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 junior middle school's angle 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.
Third, 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.
Fourth, other matters needing attention
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.
Five, some suggestions about 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.