Junior high school mathematics learning methods:
First teach you how to learn junior high school mathematics well.
Junior high school mathematics learning should not only be satisfied with getting a correct answer, but also carefully consider the basis of each step in the operation process, whether the expression is reasonable, whether there is a simpler algorithm, and improve your operation ability over time.
Mastering mathematical concepts: There are two ways to master mathematical concepts: concept, principle, definition, formula and operation method. Firstly, the key features are summarized from a large number of examples, and the concepts are summarized and abstracted, which is called the formation of concepts. The second is to use the existing knowledge to understand and master new concepts, which is called conceptual assimilation. When learning concepts, we should grasp three points: ① the connotation of concepts. That is, the essential attribute of the object revealed by the concept; ② Extension of the concept. That is, the whole object contained in the concept; ③ Symbolic representation of concepts. Mathematical concepts generally have concise and strict symbols. Only by mastering the symbolic representation of the concept can the operation be possible. When mastering the concept, we should also pay attention to: ① mastering other expressions of the essential attributes of the concept to deepen our understanding of the concept; (2) Grasp the essential differences and interrelationships between related concepts, and make the acquired knowledge systematic and organized; ③ Define the condition in the concept as a necessary and sufficient condition, that is, it can be used as both a judgment theorem and a property theorem.
Mastering the essentials of mathematics: Because mathematics has a high degree of generality and abstraction, it is difficult to learn. Only by mastering the essence of mathematics can we understand, master and use mathematical knowledge well and play a multiplier role. The essentials of mathematics learning mainly include: ① understanding and accurately mastering basic knowledge such as mathematical concepts, formulas, axioms, theorems and laws; (2) In-depth study of examples, diligent questioning, analysis of its structural characteristics, analysis and summary of general problem-solving ideas, methods, skills and laws; ③ Dig deep into the knowledge points of mathematics, compare the old and new knowledge, promote the flexibility and transformation of knowledge, and break through the difficulties and key points; ④ Make great efforts in reviewing and consolidating, select review questions with certain gradient, inspiration, thinking, flexibility and creativity, carry out diversified training, make full use of the methods of thinking analysis and synthesis, comparison and classification, abstraction and generalization, induction and deduction, systematization and concretization, strengthen understanding and memory, improve problem-solving ability and consolidate learned knowledge.
Second, learning junior high school mathematics should pay attention to three aspects.
1, comprehensive review, reading book.
A comprehensive review is not about memorizing all the knowledge. On the contrary, it is about grasping the essence of the problem and the essential connection between the content and the method, and minimizing the things to be memorized (try to make yourself understand what you have learned, grasp the connection of the problem more, and memorize less knowledge). Moreover, if you don't remember, you will be relieved. Facts have proved that some memories will never be forgotten, while others can be based on remembering basic knowledge. This is the significance of comprehensive review.
2. Highlight key points and strive for perfection.
In the requirements of the examination syllabus, there are three levels of requirements for the content: understanding, understanding and knowing; Generally speaking, the content to be understood and the methods to be mastered are the focus of examination. In previous years' exams, the probability of this aspect is relatively high; The same test paper, the test questions in this area also occupy more scores. People who "guess the questions" often have to work hard in this respect. Generally speaking, you can really guess a few points. But when it comes to comprehensive questions, these questions contain secondary content in the main content. At this time, "guessing questions" will not work. When we talk about highlighting the key points, we should not only work hard on the main content and methods, but more importantly, we should find the connection between the key content and the secondary content, so that the main content is the secondary content and the key content covers all the content. The main content is thoroughly understood, and other contents and methods will be readily solved. In other words, grasping the main content is not to abandon the secondary content and isolate the main content, but to naturally highlight the main content from the analysis of the relationship between the contents.
3. Basic training is repeated.
When learning mathematics, we must do a certain number of problems and practice the basic skills thoroughly. However, we don't advocate the tactic of "questioning the sea", but advocate refinement, that is, doing some typical problems repeatedly, so that one problem can be solved with multiple solutions and one problem can be varied. The ability to train abstract thinking, the proof of some basic theorems, the derivation of basic formulas and some basic exercises need not be written, just like a chess player's "blind chess", and the correct answer can be obtained by meditation with his brain. This is what we often say, 20 minutes to complete 10 objective questions. Some questions can be answered at a glance without writing, which is called well-trained. People with solid basic skills of "Practice makes perfect" have many ways to encounter problems and are not easily stumped. On the contrary, when you do a problem, you are always looking for a difficult problem. In this way, when you go to the examination room, you may not encounter similar problems you have done before; Many candidates misjudge the questions they can do, which is classified as carelessness. Indeed, people will be careless, but people with solid basic skills will find out immediately when they make mistakes, and rarely make "careless" mistakes.
Third, if you have doubts, you must ask? get twice the result with half the effort
It is a very important task for teenagers to learn to learn, master the rules and methods of learning and cultivate their knowledge-seeking ability. Only by using good learning methods can we achieve it? Get twice the result with half the effort.
For mathematics learning, there are the following suggestions for your reference.
I. Reading Comprehension At present, there is a serious problem for junior middle school students to learn mathematics, that is, they are not good at reading mathematics textbooks and often memorize them. Paying attention to reading methods is very important to improve junior high school students' learning ability. To learn a new chapter, first read it roughly, that is, browse the branches of what you have learned in this chapter, then tick while reading, get a general understanding of the content of the textbook and its key points and difficulties, and mark the places you don't understand. Then read carefully, that is, according to the learning requirements of each chapter after the festival, read the content of the textbook carefully, understand the essence of mathematical concepts, formulas, laws and thinking methods and their causal relationship, grasp the key points and break through the difficulties. Read it again as a researcher, that is, discuss the context, structural relationship and arrangement intention of knowledge from the perspective of development, summarize the main points, finish reading the book, form a knowledge network and improve the cognitive structure. When students master these three reading methods and form habits, they can essentially change their learning methods and improve their learning efficiency.
Second, to improve the quality of lectures, we should cultivate the habit of listening and understanding lectures. Pay attention to the learning emphasis emphasized by the teacher in each class, the introduction and derivation methods and processes of theorems, formulas and rules, the tips and treatment methods of key parts of examples, the explanation of difficult problems, and the final summary of a class. In this way, grasping the important and difficult points and attending classes along the process of knowledge development can not only improve the efficiency of attending classes, but also improve the efficiency of attending classes. Listen. Become? Will you listen? .
3. Asking questions is an effective way to improve learning efficiency. In the process of learning, when encountering problems, take the time to ask teachers and classmates, and master the knowledge that you don't understand or learn in the shortest time. Set up your own error book and read it often to remind yourself not to make the same mistake twice. So as to improve the learning efficiency.
Suggestions on junior high school mathematics learning methods;
1, comprehensive review, reading book.
A comprehensive review is not about memorizing all the knowledge. On the contrary, it is about grasping the essence of the problem and the essential connection between the content and the method, and minimizing the things to be memorized (try to make yourself understand what you have learned, grasp the connection of the problem more, and memorize less knowledge). Moreover, if you don't remember, you will be relieved. Facts have proved that some memories will never be forgotten, while others can be based on remembering basic knowledge.
2. Highlight key points and strive for perfection.
In the requirements of the examination syllabus, there are three levels of requirements for the content: understanding, understanding and knowing; Generally speaking, the content to be understood and the methods to be mastered are the focus of examination. In previous years' exams, the probability of these problems is very high. The same test paper has many scores in this respect. People who "guess the questions" often have to work hard in this respect. Generally speaking, they can guess several points. But when they encounter comprehensive questions, these questions contain secondary content in the main content. At this time, "guessing questions" will not work. When we talk about highlighting the key points, we should not only work hard on the main contents and methods, but more importantly, find the key contents. Cover the whole content with key content. The main content is thoroughly understood, and other contents and methods will be readily solved. In other words, grasping the main content is not to abandon the secondary content and isolate the main content, but to naturally highlight the main content from the analysis of the relationship between the contents.
3. Basic training is repeated.
To learn mathematics, we should do a certain number of problems and practice the basic skills thoroughly, but we do not advocate the tactic of "sea of problems" and advocate simplicity, that is, we should do some typical problems repeatedly, so that one problem can be solved many times and one problem can be varied. We should train our abstract thinking ability, prove some basic theorems, deduce some basic formulas and practice some basic problems, so that we can do without writing, just like a "blind" chess player. In other words, we can get the correct answer. This is what we often say, we can complete 10 objective questions in 20 minutes. Some questions can be answered at a glance without writing. This is called well-trained, "practice makes perfect", and people with solid basic skills have many ways to encounter problems and are not easily stumped. On the contrary, when doing exercises, they are always looking for problems. Many candidates misjudge the questions they can do, which is classified as carelessness. Indeed, people will be careless, but people with solid basic skills will find out immediately when they make mistakes, and rarely make "careless" mistakes.