimize calculation, avoid "make a mountain out of a molehill",. Neat writing, standard expression, simple process, learning estimation and checking. Correct mistakes in time, repeat and persevere. Don't be impatient, quiet can proce wisdom< Second, form a problem-solving style. Careful examination, clear goal, answer must be asked, calculation orderly, grasp the rhythm, rigorous thinking, strengthen checking, pay attention to the choice, strengthen character operation, overall operation, strengthen memory, pay attention to the method, one problem multi solution< Third, improve the operation skills. Master some common mathematical operation skills, methods and rules, familiar with some common questions and answer methods. Return to teaching materials, integrate knowledge points, strengthen training for the weak points of knowledge and methods, rece calculation, and carry out a certain amount of training, so that their psychology is in a good state of adaptation
special attention should be paid to strengthen the ability training of multiple solutions to one problem, multiple solutions to one problem, divergence and deformation, and expand the ability of thinking and flexible use of knowledge. For solving problems of operation, the more steps, the more complicated, and the easier to make mistakes. However, many problems can be considered in many ways, from many angles, with many ways of thinking. Because of the different ways of thinking in solving the problem, the time spent in solving the problem must be different. Often pay attention to select some problems with multiple solutions or relatively large difference in calculation amount, use plenty of time to think and do, and combine with these practical problems, timely and flexibly use concepts, properly choose formulas, and reasonably use mathematical thinking methods, so as to achieve the purpose of simplifying operation and improving operation speed
in a word, we should carefully reflect on the error prone points in our study, develop good calculation methods and habits at ordinary times, maintain a calm and calm attitude, and be willing to spend time in calculation, so as to improve the accuracy and speed of calculation, strive to achieve the normal level in the examination and maximize the results
there are clear requirements for the "operation ability" of mathematics in the "examination outline" of college entrance examination: "be able to carry out correct operation, deformation and data processing according to the rules and formulas; According to the conditions of the problem, we can find and design a reasonable and simple way of calculation; Be able to estimate and approximate the data according to the requirements. ", In particular, it is mentioned that "operation ability is the combination of thinking ability and operation skills. Operation includes the calculation, estimation and approximate calculation of numbers, the combination and decomposition deformation of formulas, and the calculation and solution of geometric quantities of geometric figures. Operation ability includes the analysis of operation conditions, exploration of operation direction, selection of operation formula, selection of calculation method and calculation method The thinking ability in a series of processes, such as determining the operation program, also includes the ability to adjust the operation when encountering obstacles in the process of operation, and the skills of operation and calculation. "
there are at least three reasons for calculation errors: one is writing errors. For example, the symbols and coefficients of numeral and formula operation, the handwriting is sloppy, and the mistakes of reading and ing when looking "in a trance", etc; Second, the memory of formula, theorem, definition and rule is not accurate, the understanding is not deep, and the application is not flexible. For example, the nature of the function, logarithmic algorithm, trigonometric difference times and a half formula, vector proct and geometric meaning, conic nature, trinomial theorem, several types of probability judgment, derivative algorithm and so on. Third, the thinking training of problem solving is not in place and the process control is not strict. For example, the method of making questions depends on the impression, the lack of solving strategies for multiple-choice questions, fill in the blanks and answer questions, the diversity of thinking and the evaluation of the amount of calculation
in mathematics learning, operation is always accompanied by mathematics learning. In the calculation, it is not uncommon for students to make mistakes in one step, or waste a lot of time e to complicated calculation. In recent years, in order to realize the cultivation of students' computing ability, I have put forward a set of solutions: "independent", "accurate", "rapid", "reasonable" and "standard". Please self diagnose the type and train in time. According to the problems in each test paper, you should solve them in a timely and targeted way. First, you should see what mistakes you have made, and then make reasonable plans and solutions according to different situations, so as to achieve a better effect. Don't think that your computing ability is not good in general, and negate your computing ability blindly and comprehensively< First, pay attention to the learning process. Solid foundation, flexible method, pay attention to calculation, optimize calculation, avoid "make a mountain out of a molehill",. Neat writing, standard expression, simple process, learning estimation and checking. Correct mistakes in time, repeat and persevere. Don't be impatient, quiet can proce wisdom< Second, form a problem-solving style. Careful examination, clear goal, answer must be asked, calculation orderly, grasp the rhythm, rigorous thinking, strengthen checking, pay attention to the choice, strengthen character operation, overall operation, strengthen memory, pay attention to the method, one problem multi solution< Third, improve the operation skills. Master some common mathematical operation skills, methods and rules, familiar with some common questions and answer methods. Return to teaching materials, integrate knowledge points, strengthen training for the weak points of knowledge and methods, rece calculation, and carry out a certain amount of training, so that their psychology is in a good state of adaptation
special attention should be paid to strengthen the ability training of multiple solutions to one problem, multiple solutions to one problem, divergence and deformation, and expand the ability of thinking and flexible use of knowledge. For solving problems of operation, the more steps, the more complicated, and the easier to make mistakes. However, many problems can be considered in many ways, from many angles, with many ways of thinking. Because of the different ways of thinking in solving the problem, the time spent in solving the problem must be different. Often pay attention to select some problems with multiple solutions or relatively large difference in calculation amount, use plenty of time to think and do, and combine with these practical problems, timely and flexibly use concepts, properly choose formulas, and reasonably use mathematical thinking methods, so as to achieve the purpose of simplifying operation and improving operation speed
in a word, we should carefully reflect on the error prone points in our study, develop good calculation methods and habits at ordinary times, maintain a calm and calm attitude, and be willing to spend time in calculation, so as to improve the accuracy and speed of calculation, strive to achieve the normal level in the examination and maximize the results
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