Steps/methods
1
Know the state of learning ability
1, psychological quality. Whether a student's sense of honor and success in a specific junior high school environment can be brought to senior high school depends on whether he or she has the ability to face setbacks, calmly analyze problems and find ways to overcome difficulties and get out of trouble. Students who can learn can get good grades because they learn well. Good grades can stimulate interest, enhance confidence and want to learn more. The further development of knowledge and ability has formed a virtuous circle. Students who can't learn can't learn well and get poor grades. If they can sum up their lessons in time and change their learning methods, they will not learn badly, but they can still catch up with them after some efforts. If left unchecked, they will not make progress, work hard, lack perseverance and confidence, and their grades will get worse and worse. Therefore, high school study is a test of students' psychological quality.
2. Reflection and understanding of learning methods and habits.
(1) Learning initiative. After entering high school, many students still have strong dependence psychology like junior high school. They follow the teacher's inertia and have no initiative in learning. They don't make plans, wait for classes, don't preview before classes, don't understand what the teacher is going to do in class, are busy taking notes in class, ignore the real class task, attend to one thing and lose sight of another, and learn passively.
(2) the organization of learning. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation and extension of concepts, analyze key points and difficulties, and highlight thinking methods. But some students don't pay attention in class, don't hear the main points clearly or can't hear them completely, take a lot of notes and have a lot of problems. After class, I can't consolidate, summarize and find the connection between knowledge in time, but I am busy with homework and confused questions, and I know little about concepts, laws, formulas and theorems.
(3) ignoring the foundation. Some students who feel good about themselves often despise the study and training of basic knowledge, skills and methods, and often only know how to do it, but they are interested in difficult problems to show their level. They aim high, value quantity over quality, and fall into the ocean of problems, either making mistakes in calculation or giving up halfway in formal homework or exams.
(4) Students' bad habits in practice and homework. Mainly answer, do not believe in their own conclusions, lack of confidence and determination to solve the problem; Discuss problems without thinking independently, and develop a psychological quality of dependence; Slow work, not talking about speed, can not train the agility of thinking; My thoughts are not concentrated, and my homework and practice are not efficient.
3. Cohesive ability of knowledge.
The content of junior high school mathematics textbooks is popular and concrete, mostly constant, and the questions are few and simple; However, the content of high school mathematics is abstract, and the study of variables and letters focuses on both calculation and theoretical analysis, which increases the difficulty compared with junior high school.
On the other hand, compared with junior high school, senior high school mathematics requires a qualitative leap in the depth, breadth and ability of knowledge, and requires students to master basic knowledge and skills to prepare for further study. Because of the low starting point of junior high school textbooks, the requirements for students' ability are also low. In recent years, due to the adjustment of the content of textbooks, although the difficulty of junior high school textbooks has been reduced, in contrast, the reduction of junior high school textbooks is relatively large, and some contents are not mentioned or talked about very shallowly to cope with the senior high school entrance examination (such as quadratic function and its application). This part of the content is not in high school textbooks, but it needs to be often mentioned or applied to solve other math problems. However, due to the limitation of the college entrance examination, high school teachers dare not reduce the difficulty, which leads to high school. Therefore, in a certain sense, the adjusted textbooks have not narrowed the difficulty gap between junior and senior high school textbooks, but have increased. If remedial measures are not taken, the differentiation of students' grades is inevitable. This involves the convergence of knowledge and ability in junior and senior high schools.
2
Strive to improve one's ability
1. Improve learning methods and cultivate good study habits.
Students with different learning abilities have different learning methods, so we should try our best to learn the learning methods of more successful students ... >>
Question 2: How to cultivate students' mathematical thinking ability? According to the viewpoint of modern education, mathematics teaching is the teaching of mathematical activities, that is, the teaching of thinking activities. How to cultivate students' thinking ability and develop good thinking quality in mathematics teaching is an important subject of teaching reform. Confucius said: "Learning without thinking is useless, thinking without learning is dangerous". In order to make students think actively in mathematics learning, we must teach them the basic methods of analyzing problems, which is conducive to cultivating students' correct thinking mode. To be good at thinking, students must attach importance to the study of basic knowledge and skills. Without a solid foundation, their thinking ability cannot be improved. This paper is about some attempts to cultivate students' mathematical thinking. 1. Find a breakthrough to cultivate mathematical thinking ability. Psychologists believe that cultivating students' mathematical thinking quality is a breakthrough in cultivating and developing mathematical ability. Thinking quality includes profundity, agility, flexibility, criticism and creativity, which reflects the characteristics of different aspects of thinking, so there should be different training methods in the teaching process. The profundity of thinking is the essence of mathematics, which determines that mathematics teaching should be student-oriented and cultivate students' profundity of thinking. The difference of mathematical thinking depth reflects the difference of students' mathematical ability. To cultivate the profundity of students' mathematical thinking in teaching is actually to cultivate students' mathematical ability. In mathematics teaching, students should be educated to look at the essence through phenomena, think about problems comprehensively, and form the habit of asking questions. The agility of mathematical thinking is mainly reflected in the speed problem under the correct premise. Therefore, in mathematics teaching, on the one hand, we can consider training students' operation speed, on the other hand, we should try our best to let students master the essence of mathematical concepts and principles and improve the abstraction of the mathematical knowledge they have mastered. Because the more essential and abstract knowledge is, the wider its scope of application and the faster its retrieval speed will be. In addition, the operation speed is not only the difference in understanding mathematical knowledge, but also the difference in operation habits and thinking generalization ability. Therefore, in mathematics teaching, students should always be asked about speed, so that they can master the essentials of quick calculation. In order to cultivate students' thinking flexibility, we should strengthen the variability of mathematics teaching, provide students with a wide range of thinking association space, enable students to consider problems from various angles, quickly establish their own ideas, and truly draw inferences from one another. Teaching practice shows that variant teaching plays a great role in cultivating the flexibility of students' thinking. For example, in concept teaching, let students describe concepts in equivalent language; In the teaching of mathematical formulas, students are required to master all kinds of variations of formulas, which is conducive to cultivating the flexibility of thinking. To cultivate the quality of creative thinking, students should first learn knowledge comprehensively and form the habit of independent thinking. On the basis of independent thinking, we should also inspire students to think positively and let them think more and ask more questions. Being able to ask high-quality questions is the beginning of innovation. In mathematics teaching, students should be encouraged to put forward different opinions and guide them to think positively and identify with themselves. The new curriculum standards and textbooks have opened up a broad space for us to cultivate students' creative thinking. The cultivation of critical thinking quality can focus on guiding students to check and adjust their thinking activities. Guide students to analyze the process of finding and solving problems by themselves; What are the basic thinking methods, skills and techniques used in learning, how reasonable and effective they are, and whether there are better methods; What detours have you taken, what mistakes have you made and why? 2. The method of teaching students to think requires students to be good at thinking and must pay attention to the study of basic knowledge and skills. Without a solid foundation, their thinking ability cannot be improved. Mathematical concepts and theorems are the basis of reasoning and operation, and accurate understanding of concepts and theorems is the premise of learning mathematics well. In the teaching process, we should improve students' cognitive ability of observation and analysis, from outside to inside, from here to there. Mathematical concepts and theorems are the basis of reasoning and operation. In the teaching process, we should improve students' cognitive ability of observation and analysis, from outside to inside, from here to there; In the example class, the discovery process of solving (proving) problems should be regarded as an important teaching link, so that students should not only know how to do it, but also know why and what prompted you to do it. In mathematics practice, we should carefully examine the questions, observe them carefully, have the ability to dig out the hidden conditions that play a key role in solving problems, and use comprehensive methods and analytical methods to express them in mathematical language and symbols as much as possible in the process of solving problems (proofs). In addition, we should strengthen the training of analysis, synthesis and analogy to improve students' logical thinking ability; Strengthen reverse application ... >>
Question 3: How to cultivate students' mathematical thinking ability 1. Grasping the basic knowledge of mathematics firmly is the most basic element of mathematical thinking. The basic concepts, definitions, properties, formulas, theorems and other knowledge required by the middle school mathematics syllabus are the basis of reasoning, judgment, calculus and problem solving. Only when students firmly grasp the basic knowledge of mathematics can they be clear-cut, open-minded, deeply understand mathematical knowledge and laws, and lay a solid foundation for improving their ability to find and solve problems. Second, cultivate students' mathematical thinking ability Professor Qian Xuesen pointed out: "The ultimate wit of education lies in people's thinking process." It can be seen that mathematics teaching is essentially a process in which students understand and finally solve problems through mathematical thinking activities under the guidance of teachers. Therefore, we should pay attention to cultivating students' mathematical thinking ability in mathematics teaching. There are three forms of mathematical thinking ability, including logical reasoning ability, intuitive thinking ability and divergent thinking ability. (I) Cultivation of Logical Reasoning Ability The logical reasoning ability in mathematics refers to the ability to comprehensively analyze and prove the attributes of mathematical objects or mathematical problems by using correct thinking rules and forms. It is one of the basic mathematical abilities that students must possess. Teachers should do the following in the teaching process: First, pay attention to the teaching of basic concepts and principles. Mathematical knowledge is not a definition or a rule. The accumulation of theorems, the content of each chapter and section is not only self-contained, but also includes the analysis and synthesis of learned knowledge, the comparison and contrast between abstraction and generalization, judgment and reasoning. , to further improve their analysis, judgment and reasoning ability. Secondly, seek the training of correct thinking direction. Mathematical reasoning process is composed of a series of processes, because the conclusion of the previous reasoning may be the premise of the next reasoning, and the basis of reasoning must be extracted from many points, theorems, conditions and known conclusions. Therefore, in the teaching process, teachers should first guide students to master the basic skills of reasoning, and then pay attention to cultivating them to think about problems by using the thinking of "whole-part-whole again", and enhance their ability to turn complex problems into simple problems and unknown problems into known problems. (II) Cultivation of Intuitive Thinking Ability Kadyrov, a scientist from the former Soviet Union, once said: "No creative action can be separated from intuitive activities". In teaching, teachers should first train students to pay attention to overall observation. Secondly, teachers should pay attention to cultivating students' thinking of combining numbers with shapes. Mathematics is composed of a lot of information such as mathematics, graphics, methods and patterns. Students will use this information repeatedly when solving problems, forming a knowledge module in their minds. Once they want to solve the problem, they will associate these knowledge modules, identify and analyze them intuitively, form a comprehensive judgment on the problem, and thus get the methods and ideas to solve the problem. (3) Cultivation of Divergent Thinking Ability The neo-Confucianism of modern education holds that innovative thinking depends on divergent thinking. Divergent thinking is a way of thinking that is unconventional, seeking variation and seeking answers to questions from many aspects. In teaching, first of all, when one method and one aspect can't solve the problem, students should take the initiative to jump to another method and another aspect, think from different directions, and associate known information from multiple directions and angles; Secondly, we should give students the conditions and opportunities to think and improve their own problems independently; Finally, appropriately carry out the teaching activities of "one subject is changeable", "one subject is multi-solution" and "one method is multi-purpose". To carry out "one topic is changeable", we can reveal the logical relationship between problems through the extension and change of topics. In the process of "one problem with many solutions", we can consider this problem from multiple angles and find out the relationship, advantages and disadvantages of each method. The implementation of "one method and multiple solutions" can help students understand the relationship between knowledge points, raise their thinking to a new height and improve their ability to analyze and solve problems. Third, cultivate students to develop reflective study habits. Modern educational theory holds that the essence of education is to guide students to learn, and teachers should let students learn, so that students not only know what to learn, but also know how to learn. Therefore, teachers should not only attach importance to the study of teaching methods, but also strengthen the guidance of students' learning methods, so that students can realize the importance of reflection and learn reflective teaching. First of all, reflection runs through the process of solving problems. Paulia, a famous American mathematician, believes that problem-solving activity is not a process of mechanically executing a predetermined program, but a process of constantly adjusting it, and reflection in the process of problem-solving is particularly important. However, in the actual problem-solving process, students are generally eager to do a lot of problems and are not good at reflecting on their own thinking process, which leads to the lack of systematicness and poor structure of the knowledge they have learned. Therefore, in the teaching process, teachers >>
Question 4: How to cultivate children's mathematical thinking ability is a process, which should be completed through language. Therefore, to improve students' mathematical thinking ability, we must first train their mathematical language expression ability. What do you think of each other on a question? Tell your own thinking process correctly and methodically.
Second, cultivate students' thinking methods.
1, in the teaching of computing, teach students procedural and directional thinking, that is, where to start, what to think next and what to think again.
2. In the teaching of practical problems, it is necessary to cultivate students' thinking order, that is, how to analyze the quantitative relationship, find out the known conditions and unknown problems in the problem, establish the relationship between them, and use the known conditions to solve the unknown problems.
Specific methods: list method, drawing flow chart and line segment diagram, combing the thinking order and highlighting the thinking process through these methods.
Third, strengthen variant teaching and cultivate divergent thinking. Some students will solve the problems they see, but they will be at a loss if the problems change slightly. In view of this situation, the following methods can be adopted:
1, multiple solutions to one question (multiple solutions to one question)
2, changeable problem (a variety of forms of a problem, that is, a problem changes into a variety of different types of problems)
3. Draw more than one picture (a picture should grasp its essential characteristics and use different painting methods)
4. Ask more questions (there are many different ways to ask a question)
5. Dare to question (dare to ask questions with different opinions)
6. Design more open topics.
Question 5: How to cultivate mathematical thinking ability 1. It is better to say it than to do it, and it is better to make sense than to understand it.
& gt& gt 10 problem, let's say one. After the children finish their homework, parents may wish to encourage them to explain the difficult problems in math homework. I will often send some good training questions in the group, and you can also encourage them to think about it. If they speak well, parents can also give small rewards to make their children feel more fulfilled.
& gt& gt Cultivate the habit of questioning. In family education, parents should always guide their children to ask questions, learn to question and reflect, and gradually develop habits.
After the child comes home from school, let the child review what he learned that day: how did the teacher explain and how did the students answer? When the child answered, he then asked, "Why?" "What do you think?" Inspire the child to tell the process of thinking and try to let him make his own evaluation. Sometimes, you can deliberately make some mistakes, so that children can discover, evaluate and think. Through such training, children will gradually form independent opinions on thinking and develop the habit of questioning.
Question 6: How to cultivate pupils' mathematical thinking ability 1. Starting with concrete perceptual knowledge, actively promote students' thinking.
In the teaching of basic knowledge of mathematics, we should strengthen the teaching of forming concepts, rules and laws, which is also an important means to cultivate students' initial logical thinking ability. However, the teaching in this area is abstract, and the students are young, lack of life experience, poor abstract thinking ability and difficult to learn. Students' learning of abstract knowledge is a leap on the basis of a lot of perceptual knowledge. Perceptual knowledge is the basis for students to understand knowledge, and intuition is the way and source of information for mathematical abstract thinking. When teaching, I pay attention to the transformation from intuition to abstraction, and gradually cultivate students' abstract thinking ability. In teaching the knowledge of "angle", in order to make students get the correct concept of angle, I first guide students to observe the angles formed by objects and models, such as triangles, pentagrams, open scissors and fans, and abstract the angles from these objects. Then through physical demonstration, nail one end of two thin wooden strips together and rotate one of them, which intuitively shows that a ray can get different angles by rotating around its endpoint. Students can demonstrate by themselves with prepared learning tools, and clarify the concept of angle from the perspective of movement, so as to prepare for introducing the concepts of straight angle and rounded corner.
Second, starting from the connection between old and new knowledge, actively develop students' thinking.
Mathematical knowledge has a strict logical system. As far as students' learning process is concerned, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Students' cognitive activities are always based on existing old knowledge and experience. Every time I teach a little new knowledge, I review the old knowledge as much as possible, make full use of the existing knowledge to pave the way, and guide students to use the law of knowledge transfer and develop their thinking in the process of acquiring new knowledge. For example, when teaching the relationship between the parts of addition and subtraction, I first reviewed the names of the parts of addition, and then guided the students to draw from 35+25 = 60: 60-25 = 35; 60-35=25。 By comparison, we can see that the figures in the last two formulas are actually addends in the previous formulas. Through observation and comparison, let the students sum up the formula for finding addend: one addend = and- another addend. In this way, students are guided to learn new knowledge by reviewing the past, and new knowledge is brought into the original knowledge system, which enriches knowledge, broadens their horizons and develops their thinking.
Third, carefully design questions to guide students' thinking
Pupils have poor independence, are not good at organizing their own thinking activities, and often think of what they see. Cultivating students' logical thinking ability is mainly through the demonstration, guidance and guidance of teachers in the teaching process, so that students can acquire some thinking methods in a subtle way. Teachers carefully design questions in the teaching process, put forward some enlightening questions, stimulate thinking, and mobilize students' enthusiasm and initiative to the maximum extent. Students' thinking ability can be effectively developed only when they are active in thinking. In the teaching process, teachers should put forward thoughtful questions with moderate depth according to the key points of textbooks and students' reality, so as to activate each student's thinking activities and master the newly learned knowledge through correct thinking methods.
Fourth, carry out reasoning training to promote students' thinking.
Language is the tool and shell of thinking. Strengthening language training in mathematics classroom, especially oral reasoning training, is a good way to develop students' thinking. When studying the chapter "Decimals and Composite Numbers", because decimals and composite numbers are rewritten, more knowledge needs to be comprehensively applied, which is exactly where students are prone to make mistakes. How to break through the difficulties and let students master this part of knowledge? I pay attention to strengthening reasoning training in classroom teaching. After the students learn the examples, inspire them to summarize the rewriting methods of decimal and composite numbers, and then let the students tell the process of doing the problems according to the methods. Through such repeated reasoning training, good results have been achieved, which not only deepens students' understanding of knowledge, but also promotes the development of thinking ability.
Question 7: How to improve mathematical thinking ability? Thinking ability can only be improved after exercise. First, do more problems, and they are different types of math problems, so that your thinking will become broad. Second, do the same type of math problems with different changes to improve the flexibility of your thinking. Third, stick to one thing or two, don't slack off because you have gained something, and don't give up because you can't get results temporarily.
Question 8: How to cultivate mathematical thinking According to the characteristics of middle school students' physical and mental development, it is an effective means to stimulate students' enthusiasm for learning. Studies have shown that middle school students can often study harder under competitive conditions than under normal conditions, and the learning effect is more obvious.
Question 9: How to improve students' mathematical thinking ability? Educator Paulia said: The primary duty of a math teacher is to develop students' problem-solving ability as much as possible. However, in our previous mathematics teaching, we often paid more attention to solving mathematical problems in books, and students seemed at a loss when they encountered practical problems. Therefore, as a front-line mathematics teacher, it is very important to actively and effectively stimulate students' mathematical thinking and promote students' problem-solving ability in classroom teaching. How to do this can be carried out from the following aspects. First, cultivate students' good study habits and improve their mathematical thinking ability. Learning habits refer to the fixed attitudes and behaviors formed in learning activities. Years of educational practice have made us deeply realize that good study habits are an important condition for learning knowledge, cultivating ability and developing intelligence. Study habits not only directly affect students' current study, but also have a great influence on their future study and even work. Therefore, it is an important task for teachers to cultivate students' good study habits. As a primary school math teacher, we should not only teach students, but also guide them, not only to teach math knowledge, but also to teach them how to learn math knowledge. Teach people to fish, teach people to fish. How to teach students scientific learning methods and cultivate good study habits? What we should do is to listen, watch, think and talk more, and cultivate students' habit of thinking actively and listening carefully. Will listen: listening without listening is equal to not listening. Students should remember while listening and thinking, and grasp the main points. We should not only listen carefully to the teacher's explanation, but also listen carefully to the students' speeches and listen to the problems in others' speeches. Ability to read: mainly to cultivate students' observation ability and habits. First of all, we should give students the right to observe, and don't replace students' watching with teachers' good words. Teachers must not talk or talk less about what students can find and think for themselves. Thinking: thinking, first of all, you must be willing to think. In the classroom, students should be willing to think with their brains, not only relying on the inspiration of teachers' teaching, but also relying on promotion to urge them to think with their brains. Ask students and teachers to think immediately and be ready to answer every question they ask. Will say: listen, look, think, break through. Language is the result of thinking. If you want to talk, you must think. Grasping and asking students to say this link as much as possible in class can promote students to think more; If you want to think well, think well, think well, you have to listen carefully and watch carefully. If we catch the talk, we can promote the other three meetings. Only good study habits can improve students' thinking ability. Second, cultivate students' good habit of reflection and improve their mathematical thinking ability. In teaching, we often have such confusion: when the teacher asks questions, only a few students answer them enthusiastically, while other students often remain silent or follow other people's suggestions, but they don't know why. Sometimes the teacher designs many questions in teaching. When encountering obstacles in teaching, in order to complete the teaching progress, the teacher tells the students the answer or forget it, giving up the opportunity to guide the students to think. There are many reasons for the above situation, but one thing I think is that students lack the necessary reflection, mainly because they have no awareness of reflection or don't know how to reflect, so that many students have not found a suitable learning method; Students have no time to reflect; Teachers pay attention to self-reflection and ignore the cultivation of students' reflective ability. The new curriculum concept advocates returning the classroom to students, so that each student can become the master of learning. The key is to let students learn to study, learn to think, and especially learn to reflect. Reflection is an important mathematical activity, which is the core and motivation of mathematical activities, a positive thinking activity and exploration behavior, and assimilation, exploration, discovery and re-creation. Therefore, teachers should pay attention to their own reflection in the teaching process, and at the same time encourage students to develop the habit of reflection, so that students can learn and improve in reflection. Third, cultivate students' problem-solving methods, improve students' mathematical thinking ability 1, attach importance to knowledge transfer and broaden students' thinking. In the process of learning, some old knowledge is the basis of new knowledge, and new knowledge is the extension and development of old knowledge. Use the law of migration to develop thinking in acquiring new knowledge. It can be migrated through the relationship of knowledge chain to form a good cognitive network. A factory wants to produce a batch of machines. It was originally planned to produce 75 units a day and complete them in 20 days. The actual number of machines produced every day is 65,438+0/3 more than originally planned. How many days can this batch of production tasks be completed? Students can be guided to use fractional solution, equation solution, inverse proportion solution, normalization method and engineering problem solution. Besides, there are many other solutions. Make full use of the law of knowledge transfer to solve multiple problems. You can broaden your mind, develop your intelligence and cultivate your ability. 2. Let ... >>
Question 10: How to cultivate mathematical logical thinking ability 1. Find a breakthrough in cultivating mathematical thinking ability.
2. Teach students how to think.
3. Be good at mobilizing students' inner thinking ability.