Because the students in any class will be divided into three levels with the progress of teaching, some students find it difficult to learn mathematics and can't keep up with their work. Therefore, organizing students with learning difficulties to participate in teachers' purposeful activities is an effective way to improve the quality of mathematics teaching in a large area.

To transform students with learning difficulties, teachers should do a good job in ideological education and academic counseling for all kinds of students in accordance with the principle of teaching students in accordance with their aptitude, so that they can all improve and develop themselves. Generally speaking, there are many reasons for students' poor grades. First of all, their intelligence development level is low, and their observation and analysis ability is poor. Secondly, their non-intelligence factors are also poor, their curiosity is low, they lack confidence in learning, their attitude towards mathematics learning is incorrect and they are not interested. To do a good job in transformational learning of students with learning difficulties, teachers must deeply understand the reasons for their backwardness, strive to develop the intellectual and non-intellectual factors of students with learning difficulties according to their actual situation, introduce suitable learning methods in a planned way, and make a series of learning method guidance from each learning link.

First, put the cultivation of non-intellectual factors of students with learning difficulties in the first place.

Non-intelligence factors play a dynamic role in the learning process. Many poor students often show a lack of interest in learning mathematics and a strong will to overcome difficulties. To solve this problem, in addition to teachers' constant concern for getting close to them and guiding and encouraging them, they should actually be introduced to some methods to cultivate their interest and exercise their will, and provide some activities that they can enjoy learning.

1. The operation mode for students with learning difficulties to consciously cultivate their interest in mathematics learning.

Look at some interesting math materials.

Consciously appreciate the beautiful characteristics of simplicity, unity, symmetry and ingenuity in mathematics.

(3) to find and solve math problems directly related to oneself.

④ Learn mathematics in the game.

⑤ Determine the small goals of learning and experience the joy of success.

6. Solve problems and read books with your favorite friends. When you can't understand the textbook, try to copy it and concentrate on your study slowly.

⑦ If you understand a lesson, you will solve a problem and gradually become interested in mathematics.

2. Operation mode of exercising strong will quality.

Mathematics learning is more difficult than other subjects, which requires hard work and stronger perseverance and patience. Students with learning difficulties are often determined to study hard, and will soon be replaced by various desires, so that their learning mind can not concentrate on learning. Therefore, we give the following suggestions for exercising the will:

Write your vows in front of you, set a goal, have the idea of not giving up until you reach your goal, and praise yourself once and for all, thus gradually extending your study time.

The way to change your mind suddenly, when a non-learning activity attracts you very much, suddenly tell yourself to study, so as to overcome your original desire and succeed, which shows that you have become a strong-willed "giant".

③ Use the characteristics of mathematics itself to cultivate one's consciousness, tenacity and self-control.

④ Learn to stick to the plan, finish math homework on time, and form the habit of self-inspection, self-supervision and self-encouragement.

Secondly, developing intelligence factors is an urgent task for students with learning difficulties.

Lack of concentration, poor memory and poor imagination make it difficult for students with learning difficulties to learn mathematics at the same price as those with good grades. Recite the same mathematical law once or twice, and gifted students may not be able to recite it more than ten times. Every time this happens, students with learning difficulties will think that they are "born stupid" and give up learning. At this point, teachers should make it clear that memory requires methods and memory ability is also acquired through exercise. The super learning method and quick memory method mentioned above should be introduced to poor students for trial use; Calm yourself down by taking a deep breath and reach the alpha wave state by self-adjustment. This programmed training may make a "stupid child" smart immediately. As long as students with learning difficulties can quickly remember the contents of the textbooks they have learned, their learning situation will soon change.

Third, students with learning difficulties should also be guided by specific learning methods.

It is common to see some children recite texts and formulas, just reading and writing repeatedly, but not analyzing and thinking, reviewing and telling themselves, while eugenics uses a completely different and efficient method, that is, remembering and repeating when it begins to recite. Thus, for students with learning difficulties, some very small learning links still need guidance. What should I do if I can't solve a math homework problem? This is a common problem for gifted students, but students with learning difficulties can't imitate writing by reviewing textbooks and reading examples, so as to understand the problems they face. Mentality, mental outlook and the combination of listening, writing, reading and speaking are the key factors that affect the effect of listening. However, students with learning difficulties have been listening to math classes inefficiently for several years. This specific operation method is the main reason for the poor learning effect of students with learning difficulties and needs the guidance of teachers.

Four-round learning method also introduces some specific methods, such as four-round review method:

① Read through and review systematically;

2 intensive reading, focusing on review;

(3) Exercises, reviewing and solving problems;

(4) Recall and test review.

Four-step problem solving method:

1 Review the topic and find out what it is;

2 conceive and find out the reasons;

3 answer, think clearly what to do;

(4) Inspection and verification.

Four-step memory method: memory, retention, recognition and reproduction.

These seemingly ordinary steps, but once you can follow them, the learning effect will immediately appear.

Some students feel at a loss when solving math problems and don't know how to think. Then we can introduce Paulia's self questioning method in solving mathematical problems, so that he can learn to think and explore.

(1) What kind of solution did I choose?

Why did I make such a choice?

(3) What stage have I reached now?

(4) What is the position of this step in the whole problem-solving process?

5] What are the main difficulties I am facing at present?

[6] What is the prospect of solving the problem?

In different stages of mathematics learning, the learning methods should be changed accordingly, which also requires the careful guidance of teachers. For example, in the second semester of senior one, students always find it difficult to get started when studying solid geometry in senior two and senior one. Many old teachers agree with the following methods. Poor students can try it in class or by themselves.

1. Look at the topic drawing (or copy the topic drawing);

2. Examine the questions to find ideas (or listen to the teacher explain ideas);

3. Read the proof process in the book;

4. Recall and write the proof process.

How to preview, how to attend classes, how to review in time and how to summarize are all unknown to students with learning difficulties. Teachers can refer to the "eight-link learning method" and give guidance according to the actual situation of students.

Fourthly, Japan's "Mathematics Super Learning Method" points out a feasible way for students with mathematics learning difficulties.

Yukio Noguchi of Japan wrote the book Super Learning Method. This paper introduces the super learning method of mathematics-airborne learning method, which is specially written for students with poor mathematical foundation. Most people will think that the foundation is very important. We should start from the foundation and understand it step by step. If you don't know anything, you must return to the basics. Because of this, students with learning difficulties will give up studying mathematics, but the airborne learning method does not need to feel guilty to recognize students with poor foundation. Omitting the mountaineering process, you can enjoy the mountain scenery directly by cable car, and you can watch it on TV without knowing the semiconductor principle. Therefore, when students with poor foundation make up their minds to learn mathematics, it is not necessary to start reviewing from a very low knowledge base, and they can start from the correct central part. If people who can't learn math well think that they have to fully understand the basics first, it is equivalent to waiting for the Yellow River to clear. The foundation is the most difficult part in mathematics. What people who are not good at math have in common is to learn from the basics. As a result, after learning a few pages, they feel bored and surrender. In fact, what they should do is to try their best to understand what they are learning at present, because as long as they understand this place, the difficulties ahead will naturally be understood.

Airborne learning method, as long as you land in "the place where you are currently studying" by skydiving. The reason is that as long as you understand what you are learning now, you will understand what you didn't understand before. For high school students, if the junior high school mathematics foundation is poor, but the senior high school set, function and solid geometry are carefully studied, the junior high school mathematics content will be easy to understand. Therefore, students with learning difficulties don't have to feel inferior because they don't learn well. Instead, we should use the idea of "airborne learning" and concentrate on understanding every problem we face. If they do encounter the confusion of previous knowledge, then consult teachers and classmates or consult relevant materials, and fall on the level of the required basic knowledge and make up this foundation at any time.

Finally, let's introduce the basic three principles of Noguchi's super learning method:

(1) Learn interesting things;

② Starting from understanding the whole content;

3 understand that 80% is moving forward.

It is very important for students with learning difficulties to abide by these three principles. Because you have to learn what you are interested in first, so it is easy to get started. After you have some experience, you will have new interests. To understand the whole content, you need to remember the general framework and grasp the key content. Don't want to remember everywhere. The mental burden is too heavy, which easily makes students with learning difficulties lose confidence. 80% of them have mastered the general content, and some people will understand it automatically after learning the following content. Therefore, students with learning difficulties need not worry about problems they don't understand, but should learn new knowledge with confidence.

Ten secrets of top students

1, in their minds, learning comes first. Learning is a business and should precede entertainment.

2. Learn the words you recite when you run every day. Stick a vocabulary beside the washbasin and recite a new word when brushing your teeth every day; No matter how unique they are, there is one thing in common: ensuring study time and perseverance.

3. Pay attention to organization. Put all the common items related to study at your fingertips, and put important school supplies and materials in a carton or drawer to avoid rummaging around.

4. Learn to read, learn to read quickly, improve the unit reading, learn to read the contents, charts and illustrations of a book, so as to know the contents of the book in advance and get more effective information; Be an active reader-keep asking questions until you understand all the information between the lines.

5. Make reasonable arrangements and encourage yourself to finish your homework that day.

6. Be good at taking notes and emphasize the efforts to take notes. Top students often take notes in class. Some draw a line in the middle of the notebook, half extract the abstract of the text, and the other half write down what the teacher added.

7. The handwriting is neat.

8. Ask questions in time.

9. Students who learn to help each other often discuss difficult problems in their homework together, use different problem-solving methods and exchange experiences with each other.

10. When taking notes from the self-study exam, pay special attention to the knowledge points you think may be taken in the exam. After class, you can do your own simulation questions according to these knowledge points and give a written answer on the eve of the exam. If the answer is not satisfactory, come back to review.

1 1, learn in advance.

In addition, most top students have a secret, and that is the influence of parents. Their parents induced their children to love reading from an early age, and put forward reasonable standards and strict requirements, doing everything possible to motivate their children to study hard. Its teaching method can be summarized in one sentence: instill a sense of responsibility in children and let them turn their sense of responsibility into action.

Learning the basic knowledge of mathematics in junior middle school

First, the learning methods of mathematical concepts

There are many concepts in mathematics. How to make students master the concept correctly should explain what kind of process is needed and to what extent. Mathematical concept is a form of thinking that reflects the essential attributes of mathematical objects. Its definition is descriptive, indicating the extension of alien species, and there is a way to add concepts to categories. A mathematical concept needs to remember the name, describe the essential attributes, realize the scope involved, and use the concept to make accurate judgments. These questions are not required by teachers. Without learning methods, it is difficult for students to study regularly.

Let's summarize the learning methods of mathematical concepts:

1. Read concepts and remember names or symbols.

2. Recite the definition and master the characteristics.

3. Give two positive and negative examples to understand the scope of conceptual reflection.

4. Practice and judge accurately.

Second, the learning methods of mathematical theorems

A definite reason consists of two parts: conditions and conclusions. This theorem must be proved. Proving process is a bridge connecting conditions and conclusions, and learning theorem is to better apply it to solve various problems.

Let's summarize the learning methods of mathematical theorems:

1. Recite the theorem.

2. Conditions and conclusions of distinguishing theorem.

3. Understand the proof process of theorem.

4. Prove related problems by applying theorems.

5. Understand the internal relations between theorems and related theorems and concepts.

Some theorems contain formulas, such as Vieta Theorem, Pythagorean Theorem and Sine Theorem, and their learning should be combined with the learning method of the formula with the same sign.

Third, the learning method of learning formula

The formula is abstract, and the letters in the formula represent infinite numbers in a certain range. Some students can master the formula in a short time, while others have to experience it repeatedly to jump out of the ever-changing digital relationship. Teachers should clearly tell students the steps needed in the process of learning formulas, so that students can master formulas quickly and smoothly.

The learning method of the mathematical formula we introduced is:

1. Write the formula and remember the relationship between the letters in the formula.

2. Understand the ins and outs of the formula and master the derivation process.

3. Check the formula with numbers and experience the law embodied in the formula in the process of concretization.

4. Make various transformations on the formula to understand its different forms of change.

5. Imagine the letters in the formula as an abstract framework, so that the formula can be used freely.

High school mathematics learning methods

First of all, we should have a good interest in learning.

More than 2,000 years ago, Confucius said, "Knowing is not as good as being kind, and being kind is not as good as being happy." It means that it is better to love something than to do it, to know it, to understand it, and to enjoy it than to like it. "Good" and "happy" mean willing to learn and enjoying learning, which is interest. Interest is the best teacher. Only when you are interested can you have hobbies. If you like it, you have to practice and enjoy it. With interest, we can form the initiative and enthusiasm of learning. In mathematics learning, we turn this spontaneous perceptual pleasure into a conscious and rational "understanding" process, which will naturally become the determination to learn mathematics well and the success of mathematics learning. So how can we establish a good interest in learning mathematics?

1. preview before class, and have doubts and curiosity about what you have learned.

2. Cooperate with the teacher in class to satisfy the excitement of the senses. In class, we should focus on solving the problems in preview, regard the teacher's questions, pauses, teaching AIDS and model demonstrations as appreciating music, answer the teacher's questions in time in class, cultivate the synchronization of thinking and teachers, improve the spirit, and turn the teacher's evaluation of your questions into a driving force to spur learning.

3. Think about problems, pay attention to induction, and tap your learning potential.

4. Pay attention to the teacher's mathematical thinking when explaining in class, and ask why you think so. How did this method come about?

5. Let the concept return to nature. All disciplines are summarized from practical problems, and mathematical concepts also return to real life, such as the concept of angle, the generation of rectangular coordinate system and the generation of polar coordinate system are all abstracted from real life. Only by returning to reality can the understanding of concepts be practical and reliable and accurate in the application of concept judgment and reasoning.

Second, form a good habit of learning mathematics.

Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class. Let your math study get used to all aspects of math classroom learning.

Third, timely understand and master the commonly used mathematical ideas and methods.

To learn high school mathematics well, we need to master it from the height of mathematical thinking methods. Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts. With mathematical ideas, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In terms of specific methods, commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and special, finite and infinite, abstraction and generalization.

1, turn your attention to ideological learning.

People's learning process is to understand and solve unknown knowledge with mastered knowledge. In the process of mathematics learning, old knowledge is used to lead out and solve new problems, and new knowledge is used to solve new knowledge when mastered. Junior high school knowledge is the foundation. If you can answer new knowledge with old knowledge, you will have the idea of transformation. It can be seen that learning is constantly transforming, inheriting, developing and updating old knowledge.

2. Learn the mathematical thinking method of mathematics textbooks.

Mathematical thinking methods in learning mathematics textbooks. Mathematics textbooks melt mathematics thoughts into mathematics knowledge system by means of suggestion and revelation. Therefore, it is very necessary to sum up and summarize mathematical thoughts in time. Summarizing mathematical thought can be divided into two steps: one is to reveal the content law of mathematical thought, that is, to extract the attributes or relationships of mathematical objects; The second is to clarify the relationship between mathematical ideas, methods and knowledge, and refine the framework to solve the whole problem. The implementation of these two steps can be carried out in classroom listening and extracurricular self-study.

Classroom learning is the main battlefield of mathematics learning. In class, teachers explain and decompose mathematical ideas in textbooks, train mathematical skills, and enable high school students to acquire rich mathematical knowledge. Scientific research activities organized by teachers can make mathematical concepts, theorems and principles in textbooks be understood and excavated to the greatest extent. For example, in the teaching of the concept of reciprocal in junior high school, teachers often have the following understanding in classroom teaching:

① Find the reciprocal of 3 and -5 by definition, and the reciprocal is _ _ _ _ _.

② Understanding from the angle of number axis: Which two points indicate that numbers are opposite? (a point symmetrical about the origin)

③ In terms of absolute value, the two numbers of absolute value _ _ _ _ _ are opposite.

④ Are the two numbers that add up to zero opposite?

These different angles of teaching will broaden students' thinking and improve their thinking quality. I hope that students can take the classroom as the main battlefield for learning.

When solving mathematical problems, we should also pay attention to solving the problem of thinking strategy, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics include: controlling complexity with simplicity, combining numbers with shapes, advancing forward and backward with each other, turning life into familiarity, turning difficulties into difficulties, turning retreat into progress, turning static into dynamic, and separating and combining.

Fourth, gradually form a "self-centered" learning model.

Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration; Correctly treat difficulties and setbacks in learning, persevere in failure, be neither arrogant nor impetuous in victory, and develop good psychological qualities of initiative, perseverance and resistance to setbacks; In the process of learning, we should follow the cognitive law, be good at using our brains, actively find problems, pay attention to the internal relationship between old and new knowledge, not be satisfied with the ready-made ideas and conclusions, and often think about the problem from many aspects and angles and explore the essence of the problem. When learning mathematics, we must pay attention to "living". You can't just read books without doing problems, and you can't just bury your head in doing problems without summing up the accumulation. We should be able to learn from textbooks and find the best learning method according to our own characteristics.

Five, according to their own learning situation, take some concrete measures.

Take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extracurricular knowledge that teachers expand in class. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.

Establish a mathematical error correction book. Write down error-prone knowledge or reasoning in case it happens again. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply understand the right things from the opposite side; Guo Shuo can get to the root of the error, so as to prescribe the right medicine; Answer questions completely and reason closely.

Recite some mathematical rules and small conclusions, so that your usual operation skills can reach the level of automation or semi-automation proficiency.

Often organize the knowledge structure into plate structure and implement "full container", such as tabulation, so that the knowledge structure can be seen at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Several kinds of problems boil down to the same knowledge method.

Read math extracurricular books and newspapers, participate in math extracurricular activities and lectures, do more extracurricular math problems, increase self-study and expand knowledge.

Review in time, strengthen the understanding and memory of the basic concept knowledge system, carry out appropriate repeated consolidation, and eliminate learning without forgetting.

Learn to summarize and classify from multiple angles and levels. Such as: ① classification from mathematical thoughts, ② classification from problem-solving methods, ③ classification from knowledge application, etc. , so that the knowledge learned is systematic, organized, thematic and networked.

Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, what is the mathematical thinking method, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem have been used in solving other problems.

Whether it is homework or exams, we should put accuracy first and general methods first, rather than blindly pursuing speed or skills. This is an important problem to learn mathematics well.