Mathematical problem solving power
Publish: 2021-04-14 06:27:37
1. Generally, you can't be hungry or rich, but the iron rice bowl is still very good
2. PI currency now has two exchanges selling air currency, the name of the exchange will not be issued, as we all know, after all, the official has issued a notice, if you buy the currency in the exchange, then I wish you good luck, if not, it should be waiting for the function of internal transfer to start, now the news is that the identity authentication will be started on December 14, and internal transfer will be started on December 20, now dig up a lot!!
3. I hope the following answers can help you:
1. Strengthen the teaching of basic knowledge and basic skills, and improve the accuracy of calculation.
the basic knowledge in mathematics is the basis of calculation, which has guiding significance for calculation. The basic knowledge is confused, fuzzy, and the basic knowledge is not solid. In the past, it is the root cause of calculation errors, Therefore, to strengthen and implement the double base teaching is a very practical problem to improve the operation ability, which requires students to do:
(1) memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correct memory formulas and rules are the premise of accurate operation. Among the mathematical concepts, formulas, rules and properties, some are the basis of operation, explaining the reasons for "why it can be done like this", and some are the methods and steps of operation. It gives the proceres of how to do, that is, algorithms. Students learn the relevant concepts, properties and formulas, and memorize, rules and steps on the basis of understanding, Then, through a series of operation activities (i.e. practice), some kind of operation skills are graally formed
(2) correctly understand the concepts and definitions, and master the derivation of formulas. Only by understanding the derivation of some concepts and formulas, can we achieve the positive, reverse and flexible use of formulas, so as to improve the computing ability. The reason of incorrect operation in mathematics learning is often the result of fuzzy concept, formula, rule forgetting, confusion or rigid application
2. Strengthen the reasoning training of scientific system to improve the rapidity of operation
the poor operation ability is often caused by the weak thinking ability. In teaching, we should strengthen the reasoning training on the basis of students' mastering the basic knowledge. In normal practice, we should make sure that there is a basis step by step, there are sufficient reasons, and pay attention to the sequence of operation. Generally, we should pay attention to the following aspects:
1) training must be orderly. Practice must be planned and carried out step by step. In mathematics teaching, practice can be divided into three stages: first, imitation practice stage. This is an exercise carried out under the example demonstration of the teacher after learning the new knowledge. The difficulty of the selected exercises is not high and the change is not big. Students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to put forward the speed requirements; Second, the mastery stage. This is a study organized on the basis of students' preliminary mastery of knowledge and skills. The difficulty of the exercises is appropriately increased, and the forms of the exercises are changed. Students are not only required to operate correctly, but also required to summarize and summarize the process, basis and methods of operation after obtaining the correct answers, so as to promote the operation mode to the theoretical level; Third, comprehensive application stage. At this time, we can choose some difficult comprehensive questions to train students' ability to determine the direction of operation and flexibly use the rules
(2) carry out variant exercises. In order to make students skillful, we must organize variant exercises. The so-called variant practice is the change of concepts and rules under the condition that other effective learning conditions remain unchanged. For mathematical operations, it is to change the non essential characteristics of the problem and keep its structural components unchanged. The concrete ways include the change of expression of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc
(3) understand the effect of practice in time and correct the mistakes in practice in time. In ability practice, it is an effective way to let students know the effect of practice in time. Psychological research shows that if the following feedback information is provided to the students who are carrying out the ability training: ① know the score of each exercise; ② encourage and urge them continuously in the process of practice; ③ analyze the mistakes in practice, then the practice effect will be significantly improved. This is because, on the one hand, students know the problem according to the feedback information, so as to adjust the learning activities and make the practice more effective; On the other hand, it also increases learning motivation to strive for better results or avoid making similar mistakes again
3. The training of thinking flexibility in the process of operation
because mathematical operation is an intelligent operation with clear direction and in line with certain rules, after a certain amount of practice, this kind of operation experience will form a fixed reaction mode and play a tendentious role in the selection of operation direction in subsequent learning, This is the "set" phenomenon in learning. When the formed inertial thinking is consistent with the way to solve new problems, it can quickly respond and get the correct answer. The phenomenon of "shrinking" and "skipping" appears in the process of calculation. This is the positive role of the fixed trend, and also the sign of students mastering knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of using formula method and factorization method to solve quadratic equation of one variable. In the later study of quadratic function, when they encounter the operations related to quadratic equation of one variable, they will quickly make the correct response. When the conventional way of thinking is not completely consistent with or contrary to the solution of new problems, it can not be solved in a simple and flexible way, and the operation process is tedious and tedious, which leads to the wrong solution of the problem. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative effect of "stereotype" and cultivate the flexibility of students' calculation
4. Pay attention to cultivate students' ability of operation rationality
reasonable calculation is to make full use of operation law, proct invariance and quotient invariance, change the data and order of operation, and make the operation as simple, fast and correct as possible. The cultivation of students' simple operation ability is not only the improvement of operation ability, because in the process of cultivation, it must involve the cultivation of observation ability, inctive ability and other abilities, so the cultivation of simple operation ability is actually the cultivation of comprehensive ability. At the same time, it is necessary to cultivate students' overall view of mathematical operation. Before calculation, students should have an overall view of the overall situation. They should grasp the steps of operation, what should be calculated first and then, what are the characteristics of the numbers in the title, and what contains information, etc.
1. Strengthen the teaching of basic knowledge and basic skills, and improve the accuracy of calculation.
the basic knowledge in mathematics is the basis of calculation, which has guiding significance for calculation. The basic knowledge is confused, fuzzy, and the basic knowledge is not solid. In the past, it is the root cause of calculation errors, Therefore, to strengthen and implement the double base teaching is a very practical problem to improve the operation ability, which requires students to do:
(1) memorize some important data formulas and rules, because accuracy is the basic requirement of operation, and correct memory formulas and rules are the premise of accurate operation. Among the mathematical concepts, formulas, rules and properties, some are the basis of operation, explaining the reasons for "why it can be done like this", and some are the methods and steps of operation. It gives the proceres of how to do, that is, algorithms. Students learn the relevant concepts, properties and formulas, and memorize, rules and steps on the basis of understanding, Then, through a series of operation activities (i.e. practice), some kind of operation skills are graally formed
(2) correctly understand the concepts and definitions, and master the derivation of formulas. Only by understanding the derivation of some concepts and formulas, can we achieve the positive, reverse and flexible use of formulas, so as to improve the computing ability. The reason of incorrect operation in mathematics learning is often the result of fuzzy concept, formula, rule forgetting, confusion or rigid application
2. Strengthen the reasoning training of scientific system to improve the rapidity of operation
the poor operation ability is often caused by the weak thinking ability. In teaching, we should strengthen the reasoning training on the basis of students' mastering the basic knowledge. In normal practice, we should make sure that there is a basis step by step, there are sufficient reasons, and pay attention to the sequence of operation. Generally, we should pay attention to the following aspects:
1) training must be orderly. Practice must be planned and carried out step by step. In mathematics teaching, practice can be divided into three stages: first, imitation practice stage. This is an exercise carried out under the example demonstration of the teacher after learning the new knowledge. The difficulty of the selected exercises is not high and the change is not big. Students are required to operate according to the steps and rules of the examples to ensure the correctness of the operation. At this time, it is not appropriate to put forward the speed requirements; Second, the mastery stage. This is a study organized on the basis of students' preliminary mastery of knowledge and skills. The difficulty of the exercises is appropriately increased, and the forms of the exercises are changed. Students are not only required to operate correctly, but also required to summarize and summarize the process, basis and methods of operation after obtaining the correct answers, so as to promote the operation mode to the theoretical level; Third, comprehensive application stage. At this time, we can choose some difficult comprehensive questions to train students' ability to determine the direction of operation and flexibly use the rules
(2) carry out variant exercises. In order to make students skillful, we must organize variant exercises. The so-called variant practice is the change of concepts and rules under the condition that other effective learning conditions remain unchanged. For mathematical operations, it is to change the non essential characteristics of the problem and keep its structural components unchanged. The concrete ways include the change of expression of mathematical sentences, the exchange of conditions and conclusions, the change of problems and backgrounds, etc
(3) understand the effect of practice in time and correct the mistakes in practice in time. In ability practice, it is an effective way to let students know the effect of practice in time. Psychological research shows that if the following feedback information is provided to the students who are carrying out the ability training: ① know the score of each exercise; ② encourage and urge them continuously in the process of practice; ③ analyze the mistakes in practice, then the practice effect will be significantly improved. This is because, on the one hand, students know the problem according to the feedback information, so as to adjust the learning activities and make the practice more effective; On the other hand, it also increases learning motivation to strive for better results or avoid making similar mistakes again
3. The training of thinking flexibility in the process of operation
because mathematical operation is an intelligent operation with clear direction and in line with certain rules, after a certain amount of practice, this kind of operation experience will form a fixed reaction mode and play a tendentious role in the selection of operation direction in subsequent learning, This is the "set" phenomenon in learning. When the formed inertial thinking is consistent with the way to solve new problems, it can quickly respond and get the correct answer. The phenomenon of "shrinking" and "skipping" appears in the process of calculation. This is the positive role of the fixed trend, and also the sign of students mastering knowledge and skills. For example, through the study of "quadratic equation of one variable", students have mastered the skills of using formula method and factorization method to solve quadratic equation of one variable. In the later study of quadratic function, when they encounter the operations related to quadratic equation of one variable, they will quickly make the correct response. When the conventional way of thinking is not completely consistent with or contrary to the solution of new problems, it can not be solved in a simple and flexible way, and the operation process is tedious and tedious, which leads to the wrong solution of the problem. This is the negative effect of stereotype. In practical teaching, we should overcome and prevent the negative effect of "stereotype" and cultivate the flexibility of students' calculation
4. Pay attention to cultivate students' ability of operation rationality
reasonable calculation is to make full use of operation law, proct invariance and quotient invariance, change the data and order of operation, and make the operation as simple, fast and correct as possible. The cultivation of students' simple operation ability is not only the improvement of operation ability, because in the process of cultivation, it must involve the cultivation of observation ability, inctive ability and other abilities, so the cultivation of simple operation ability is actually the cultivation of comprehensive ability. At the same time, it is necessary to cultivate students' overall view of mathematical operation. Before calculation, students should have an overall view of the overall situation. They should grasp the steps of operation, what should be calculated first and then, what are the characteristics of the numbers in the title, and what contains information, etc.
4. First, memorize all kinds of calculation rules
as parents, we think it's very simple to do primary school students' calculation problems. However, for the children who are in primary school, all kinds of operation rules are not small challenges to them
simple addition and subtraction calculation is OK. When encountering mixed operation, the rules are relatively complex, and at this time, many children feel confused< (1) if there are no brackets, there are only addition and subtraction operations or only multiplication and division operations, which only need to be calculated from left to right 2) When there are brackets, if there are multiplication and division and addition and subtraction in brackets, we should calculate multiplication and division first and then addition and subtraction 3) If there are brackets in the formula, the one inside the brackets should be calculated first, and then the one outside the brackets
memorizing the calculation rules of various types of questions is an important guarantee for children to calculate without losing a cent. If we don't master these basic operation rules well, what can we expect high scores? Of course, these rules should not be memorized. The most important thing is to let children understand why they should do so
Second, summarize and analyze the calculation methods
it is not enough to just memorize the calculation rules of various types of questions, because the rules are only a textual overview. Students need to correctly apply these concepts to the calculation types, so as to play the role of increasing scores
many children lose points when they calculate because they usually don't summarize and analyze the question types enough. After getting a strange question type, the teacher explains the answers and steps, and then it's over. Few students make this an important mark and take it out when they review. As everyone knows, the summary and analysis of these questions are the important guarantee to deal with all kinds of calculations calmly in the future
of course, when tutoring children's homework, parents should not only care about the right and wrong answers, but also pay more attention to the reasons for their children's mistakes. If it's the first time that a child is exposed to a similar type of question, parents should be more patient when tutoring, and teach the child how to calculate and what the correct steps are< Thirdly, we should strengthen the practice of various types of questions. It's not enough to memorize concepts. Although I don't advocate sea warfare, the necessary exercises must be completed
in the process of practice, it can not only help children sort out and summarize various types of questions, but also correctly apply the concept of words to them. In fact, the vast majority of children make mistakes in calculation because they are not proficient in the types of questions or do not grasp the calculation rules and steps firmly enough, and appropriate practice can quickly solve these problems
of course, in the process of practice, the question type should not be too single. We can make one or two of all the calculation questions that children have learned, so that children can consolidate their knowledge while learning new knowledge
when many children practice separately, they can always do all the right things. However, when they come across the exam, which is a comprehensive summary, the part that children lack will be highlighted immediately
it is the key for children to summarize the reasons for their mistakes and find ways to improve in the process of practice< Fourthly, we should pay attention to quality first, and then speed. Let the child complete many questions in a short time. Once the child is flustered, the accuracy of the calculation can not be guaranteed
in the early stage, especially for the lower grade pupils, parents should not pay too much attention to the speed and ignore the quality of guidance
give children enough time to calculate each topic carefully. If necessary, use other methods to check it. For example, the vertical calculation of addition can be checked by subtraction. First of all, the quality is guaranteed, and then we slowly emphasize the speed of children's problem-solving. These all have a process. Parents should not rush for quick success and instant benefit
in fact, there is another advantage of focusing on quality first and then on quantity - improving children's computing confidence. I found that in daily life, some parents always like to give their children hundreds of calculation problems in a short time. When children make some mistakes, they start to blame and punish, which greatly weakens their confidence in calculation and even becomes afraid of calculation.
as parents, we think it's very simple to do primary school students' calculation problems. However, for the children who are in primary school, all kinds of operation rules are not small challenges to them
simple addition and subtraction calculation is OK. When encountering mixed operation, the rules are relatively complex, and at this time, many children feel confused< (1) if there are no brackets, there are only addition and subtraction operations or only multiplication and division operations, which only need to be calculated from left to right 2) When there are brackets, if there are multiplication and division and addition and subtraction in brackets, we should calculate multiplication and division first and then addition and subtraction 3) If there are brackets in the formula, the one inside the brackets should be calculated first, and then the one outside the brackets
memorizing the calculation rules of various types of questions is an important guarantee for children to calculate without losing a cent. If we don't master these basic operation rules well, what can we expect high scores? Of course, these rules should not be memorized. The most important thing is to let children understand why they should do so
Second, summarize and analyze the calculation methods
it is not enough to just memorize the calculation rules of various types of questions, because the rules are only a textual overview. Students need to correctly apply these concepts to the calculation types, so as to play the role of increasing scores
many children lose points when they calculate because they usually don't summarize and analyze the question types enough. After getting a strange question type, the teacher explains the answers and steps, and then it's over. Few students make this an important mark and take it out when they review. As everyone knows, the summary and analysis of these questions are the important guarantee to deal with all kinds of calculations calmly in the future
of course, when tutoring children's homework, parents should not only care about the right and wrong answers, but also pay more attention to the reasons for their children's mistakes. If it's the first time that a child is exposed to a similar type of question, parents should be more patient when tutoring, and teach the child how to calculate and what the correct steps are< Thirdly, we should strengthen the practice of various types of questions. It's not enough to memorize concepts. Although I don't advocate sea warfare, the necessary exercises must be completed
in the process of practice, it can not only help children sort out and summarize various types of questions, but also correctly apply the concept of words to them. In fact, the vast majority of children make mistakes in calculation because they are not proficient in the types of questions or do not grasp the calculation rules and steps firmly enough, and appropriate practice can quickly solve these problems
of course, in the process of practice, the question type should not be too single. We can make one or two of all the calculation questions that children have learned, so that children can consolidate their knowledge while learning new knowledge
when many children practice separately, they can always do all the right things. However, when they come across the exam, which is a comprehensive summary, the part that children lack will be highlighted immediately
it is the key for children to summarize the reasons for their mistakes and find ways to improve in the process of practice< Fourthly, we should pay attention to quality first, and then speed. Let the child complete many questions in a short time. Once the child is flustered, the accuracy of the calculation can not be guaranteed
in the early stage, especially for the lower grade pupils, parents should not pay too much attention to the speed and ignore the quality of guidance
give children enough time to calculate each topic carefully. If necessary, use other methods to check it. For example, the vertical calculation of addition can be checked by subtraction. First of all, the quality is guaranteed, and then we slowly emphasize the speed of children's problem-solving. These all have a process. Parents should not rush for quick success and instant benefit
in fact, there is another advantage of focusing on quality first and then on quantity - improving children's computing confidence. I found that in daily life, some parents always like to give their children hundreds of calculation problems in a short time. When children make some mistakes, they start to blame and punish, which greatly weakens their confidence in calculation and even becomes afraid of calculation.
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