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 teachers are going to do in class, are busy taking notes in class, ignore the real class tasks, 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 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 and open-minded, and they can deeply understand the knowledge and laws of mathematics, laying 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 3: How to cultivate mathematical thinking ability 1. It is better to say it than to do it, and it makes more sense 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 4: How to Cultivate Mathematical Thinking Mode How to Cultivate Mathematical Thinking Mode
Think more about whether you can do the same problem in different ways when you usually do it.
Learn to observe a topic with your eyes and find the angle that the questioner wants to take. Each problem has its own unique characteristics. Grasp the characteristics and use the knowledge accumulated in books to answer. Mathematical thinking: If it's for the college entrance examination, it's enough to ask sea tactics. When the number of questions goes up, the so-called sense of problems comes out. If you want to take part in the competition and take part in the independent entrance examination, you must have a new perspective of topic selection, and you may have to use some clever ways of thinking, that is, to establish a mathematical model, to have an incisive analysis angle and to have a direction that others can't think of. Sometimes you should look at the topic in combination with the answer, so that you can see the gap between yourself and the answer and remember the shortcut to the answer (of course, if you have enough study time, you should read the logical reasoning article after class and analyze the difference between your own analysis angle and the author's angle, and you may have some feelings after reading it)
Question 5: How to improve mathematical thinking? Mathematics is a subject that needs strong thinking.
In the critical period of Gong High School's reflection on his own thinking intensity,
You can do some high-level brain teasers at ordinary times.
Find some calculus books if you are interested.
Calculus is a strong exercise for people's thinking! !
Question 6: How to cultivate 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.
2. Teach students how to think
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. 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.
3. Be good at mobilizing students' inner thinking ability.
First of all, we should cultivate interest and let students think in the process of generation. Teachers should carefully design each class to make it vivid, deliberately create moving situations, set attractive suspense, stimulate students' thinking sparks and desire for knowledge, and often guide students to explain their familiar practical problems with the mathematical knowledge and methods they have learned.
Question 7: 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 8: How to cultivate correct mathematical thinking As a mathematics teacher and researcher, I have been thinking about what kind of system mathematics is and how to teach it. I have had more contact and thought, and I have some own summary and experience, which I want to share with you.
The first question is, what is mathematics? There are different answers to this question from different angles. Generally speaking, the classic definition is that mathematics is a science that studies the quantitative relationship and spatial position relationship of objective reality. My answer is that mathematics is a language. We know that the function of language is communication. How to communicate? Communicate through description. In other words, the function of language is mainly embodied in "description", and the purpose of communication is achieved by describing the object to be expressed. So what does the language of mathematics describe? In what way is it described? What kind of system is it? Next, I will answer these questions step by step and propose how to cultivate mathematical thinking.
First of all, mathematics is a description and summary of objective reality. What is mathematics? As the name implies, mathematics is the study of numbers. Mathematics describes the objective quantitative relationship and spatial position relationship. Mathematics is a quantitative description of the real world and an abstract summary of objective laws. So the first step is to perceive and understand mathematics in real life. In other words, the first step is to learn mathematics intuitively and directly.
Children generally know the world through intuition, that is, they perceive the world directly and intuitively, rather than analyzing it. For example, if we ask children why they are afraid of fire, they will hold out their burned hands and say they are hot. This is the most direct feeling. Generally speaking, primary school students learn mathematics mainly through direct perception. Think about how we learned mathematics for the first time when we were children. I learned 1+2=3 when I was a child. How should I learn? Take an apple, add two apples and count three apples. So 1+2=3. All this needs to be felt and recognized through real things. I remember we learned arithmetic by counting our fingers when we were young. I learned a lot later, and my fingers were not enough. What should I do? I'm very clever, so whenever I meet an arithmetic problem, I pick up a pile of pebbles and count them.
Understanding the world through intuition is the most primitive instinct. It can even be said to be self-taught. So even people who haven't read books know how to calculate the addition, subtraction, multiplication and division of numbers. Primary school students learn mathematics mainly through this vivid and intuitive way. Now that we are middle school students, the corresponding methods of learning mathematics have also changed.
As we know, mathematics in primary schools mainly deals with specific numbers. In middle school, I got rid of specific numbers and mainly dealt with abstract letters and mathematical symbols. The main body of middle school mathematics is algebra and geometry, and geometry is mainly expressed and operated by letters. Algebra, as its name implies, is to replace numbers, and to replace concrete numbers with abstract letters and symbols. From this point, we can clearly see the essential difference between middle school mathematics and primary school mathematics. Many people think that middle school mathematics only learns more knowledge than primary school mathematics, but it is not. From elementary school mathematics to middle school mathematics, the most important thing is not that knowledge, but the change of thinking mode, from intuitive thinking to abstract logical thinking.
Now calculate 1+2=3. Of course, we don't have to count our fingers any more, and we can get the answer directly. On the one hand, practice makes perfect because of a lot of computing experience. On the other hand, it is because we can calculate directly through abstract logic without intuition and external concrete images. At this time, we have reached the second level, and we should treat mathematics abstractly and logically.
Question 9: How to cultivate students' mathematical thinking methods? Zankov, a famous educator, pointed out: "In the teaching of various subjects, we should always pay attention to developing students' logical thinking and cultivating students' flexibility and creativity." The cultivation of mathematical thinking is the soul of mathematics teaching, and the development of students' thinking is the core of mathematics teaching. It can be said that without mathematical thinking, there is no real mathematics learning. Therefore, the new curriculum standard of primary school mathematics puts forward the goal of "mathematical thinking", which refers to the development of students' general thinking level related to mathematics in primary school mathematics teaching activities, and clearly requires teachers to pay attention to enlightening and developing students' thinking and forming and developing students' mathematical thinking ability while guiding students to learn mathematics knowledge. How to cultivate primary school students' mathematical thinking ability can take the following five ways:
First, stimulate curiosity and cultivate the initiative of thinking.
Students have poor independence of thinking. They 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. In the teaching process, teachers can carefully design questions, put forward some enlightening questions, stimulate thinking, and mobilize students' enthusiasm and initiative to the maximum extent, so that students can always devote themselves to learning and thinking with high emotions and devote themselves wholeheartedly to learning.
For example, in the first class, "Understanding the Circle" is taught. The teacher first asks the students to take out a round piece of paper, fold it in half, then fold it in half before opening it. Repeatedly, let the students observe what they see on the circular piece of paper. The students suddenly concentrated to see what was left on the round paper. I found in my life that there are creases on the round paper. In another life, I found countless creases on the round paper. The teacher asked the students to continue to observe carefully. Other students spoke in succession: all the creases on the circular surface intersect at one point, and the figures on both sides of the creases are completely coincident. At this time, the teacher asked the students to open their textbooks and see what the intersection was called. What is the name of the crease? The students quickly found the answer and remembered it. When learning the relationship between the diameter and radius in the same circle, the teacher asked the students to take out a ruler and measure the diameter and radius of the round paper in their hands and the round paper in their classmates' hands respectively, which inspired the students to find out. The students quickly came to a conclusion. If you want to draw a circle, the teacher still doesn't talk about painting. Let the students draw first, satisfy their curiosity of operating compasses, and let the students discover the methods and steps of drawing circles by themselves. Throughout the class, all students have the opportunity to operate with their hands, observe with their eyes, reason with their mouths, think with their brains, observe and find problems by themselves, and actively explore and draw conclusions. The teaching effect is good. For another example, when teaching "knowing corners", students list the corners they have seen in their lives. When it comes to corners, there are different views. Some students think it is a corner, while others think it is not. How did you know? I let students learn the concept of "angle" with this riddle, and then discuss it from several directions, so that students' learning mood is always in an exciting state in acquiring new knowledge, which is conducive to the positive development and in-depth discussion of students' thinking activities.
Second, change the angle of thinking and cultivate the opposite sex.
Students' thinking ability can be effectively developed only when they are active in thinking. In the teaching process, teachers should put forward questions with moderate depth and strong thinking according to the key points of textbooks and students' reality, cultivate them to dare to seek differences, develop their thinking of seeking differences, and then develop the habit of thinking and solving problems independently.
For example, in the first lesson on the meaning of multiplication, an addition question was put forward: 9+9+9+5+9=? Let the students calculate in a simple way. One student put forward the method of 9×4+5, and another student put forward a "new scheme", suggesting the method of 9×5- 4. The student's thinking is original, and this scheme was discovered by himself. In his thinking activities, he "saw" a nonexistent 9. He assumes that the position of 5 is 9, so the topic can be assumed as 9×5 first. Then his thinking participated in the argument: 9- 4 is the actual 5 in the original question. This kind of finding and asking questions in problems that others can't see is a flash of creative thinking, and teachers should cherish and cherish it. In teaching, I often find that some students are only used to positive thinking, but not to reverse thinking. In the teaching of practical problems, guide students to ..................................................................................................................................................................... & gt
Question 10: 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 calculation, 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.