First, the 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 how to solve the fractional equation in several steps, what to look at first and then what to look at with factorization. Even for plane geometry problems with flexible thinking, they have determined their own thinking routines for equal line segments, equal angles,,, and. Therefore, junior high school students are used to the stereotype that machinery is easy to operate, while senior high school mathematics has undergone great changes in its thinking form. As mentioned in the last section, 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.
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. This requires, first, to review 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", such as tabulation, so that the knowledge structure can be seen 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, learning habits are backward because of dependence.
The dependence of junior high school students on learning is obvious. First, in order to improve scores, teachers list various types of questions in junior high school mathematics teaching, and students rely on teachers to provide them with "model essays" to apply; 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 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 the first and second days of junior high school, but only worked hard for a month or two before the junior high school exam, and some may be key classes in key middle schools. Therefore, they think there is no need to study hard in high school. 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. Because in Guangzhou, it can be said that high school education has been popularized, and there is no obvious selectivity in the topics of the senior high school entrance examination, so it is easy for students to get high marks. But the college entrance examination is different. At present, it is impossible to popularize higher education in our country. Higher education can still be said to be elite education, and only some students with good grades can be selected to go to college. Therefore, the topics of the college entrance examination are highly selective. If you are lucky enough to want to go to college in senior three, you will regret it in the end. Students may wish to check the current senior three. How many students are anxious to find a tutor because they don't study hard in Grade One and Grade Two? Now they are approaching the college entrance examination and find that they have missed a lot of knowledge.
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, basic skills and basic methods, and often only know how to do it, but they are very interested in difficult problems to show their "level", set too high a goal, emphasize "quantity" over "quality" and fall into the sea of questions. 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 parametric 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, scientific study.
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 our 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. 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) 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 and recording it all.