The mathematical language of 1 is abrupt in abstraction. Many students reflect that the concepts of set and mapping are difficult to understand, and they feel far away from life and seem to be "mysterious". Indeed, 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 abstract set language, logical operation language, functional language, space solid geometry and so on.
2. Transition of thinking method to rational level. The thinking method of high school mathematics is very different from that of junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as solving fractional equations in several steps; Factorization depends on what you look at first, and then what you look at. Even for plane geometry problems with very flexible thinking, their respective thinking routines are determined for equal line segments and equal angles. So junior high school students are used to this mechanical and easy-to-operate stereotype. Great changes have taken place in the thinking form of senior high school mathematics, and the abstraction of mathematical language puts forward high requirements for thinking ability. Of course, the cultivation of ability is gradual, not overnight. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades. Freshmen in senior high school must be able to transition from empirical abstract thinking to theoretical abstract thinking, and finally need to initially form dialectical thinking.
The total amount of knowledge content has increased significantly. High school mathematics has greatly increased the amount of knowledge content. For example, the first chapter of senior one algebra has 52 basic concepts and 28 mathematical symbols. The first chapter of solid geometry has 37 basic concepts and 2 1 basic axioms, theorems and inferences. Add up to only 89 basic concepts, concentrated in the first semester of senior one, forming the stage of concept intensive learning. In addition, there are only more than 70 class hours in the first semester of senior one, and the class hours for assisting practice and digestion are also reduced accordingly. It makes the math class tense, so the teaching progress is generally faster, which increases the difficulty of teaching and learning. In this way, it is inevitable that students will not adapt to high school mathematics learning, which will affect the improvement of their grades. This requires: first, do a good job of reviewing after class and remember a lot of knowledge. Second, we should understand and master the internal relationship between old and new knowledge, so that the new knowledge can be assimilated into the original knowledge structure smoothly. Thirdly, because knowledge teaching is mostly carried out in a piecemeal way, when the amount of knowledge information is too large, its memory effect will not be very good. Therefore, we should learn to sort out the knowledge structure, form a plate structure and implement "full container". If tabular, let the knowledge structure be clear at a glance; Classification, from one case to one class, from one class to many classes, from many classes to unity; Make several kinds of problems isomorphic to the same knowledge method. Fourth, it is necessary to summarize and classify more and establish a knowledge structure network of disciplines.
Second, the learning state is poor.
1 is backward in study habits because of dependence. The dependence of junior high school students on learning is obvious. First, junior high school math teachers list all kinds of questions one by one in order to improve their scores, and students rely on teachers to provide them with "models" to apply; Second, parents are eager for their children to succeed, and counseling is also common after returning to China. After entering high school, teachers' teaching methods have changed, the applied "model" has disappeared, and parents' counseling ability can't keep up. After entering high school, many students, like junior high school, are very dependent, follow the inertia of teachers and have no initiative in learning. It is manifested in the uncertain plan, waiting for class, not previewing before class, not knowing the teacher's class content, being busy taking notes in class and not hearing the "doorway".
2 lax thinking. Some students transplanted their ideas from junior high school to senior high school. They think that they didn't study hard in Grade One and Grade Two. They only worked hard for a month or two before the third grade exam, and they were easily admitted to high school. Some are key classes in key middle schools, so I think there are so many high schools. Senior one and senior two don't need to study so hard at all. As long as you work hard for a month or two before the third grade exam, you can still be admitted to an ideal university. Students who have this idea are all wet. How many students are approaching the college entrance examination because they don't study hard in Grade One and Grade Two? When they find that they have missed a lot of knowledge, it is too late to make up for their regrets.
You can't learn law. Teachers usually explain the ins and outs of knowledge in class, analyze the connotation of concepts, analyze key and difficult points, and highlight thinking methods. However, some students didn't concentrate in class, didn't hear the main points clearly or didn't listen completely, took a lot of notes and had many problems; After class, we can't consolidate, summarize and discover the connection between knowledge in time. I just do my homework, mix questions, have a little knowledge of concepts, laws, formulas and theorems, imitate mechanically and memorize by rote. Some students work overtime at night, are listless during the day, or don't listen at all in class, so they have another set. The result is half the effort, with little effect.
4 don't pay attention to the foundation. Some students who "feel good about themselves" often despise the study and training of basic knowledge, basic skills and basic methods, and often only know how to do it, but they are interested in difficult problems to show their "level". The goal is too high, and the "quantity" ignores the "quality" and falls into the sea of questions. In regular homework or exams, either calculus is wrong or "stuck" in the middle.
5 further study conditions are not available. Compared with junior high school mathematics, senior high school mathematics is a leap in depth, breadth and ability requirements. This requires you to master basic knowledge and skills to prepare for further study. High school mathematics is difficult in many places, with new methods and high analytical ability. For example, the solution of quadratic function value, the discussion of real root distribution and parameter variables, the deformation and flexible application of triangular formula, the formation of spatial concept, the application of permutation and combination and practical application problems. Some contents are still out of touch with junior high school textbooks. If we don't take remedial measures, we can't keep up with the requirements of senior three.
Third, study scientifically.
It is not enough for senior high school students to study, but also to "learn", pay attention to scientific learning methods, improve learning efficiency, change passive learning into active learning, and improve academic performance.
1 Cultivate good study habits. Repeated use of methods will become people's habit. What is a good study habit? Good study habits include making plans, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
(1) Making a plan makes the learning purpose clear, the time arrangement reasonable, unhurried and steady, which is the internal motivation to promote active learning and overcome difficulties. But the plan must be practical, with both long-term plans and short-term arrangements. In the process of implementation, we must be strict with ourselves and temper our learning will.
(2) Self-study before class is the basis of good new lessons and good learning results. Self-study before class can not only cultivate self-study ability, but also improve interest in learning new lessons and master the initiative in learning. Self-study should not go through the motions, but pay attention to quality, try to understand the teaching materials before class, pay attention to the teacher's ideas in class, grasp the key points, break through the difficulties and solve the problems in class as much as possible.
(3) Classroom is the key link to understand and master basic knowledge, skills and methods. "Learning is not enough." Students who have taught themselves before class can concentrate more on the class. They know what should be detailed and what can pass by, so they can write down what they should remember instead of copying it all down and recording it.
(4) Timely review is an important part of efficient learning. By reading textbooks repeatedly and consulting relevant materials in multiple ways, we can strengthen our understanding and memory of the basic conceptual knowledge system, link the new knowledge we have learned with the old knowledge, analyze and compare the results, and arrange the review results in the notebook at the same time, so that the new knowledge we have learned can be changed from "understanding" to "knowing".
(5) Independent homework is a process of thinking independently, analyzing and solving problems flexibly, further deepening the understanding of new knowledge and mastering new skills. This process is also a test of will and perseverance, so that the learned knowledge can be changed from "knowledge" to "familiarity" through application.
(6) Problem-solving refers to the process of making ideas flow by enlightening and supplementing answers to knowledge errors exposed in the process of independently completing homework or missing answers due to blocked thinking. Perseverance is needed to solve problems. Did the wrong homework again. Think carefully about the mistakes. If you can't really solve the problem, you should consult your teachers and classmates, review and strengthen the knowledge that is easy to make mistakes, and do appropriate repeated exercises to digest what the teacher asks the students to acquire into your own knowledge, so that the learned knowledge can be changed from "familiar" to "live".
(7) Systematic summarization is an important link to master knowledge and develop cognitive ability comprehensively, systematically and profoundly through positive thinking. To sum up, we should, on the basis of systematic review, take teaching materials as the basis, refer to notes and materials, and reveal the internal relationship between knowledge through analysis, synthesis, analogy and generalization, so as to achieve the purpose of mastering what we have learned. Frequent multi-level summary can change knowledge from "living" to "understanding".
(8) Extracurricular learning includes reading extracurricular books and newspapers, participating in academic competitions and lectures, and visiting senior students or teachers to exchange learning experiences. Extracurricular learning is a supplement and continuation of in-class learning. It can not only enrich students' cultural and scientific knowledge, deepen and consolidate what they have learned in class, but also satisfy and develop students' hobbies, cultivate students' ability to study and work independently, and stimulate students' thirst for knowledge and enthusiasm for learning.
Step by step to prevent impatience. Because of their young age and limited experience, a large number of students are prone to impatience. Some students are greedy and swallow dates; Some students want to "sprint" in a few days; Some people are complacent when they get a little success, and will never recover when they encounter setbacks. Students should know that learning is a long-term accumulation process of consolidating old knowledge and discovering new knowledge, which can never be achieved overnight. Why do you have to go to high school for three years instead of three years! A very important reason why many excellent students can get good grades is that their basic skills are solid, and their reading, writing and computing abilities have reached the level of automation or semi-automation.
Pay attention to the characteristics of the subject and find the best learning method. Mathematics is responsible for cultivating computing ability, logical thinking ability, spatial imagination and the ability to analyze and solve problems by using what you have learned. It is characterized by a high degree of abstraction, logic and wide applicability, and requires high ability. 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.
Methods vary from person to person, but four steps (preview, class, homework and review) and one step (induction and summary) are indispensable.