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. What is a good study habit? Including making plans, self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
(1) Make a plan. Therefore, clear learning objectives, reasonable time arrangement, unhurried and steady progress are the internal motivation to promote students' 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 hone our will to learn.
(2) self-study before class. This 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. Don't go through the motions in self-study, 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) concentrate on class. "Not learning enough" is the key link to understand and master basic knowledge, skills and methods. Students who have taught themselves before class can pay more attention to the class. They know where to listen carefully and where to go through, and then write down what they should remember, instead of copying it all.
(4) Review in time. This 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) work independently. This is a necessary process for mastering independent thinking, analyzing and solving problems, and further deepening the understanding of new knowledge and skills. This process is also a test of students' will and perseverance. Through homework exercises, students can change from "knowing" to "being familiar with" what they have learned.
(6) solving problems. Here refers to the misunderstanding of knowledge exposed in the process of independently completing homework, or the process of missing answers because of blocked thinking, which makes the thinking smooth and supplements the answers through inspiration. You must be persistent in solving problems, and do your homework if you do it wrong. If you don't understand the mistakes clearly, you should think again and again. If you can't solve it, ask teachers and classmates, review and strengthen the mistakes that are easy to make, do appropriate repeated exercises, digest what you get from teachers and classmates into your own knowledge, and persist in changing knowledge from "familiar" to "alive" for a long time.
(7) system summary. This 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".
Step by step to prevent impatience. Because students are young and have limited experience, many students are prone to impatience. Some students are greedy and quick, swallowing dates. Some want to "sprint" for a few days, some are complacent when they have achieved a little, and they will never recover when they encounter setbacks. 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 they have reached a fairly skilled level in reading, writing and calculation.
In short, the guidance of students' mathematics learning methods should strive to change ideas and teaching methods, in-class and out-of-class, learning methods and teaching methods, teachers' guidance and students' exploration, unified guidance and individual guidance, and establish a crisscross learning guidance network to promote students to master the correct learning methods.
Five kinds of bad learning states in mathematics learning in senior one.
1, learning habits are backward because of dependence. The dependence of junior high school students on learning is obvious. First, students rely on the problem "model" provided by the application teacher; Second, parents are eager for their children to succeed, and counseling is also common after returning to China. After entering senior high school, teachers' teaching methods have changed, the applied "model" is gone, and parents' counseling ability can't keep up, from "participating in learning" to "urging learning". 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 not planning, waiting for class, not previewing before class, not knowing what the teacher is going to class, 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 exam in junior high school, and they were easily admitted to senior high school, and some of them may be key classes in key middle schools. So they don't think it is necessary to study hard in senior one and senior two. As long as you work hard for a month or two before the senior three exam, you can be admitted to an ideal university. Students who have this idea are all wet. There is no obvious selectivity in the topics of the senior high school entrance examination, but the college entrance examination is different. At present, it is impossible to popularize higher education in China. Higher education can still be said to belong to an elite education, and only some students with good grades can be selected to go to college. Therefore, the topics of the senior high school entrance examination are highly selective. If you are lucky, you will regret it in the end.
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 to them all, and took a big notebook, which caused many problems. After class, we can't consolidate, summarize and find the connection between knowledge in time. We just do our homework in a hurry, confuse the problems, have a little knowledge of concepts, laws, formulas and theorems, mechanically imitate and memorize. Some students work overtime at night, are listless during the day, or don't attend classes at all.
4, do not pay attention to 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". In regular homework or exams, either calculus is wrong or "stuck" in the middle.
5. Do not have the conditions for further study. 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. Some contents are still out of touch with junior high school textbooks. If you don't take measures to check and fill the gaps, you will inevitably fail to keep up with the requirements of high school.
What changes have taken place in high school mathematics and junior high school mathematics?
Changes in the characteristics of high school mathematics and junior high school mathematics
1, the mathematical language has a sudden change 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 mode 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 dividing the equation into several steps, factorizing what to look at first and then what to look at. Even for plane geometry problems with flexible thinking, they have determined their own thinking routines for equal line segments and equal angles. 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 higher requirements for thinking ability. 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 gradually form dialectical thinking.
3. The total amount of knowledge content has increased dramatically. Another obvious difference between high school mathematics and junior high school mathematics is that it is not the "quantity" of 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. 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; Categorization, from one case to one class, from one class to many classes, from many classes to unity, makes 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.
The main reasons of mathematics learning obstacles in senior one.
After three years of study in junior high school, students enter senior high school after passing the junior high school entrance examination. However, soon after entering high school, many students (even those in key middle schools) feel uncomfortable. Faced with many learning obstacles and challenges, they are very dissatisfied with their test scores, confused and at a loss, especially in mathematics, physics, chemistry and English. Generally speaking, mathematics is the most prominent of these subjects. After the first stage, more than half of the students' interest in learning mathematics is a "numb" and "indifferent" attitude, and even nearly one-third of the students are tired of learning mathematics. If it weren't for the requirements of the college entrance examination and the timely guidance of teachers, more people would be tired of learning mathematics.
1, which is the main reason that affects the mathematics learning obstacles of senior one students.
According to the psychological characteristics of junior high school students, the present situation of junior high school teaching and the expansion of senior high school scale. Personally, I think the main factors that affect the mathematics learning obstacles in senior one are: the basic knowledge is not solid; Insufficient guidance on study habits and methods; Insufficient psychological preparation and poor psychological endurance; Interference influence of non-intelligence factors; The sharp contrast between junior high school and senior high school in teaching content, requirements and teaching methods; The teaching level of mathematics teachers in senior one is uneven.
(1) Basic knowledge is not solid.
Junior high school teaching is also affected by the pressure of entering a higher school. In order to squeeze out more time to review and prepare for the exam, squeeze out the study time of the new curriculum, and delete the contents that are not included in the exam or that I think are not important, which leads to the incomplete knowledge structure of students and poor mastery of basic knowledge. For example, junior high school students find it difficult to learn new courses such as function and plane geometry. With such a shadow, students are afraid to learn functions and solid geometry in high school, and they have a fear of learning without difficulty.
(2) The instruction of study habits and methods is not enough
Junior high school teaching pays little attention to the guidance of students' learning habits and methods, ignores the cultivation and infiltration of mathematical thinking methods (students' cognitive level is acceptable now), and is keen on mastering problem-solving methods through a lot of practice imitation, such as learning quadratic functions in junior high school.
(3) Lack of psychological preparation, weak psychological endurance and interference from non-intellectual factors.
Junior high school students enter senior high schools, especially key ones, through entrance examination. They entered high school with the joy of victory, full of pride and hope, hoping to show their talents in high school mathematics learning and get high marks like junior high school exams. In addition, because he is an "excellent student" in junior high school, he is often concerned and praised by teachers. He grows up with flowers and praise and has a sense of pride and superiority psychologically, especially in key middle schools.
In terms of advantages, we have to face fierce competition, and our sense of superiority and pride can't be taken care of by teachers in time, thus losing self-confidence and enhancing inferiority. Some students unilaterally think that after one year's (or even several months') efforts, they will get what they want. After entering high school, they want to play first, and finally try to get into college, and they are not fully prepared for the difficulties of high school study. In addition, when they suddenly encounter difficulties, their psychological endurance is not enough.
(4) The sharp contrast between junior high school and senior high school in teaching content, requirements and teaching methods.
With the implementation of junior high school curriculum reform and the continuous promotion of the nine-year consistent system, the teaching content of junior high school is constantly being deleted and the requirements are constantly being lowered. The teaching content of senior high school is to add a lot of content to the experimental revised textbook currently used. In addition, the fierce competition in the college entrance examination and the adjustment of the proposition direction of the college entrance examination (from the past knowledge-based view to the ability-based view) have led to some "strategic" adjustments in senior high school mathematics teaching, which can not keep up with the teaching progress and end the new curriculum ahead of schedule. Strive for review time regardless of the reception level of senior one students. In addition, high school mathematics teaching focuses on cultivating thinking ability, analyzing and solving problems. The training of strengthening thinking replaces the training of strengthening knowledge mastery and problem solving in junior high school. This different orientation will inevitably raise the requirements for students, which is an important factor for senior one students to feel uncomfortable.
(5) The teaching level of senior one math teachers is uneven.
The enrollment scale of each school is expanding year by year, and each school has to introduce a large number of new teachers from college graduates. Most of them were assigned to teach in the first grade. Because they don't have a deep understanding of the overall structure, system and teaching requirements of high school mathematics textbooks, and they don't have a good grasp of the physiological and psychological characteristics of freshmen, it is inevitable that they will have a high starting point (college entrance examination in one step), a long span, heavy teaching and improper handling of difficulties, even if there are. " However, due to the different teaching objects (different classes in each class), the teaching effect produced by the "old" teachers' unique expression affinity can't be simply used for reference by young teachers for a while, not to mention that freshmen in Grade One didn't trust young teachers at first and doubted their level and ability. In addition, freshmen in senior one often compare senior three teachers with junior three teachers (they have concentrated outstanding backbone teachers from various schools). Most students think that the teaching level of high school teachers is average, even worse than their junior high school teachers. The teaching level of these high school math teachers is uneven, which will have some negative effects on the math learning of freshmen. Trade Union)? Thermal Unit)? Transmission Unit)? Training Unit.
2. Suggestions on improving junior high school mathematics teaching.
In view of the main reasons that affect senior one's mathematics learning, combined with the actual situation of senior high school mathematics teaching, the following suggestions are put forward:
(1) Strengthen communication and make psychological adjustment.
As a math teacher, freshmen in senior one should clearly point out the differences and different requirements in content, requirements and learning methods between junior high school and senior high school, and lower their requirements in performance standards, so as to achieve good grades of 70-80 (100%). In the process of learning, every student will encounter learning obstacles, even severe challenges, which requires students to have the courage and perseverance to dare to challenge difficulties. Mathematics learning in senior high school needs students to use their brains and cultivate their thinking ability. There is more time and space for thinking than in junior high school. To some extent, this is much more difficult than simple mechanical imitation. ) In the process of learning, we should be good at summing up the ideas and methods to solve problems and explore the learning methods that suit us. Teachers should respect each student's personality and specialty. In the classroom, we should strive to build a relaxed, harmonious, democratic, equal and harmonious "teaching field" (to avoid serious classroom atmosphere), so that every student can dare to think and speak, pay special attention to every student's thinking, fully affirm and analyze right and wrong, seize every achievement and progress, give encouragement and praise, and help students establish self-confidence and self-improvement in learning mathematics well.
(2) Respect the foundation and cognitive level and make a smooth transition.
Objectively admit the basic knowledge structure and cognitive level of existing junior high school graduates, slow down the teaching progress and adjust the teaching strategies. According to the characteristics of the first chapter of Set and Simple Logic in Senior One, the content is abstract, there are many concepts, and there are many symbolic languages and graphic languages. It is necessary to slow down the teaching progress and appropriately reduce the teaching requirements (especially the understanding of concepts, for example, after learning the concepts of set and empty set, many teachers are eager to let students distinguish φ, {0} and {φ}, and put forward requirements for students too early, which is difficult for students to accept. ) Set attention gradient to the problem, step by step, borrow the traditional practice of junior high school, strengthen practice and make a smooth transition. For example, after completing the intersection and operation of sets, you can set the following question sequence to familiarize students with the intersection and operation of sets and establish the viewpoint of motion change.
Let the set a = {x |-3 ≤ x
①A∩B=φ ②A∩B={-3} ③A∩B={x|-3≤x≤a}
④A∩B = A⑤A∪B = { x | x & lt； 5}
For the above problems, students only need to represent sets A and B on the number axis, and move the points corresponding to real number A from left to right on the number axis to get the required range corresponding to real number A..
(3) Grasp the connection between junior high school and senior high school, and break through the teaching difficulties.
Many contents in the textbook of senior one are closely related to those in junior high school. If we can grasp their internal relations, make a comparative analysis and understanding, it will make students feel relaxed and natural in learning and eliminate learning obstacles, such as understanding the concept of function. High school students generally find it difficult. One of the important reasons is that the two narratives are not meaningful enough for students to understand. In fact, in the definition of junior high school: "If there are two variables X and Y in the process of a change, if each value of X has a unique value corresponding to it, then it is said that X is an independent variable and Y is a function of X." We can completely find out "Set A, Set B and the corresponding law F" in the definition of senior high school functions. "each value of x in the process of change" constitutes the domain of set a (function)
B (in the mapping, the elements in b do not need to have the original image). "For every value of X, Y has a unique value corresponding to it" means that there is a corresponding rule F. By analogy, the two narrative methods of junior high school are linked, so that students feel that the definition of senior high school is a transition of junior high school definition, which is broader, but the essence has not changed, and it describes a corresponding relationship (many-to-one, one-to-one). Then find out the corresponding set A, set B and corresponding rule F from the linear function, inverse proportional function and quadratic function that students are familiar with. Let students further understand the definition of function from the perspective of set mapping.
(4) Strengthen teacher training and improve teaching level.
The teaching level of teachers directly affects the transition of freshmen from junior high school to senior high school. According to the characteristics of the increase of new teachers in senior high schools, strengthening teacher training is an important means to do a good job in junior and senior high school teaching. First, we should do a good job in pre-job training, and organize training immediately after summer college students report to school. The teaching and research team leader (lesson preparation team leader) will talk about the teaching material system, key points, difficulties, keys, teaching objectives and requirements, the handling methods of each part of the teaching material, taking demonstration classes, organizing class evaluation activities, organizing new teachers to compile teaching plans, and discussing collectively. New teachers are required to finish all the exercises in the textbook during the holidays first, then do a good job of collective lesson preparation in the usual teaching process, arrange experienced teachers to prepare collective lesson plans, and conduct collective lesson preparation and discussion first. By discussing the design of lesson plans at different levels, it provides a model for young teachers to write lesson plans. In addition, young teachers are also required to strengthen classroom learning and learn the art of education and teaching that experienced teachers improvise in the classroom.
In short, there are all kinds of ideas and countermeasures to do a good job in junior and senior high school teaching. Only according to the actual situation of the school, flexible, individualized strategy is the most effective and successful approach.