The difference between junior high school mathematics and senior high school mathematics.

1, poor knowledge.

Junior high school mathematics knowledge is less, shallow, easy and comprehensive. High school mathematics knowledge is extensive, which will promote and extend junior high school mathematics knowledge and improve junior high school mathematics knowledge. For example, the concept of angle in junior high school is only within the range of "0- 1800", and there are actually 7200 and "-300" angles. Therefore, high school will extend the concept of angle to any angle, which can represent all angles, including positive and negative angles. Another example is: when studying solid geometry in high school, you will find the volume and surface area of some geometric entities in three-dimensional space; In order to solve the problems such as the number of queuing methods, we will also learn the knowledge of "permutation and combination". For example: ① There are several queuing methods for three people in a line (=6); ② Four people play table tennis doubles. How many games are there? (A: =3 kinds) Senior high schools will learn mathematical methods to count these arrangements. It is meaningless to square a negative number in junior high school, but it is stipulated in senior high school that i2=- 1, so the square root of-1 is I, that is to say, the concept of number can be extended to the range of complex numbers. These knowledge students will learn step by step in the future study.

2. Differences in learning methods.

(1) The classroom teaching in junior high school is small and the knowledge is simple. Through slow-paced classroom teaching, we strive to make all-round students understand knowledge points and problem-solving methods. After class, the teacher assigns homework, and then repeatedly understands the knowledge through a lot of in-class and out-of-class exercises and out-of-class guidance until the students master it. In senior high school, math learning is the same as the curriculum (there are nine students studying at the same time). Every day, there are at least six classes and three classes for self-study, so that the learning time of each subject will be greatly reduced, while the amount of extracurricular questions assigned by junior high school teachers will be relatively reduced, so that the time for concentrated math learning is relatively less than that of junior high school, and math teachers will supervise each student's homework and extracurricular exercises like junior high school, so that they can master knowledge for each student before starting a new class.

(2) The difference between imitation and innovation.

Junior high school students imitate doing problems, they imitate the teacher's thinking and reasoning, and senior high school students imitate doing problems and thinking. However, with the difficulty of knowledge and the wide range of knowledge, students can't imitate it all, that is to say, students can't imitate training to do problems, and they can't develop their self-thinking ability, and their math scores can only be average. At present, the purpose of mathematical investigation in college entrance examination is to examine students' ability, avoid students' high scores and low energy, avoid thinking stereotypes, advocate innovative thinking and cultivate students' creative ability. A large number of imitations of junior high school students have brought unfavorable mentality to senior high school students, and their conservative and rigid concepts have closed their rich anti-creative spirit. For example, when students compare the sizes of A and 2a, they are either wrong or have incomplete answers. Most students don't discuss in groups.

3. Differences in students' self-study ability.

Junior high school students have low self-study ability. The problem-solving methods and mathematical ideas used in general exams have been repeatedly trained by junior high school teachers. The teacher concentrated on his patient explanation and a lot of training. Students only need to recite the conclusion to do the problem (not all), and students don't need to teach themselves. But high school has a wide range of knowledge, so it is impossible for teachers to train all the questions in the college entrance examination. Only by explaining one or two typical examples can this type of exercises be integrated. If students don't learn by themselves and don't rely on a lot of reading comprehension, they will lose the answers to a class of exercises. In addition, science is constantly developing, exams are constantly reforming, college entrance examination is also deepening with the comprehensive reform, and the development of mathematics questions is also constantly diversifying. In recent years, applied questions, exploratory questions and open questions have been constantly raised. Only when students study independently can they deeply understand and innovate and adapt to the development of modern science.

In fact, the improvement of self-study ability is also the need of a person's life. It also represents a person's accomplishment from one aspect. A person's life is only 18-24 years of study with a tutor. In the second half of his life, the most wonderful life is that he has been studying all his life and finally achieved self-improvement through self-study.

4. Differences in thinking habits

Junior high school students have a small range of learning mathematics knowledge, a low level of knowledge and a wide range of knowledge, which limits their thinking on practical problems. As far as geometry is concerned, we are all exposed to the three-dimensional space in real life, but junior high school students only learn plane geometry and cannot think and judge the three-dimensional space strictly. The range of numbers in algebra is limited to real number thinking, and it is impossible to solve the type of equation roots in depth. The diversity and extensiveness of senior high school mathematics knowledge will enable students to analyze and solve problems comprehensively, meticulously, profoundly and rigorously. It will also cultivate students' high-quality thinking. Improve students' progressive thinking.

5, the difference between quantitative and variable

In junior high school mathematics, questions, known and conclusions are all given by constants. Generally speaking, the answers are constant and quantization. When students analyze problems, most of them are quantitative. Such a process of thinking and solving problems can only solve problems unilaterally and restrictively. In high school mathematics learning, we will widely use the variability of algebra to discuss the universality and particularity of problems. For example, when solving a quadratic equation with one variable, we use the solution of equation ax2+bx+c=0 (a≠0) to discuss whether it has roots and all the roots when it has roots, so that students can quickly master the solutions of all quadratic equations with one variable. In addition, in the high school stage, we will explore the ideas of analyzing and solving problems and the mathematical ideas used in solving problems through the analysis of variables.

How to learn high school mathematics well

A good beginning is half the battle. Senior high school math class is about to start, which is related to junior high school knowledge, but it is better than junior high school math knowledge system. In senior one, we will learn functions, which is the focus of senior high school mathematics. It plays an outline role in senior high school mathematics, and it is integrated into the whole senior high school mathematics knowledge, including important mathematical thinking methods in mathematics. For example, the idea of functions and equations, the idea of combining numbers and shapes, and so on. This is also the focus of the college entrance examination. In recent years, the final questions of college entrance examination are all entitled functional investigation methods. The exercises related to function thinking methods in the college entrance examination account for more than 60% of the whole test questions.

1, has 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 yourself 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 are also returned to real life, such as the concept of angle, the generation of polar 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.

2. Establish a good habit of learning mathematics.

Habit is a stable and lasting conditioned reflex and a natural need consolidated through repeated practice. 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. In addition, we should ensure that there is a certain amount of self-study time every day, so as to broaden our knowledge and cultivate our ability to learn again.

3. Consciously cultivate your abilities in all aspects.

Mathematical ability includes five abilities: logical reasoning ability, abstract thinking ability, calculation ability, spatial imagination ability and problem solving ability. These abilities are cultivated in different mathematics learning environments. In the usual study, we should pay attention to the development of different learning places and participate in all beneficial learning practice activities, such as math second class, math competition, intelligence competition and so on. Usually pay attention to observation, such as the ability of spatial imagination is to purify thinking through examples, abstract the entities in space in the brain, and analyze and reason in the brain. The cultivation of other abilities must be developed through learning, understanding, training and application. Especially in order to cultivate these abilities, teachers will carefully design "intelligent courses" and "intelligent questions", such as multi-media teaching such as solving one question, training classification by analogy, applying models and computers, which are all good courses to cultivate mathematical abilities. In these classes, students must devote themselves to all aspects of intelligence and finally realize the all-round development of their abilities.

Other preventive measures

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 constant transformation, continuous inheritance, development and renewal of old knowledge.

2. Learn the mathematical thinking method of 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 understandings in classroom teaching: ① Find the reciprocal of 3 and -5 from the perspective of definition, and the number of reciprocal is _ _ _ _ _. ② Understanding from the angle of number axis: Which two points indicate the reciprocal of numbers? (about the point where the origin is symmetrical) 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.

Some suggestions on learning mathematics.

1, take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge added by the teacher to prepare for the college entrance examination.

2. 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 strictly.

3. Memorize mathematical laws and conclusions.

4. Establish a good relationship with classmates, strive to be a "little teacher" and form a "mutual aid group" for math learning.

5. Try to do extra-curricular math problems and increase self-study.

6. Repeatedly consolidate and eliminate forgetting before school.

7. Learn to summarize and classify. Ke: ① Classification from mathematical thoughts, ② Classification from problem-solving methods and ③ Classification from knowledge application.

On the Learning Methods of Mathematics in Senior High School

After entering high school, many students often can't adapt to mathematics learning, which in turn affects their enthusiasm for learning and even their grades plummet. There are many reasons for this. But it is mainly caused by students' ignorance of the characteristics of high school mathematics teaching content and their own learning methods. According to the characteristics of high school mathematics teaching content, this paper talks about learning methods of high school mathematics for students' reference.

First, changes in the characteristics of high school mathematics and junior high school mathematics

1, mathematical language is abrupt in abstraction.

There are significant differences in mathematics language between junior high school and senior high school. Junior high school mathematics is mainly expressed in vivid and popular language. Mathematics in senior one involves very abstract set language, logical operation language, function language, image language and so on.

2. Transition of thinking method to rational level.

Another reason why senior one students have obstacles in mathematics learning is that the thinking method of mathematics in senior high school is very different from that in junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as how many steps to solve the fractional equation, what to look at first and then what to look at in factorization, and so on. Therefore, junior high school students are used to this mechanical and easy-to-operate stereotype, while senior high school mathematics has undergone great changes in the form of thinking, and the abstraction of mathematical language puts forward high requirements for thinking ability. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades.

3. The total amount of knowledge content has increased dramatically.

Another obvious difference between high school mathematics and junior high school mathematics is the sharp increase in knowledge content. Compared with junior high school mathematics, the amount of knowledge and information received per unit time has increased a lot, and the class hours for assisting exercises and digestion have decreased accordingly.

4. Knowledge is very independent.

The systematicness of junior high school knowledge is more rigorous, which brings great convenience to our study. Because it is easy to remember and suitable for the extraction and use of knowledge. However, high school mathematics is different. It consists of several relatively independent pieces of knowledge (such as a set, propositions, inequalities, properties of functions, exponential and logarithmic functions, exponential and logarithmic equations, trigonometric ratios, trigonometric functions, series, etc.). ). Often, as soon as a knowledge point is learned, new knowledge appears immediately. Therefore, paying attention to their internal small systems and their connections has become the focus of learning.

Second, how to learn high school mathematics well

1, 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.

2, 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.

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.

3. 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.

4. Take some concrete measures according to your own learning situation.

Take math notes, especially about different aspects of concept understanding and mathematical laws. The teacher is in class.

Expand extracurricular knowledge. 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 the knowledge or reasoning that is easy to make mistakes at ordinary times to prevent it from happening again.

Submit. 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 strictly.

Recite some mathematical rules and small conclusions to automate your usual operation skills.

Or semi-automated proficiency.

Knowledge structure is often combed into plate structure, and "full container" is implemented, such as tabular,

Make the knowledge structure clear 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, and take more math classes.

Foreign topics, increase self-study and expand knowledge.

Review in time, strengthen the understanding and memory of the basic concept knowledge system, and repeat it appropriately.

Solid, eliminate forgetting before school.

Learn to summarize and classify from multiple angles and levels. Such as: ① classification from mathematical thought ② solution.

Classification of questions and methods (3) Classification from knowledge application and other aspects. Make the knowledge learned systematic, organized, thematic and networked.

Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, mathematics.

What is the way of thinking, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem are used to solve other problems.

Whether it's homework or exams, we should put accuracy first, general methods first, and

Instead of blindly pursuing speed or skill, learning math well is the important issue.

Secondly, we should master the correct learning methods. In order to train their ability to learn mathematics and change their learning methods, we must change the learning methods that are simply accepted, learn to learn to learn by accepting learning and inquiry learning, cooperative learning and experiential learning, and gradually learn the learning methods of "asking questions, exploring experiments, discussing, forming new knowledge and applying reflection" under the guidance of teachers. In this way, through the change of learning methods from single to diverse, our autonomy, exploration and cooperation in learning activities have been strengthened and we have become the masters of learning.

In the new semester, we should do a good job in every class, including the concept class of knowledge generation and formation, the exercise class of problem-solving thinking exploration and law summary, and the review class of refining and integrating mathematical thinking methods with practice. We should take these classes well, learn mathematics knowledge and master the methods of learning mathematics.

conceptual class

We should attach importance to the teaching process, actively experience the process of knowledge generation and development, find out the ins and outs of knowledge, understand the process of knowledge generation, understand the derivation process of formulas, theorems and laws, change the method of rote learning, and experience the fun of learning knowledge from the process of knowledge formation and development; In the process of solving the problem, I felt the joy of success.

Exercise class

It is necessary to master the trick of "I would rather watch it once, not do it once, not tell it once, not argue it once". In addition to listening to the teacher and watching the teacher do it, you should also do more exercises yourself, and you should actively and boldly tell everyone about your experience. When encountering problems, you should argue with your classmates and teachers, stick to the truth and correct your mistakes. Pay attention to the problem-solving thinking process displayed by the teacher in class, think more, explore more, try more, find creative proofs and solutions, and learn the problem-solving methods of "making a mountain out of a molehill", that is, take objective questions such as multiple-choice questions and fill-in-the-blank questions seriously, and never be careless, just like treating big questions, so as to write wonderfully; For a topic as big as a comprehensive question, we might as well decompose the "big" into "small" and take "retreat" as "advance", that is, decompose or retreat a relatively complex question into the simplest and most primitive one, think through these small questions and simple questions, find out the law, and then make a leap and further sublimation, thus forming a big question, that is, settle for second best. If we have this ability to decompose and synthesize, coupled with solid basic skills, what problems can't beat us?

recite

In the process of mathematics learning, we should have a clear review consciousness and gradually develop good review habits, so as to gradually learn to learn to learn. Mathematics review should be a reflective learning process. We should reflect on whether the knowledge and skills we have learned have reached the level required by the curriculum; It is necessary to reflect on what mathematical thinking methods are involved in learning, how these mathematical thinking methods are used, and what are the characteristics in the process of application; It is necessary to reflect on basic issues (including basic graphics, images, etc.). ), whether the typical problems have been really understood, and which problems can be attributed to these basic problems; We should reflect on our mistakes, find out the reasons and formulate corrective measures. In the new semester, we will prepare a "case card" for math learning, write down the mistakes we usually make, find out the "reasons" and prescribe a "prescription". We will often take it out and think about where the mistakes are, why they are wrong and how to correct them. Through your efforts, there will be no "cases" in your mathematics by the time of the senior high school entrance examination. And math review should be carried out in the process of applying math knowledge, so as to deepen understanding and develop ability. Therefore, in the new year, we should do a certain number of math exercises under the guidance of teachers, so as to draw inferences from others and use them skillfully to avoid the tactics of "practicing" rather than "repeating".

Finally, we should consciously cultivate our personal psychological quality, conduct psychological training comprehensively and systematically, and have determination, confidence, perseverance and, more importantly, a normal heart.