Preview is to read the content before class, understand its outline, and be aware of it, so as to grasp the initiative in class. Preview is an attempt to learn independently. Whether the understanding of learning content is correct, whether we can grasp its key points and gain insight into the hidden thinking methods can be tested, strengthened or corrected in time in class, which is conducive to improving our learning ability and forming the habit of self-study, so it is an important part of students' learning.
Any knowledge has a strong logic and coherence, and new knowledge is often based on what has been learned. Therefore, when previewing, we should first find out where we need to learn new knowledge, and then recall or review it again. Once you find that you have not mastered or even understood what you have learned, you should take timely measures to make up for it, overcome the learning obstacles caused by not mastering or forgetting, and create conditions for learning new content smoothly. For example, previewing the section "Addition and subtraction of algebraic expressions" involves the addition and subtraction of rational numbers, the concept of similar items, the rules for merging similar items, and the rules for removing brackets. If you have a good grasp of the knowledge you have learned, you can complete the content of this textbook by yourself. Otherwise, even if you listen carefully in class, it is impossible to complete the algebraic addition and subtraction operation because you have not mastered some learned knowledge (such as the law of removing brackets).
To preview, we should also know the basic content of the new lesson, that is, we should know what to talk about, what problems to solve, what methods to adopt, and what the key points are. When previewing, you should generally draw or mark the main points, levels and connections of the content by reading, thinking and writing, write down your own opinions or places and problems that you don't understand, and finally determine the main problems or plans to be solved when listening to lectures, so as to improve the efficiency of listening to lectures. If time permits, you can also do exercises or exercises.
2, the method of listening to lectures.
Listening to lectures is the main form of students' learning. Learning under the guidance, inspiration and help of teachers can reduce detours and difficulties and get twice the result with half the effort. So attending classes is the key to learning knowledge.
Listening to classes is one way. In addition to paying attention and keeping up with the teacher's lectures, we should also use our brains to think about how teachers ask questions, analyze problems and solve problems, especially to learn thinking methods from them, such as observation, comparison, analysis, synthesis, induction, deduction, generalization and specialization. For example, in class, on the one hand, we should understand what the teacher said, think or answer the questions raised by the teacher, on the other hand, we should independently distinguish which ones have been understood, which ones have doubts or new questions, and dare to put forward our own opinions. If you can't solve the problems in class for a while, you should write down the problems or questions, leave them to your classmates and teachers to think or consult after class, and continue to listen attentively. Don't stay here because you don't understand one thing, which will affect the later lectures. Generally, when listening to a class, you should write down the contents and methods supplemented by the main points of the teacher's lecture for review.
Step 3 review methods
Review is to learn what you have learned again, so as to achieve the purpose of in-depth understanding and firm grasp. Review is also a kind of knowledge, a summary and integration of the existing knowledge structure, and a chain of one's own knowledge network. In the review, we should closely contact with lectures, recall lecture contents or refer to class notes while reading textbooks, and solve existing knowledge defects and problems in time. It's really difficult to solve the problem that day. Please consult your classmates or teachers.
Another major task of review is to communicate the internal relationship between knowledge, clarify the key points and points, and then refine and summarize them to form a knowledge system on the basis of understanding the contents of the textbook. For example, when learning the section "parallel lines", in the review process, we should first understand the content of this section, the meaning of parallel lines, the identification of parallel lines and the characteristics of parallel lines. Then, it is necessary to understand the relationship between "identification of parallel lines" and "characteristics of parallel lines" and understand that they are all based on the premise that "two straight lines are cut by the third straight line". The former studies the relationship between the angles of three octagons to judge the parallel relationship of straight lines; The latter is to give the angle relationship between two parallel lines cut by the third straight line.
Review can't just stop at the requirements of reviewing and memorizing what you have learned, but should try to think about the process of the generation, development and solution of new knowledge and how to apply and develop what you have learned. For example, after learning two completely different positional relationships of two straight lines in the same plane-parallel and vertical, have you thought about their relationship and interaction in review?
In fact, there are many problems to be studied here:
If two straight lines are parallel, is there any other way besides the relationship between fixed length and three angles? "If two straight lines are parallel to the third straight line, then the two straight lines are parallel to each other" can also be established. How many straight lines have changed here? Everything here is parallel. Change it to vertical? On the same plane? What if it's not in the same plane? And if one of the two parallel lines is perpendicular to the known straight line, is the other perpendicular to the known straight line? ..... "and so on.
In the review process, we should pay more attention to the teacher's handling methods of new problems, and master how the teacher equivalently "transforms" new problems into familiar ones, so as to solve them with the learned methods. For example, calculation is a brand-new problem for senior one students. The existing knowledge only means power, and it is difficult for many students to start. In fact, it is the product of 23 twos, that is, the product of 22 (-2), that is, the product of 22 twos (why), so it is twice the product of 22 twos, that is, the original formula =, so you can learn to solve it. Visible, in the review, constantly improve and refine the knowledge itself or from the perspective of subject thinking method, is very conducive to the development and improvement of our own ability.
4, the method of homework
The study of various subjects is often to consolidate knowledge, deepen understanding and learn to apply by doing homework, thus forming skills and developing intelligence and ability.
Homework should be done independently on the basis of review. On the one hand, homework can check your mastery of the subject knowledge and your ability level, and it is also convenient to find problems in learning so as to correct them in time.
Doing homework must be standardized and carried out according to certain procedures and steps. (1) Take time to examine the meaning of the problem, and make clear which conditions are known, which conclusions are for your verification, what operations are involved in the problem, what is the relationship between them, whether they can be expressed intuitively, whether an unknown (or quantity) can be replaced by letters, and so on. ⑵ Analyze the above contents in detail, find out the relationship between the known and the unknown, recall relevant knowledge and methods, explore and make full use of the known conditions and relevant knowledge of the organization reasonably, and obtain unknown contents. ⑶ Write and describe the problem-solving process as required according to the problem-solving scheme obtained by inquiry, and strive to be simple, clear, complete and well-founded step by step. (4) Finally, we should review the process of solving the problem, check whether there is any problem in the rationality of the process, think about whether the method of solving the problem can be improved and whether the conclusion can be popularized. And sum up the experience of solving problems, and then develop and improve the thinking method of solving problems, and sum up some regular things.
For example, compare the complementary angle of an angle with its complementary angle.
Examination: The complementary angle of an angle and the complementary angle of this angle are known in this question, and it is required to compare their sizes. Related knowledge: definition of complementary angle and complementary angle, comparison of angles.
Analysis: From the review, we know that the angle we refer to generally refers to acute angle, right angle and obtuse angle. There is no margin for right angle and obtuse angle, so "this angle" refers to acute angle.
Method: Let this angle become.
Relationship: the complementary angle of this angle is, and the complementary angle of this angle is.
Thought: The original question becomes, which is bigger?
Solution: Contrast method.
Solution: Let this angle be, then the complementary angle of this angle is, and the complementary angle of this angle is,
And ()-() = ∴ >
That is, the complementary angle of an angle is greater than that of this angle.
After understanding the solution process, do you think that the complementary angle of any acute angle is 90% greater than its complementary angle? The fact solving process is the theoretical basis of your conjecture, so "the complementary angle of an angle is 90% larger than its complementary angle?" This rule became your invention.