Four methods to improve math scores
First of all, we should start with mathematical concepts.
The learning methods of mathematics are ever-changing, but there are laws to follow after all, and the "foundation" is eternal. Only by laying a solid foundation can we make achievements in future study. Learning the basic concepts of mathematics well is one of the important ways to lay a solid foundation.
Mathematical concepts include: mathematical definition, mathematical formula, mathematical theorem and so on. Only by mastering the correct mathematical concepts can we understand the basic mathematical language, better understand the meaning of mathematics and deal with problems with mathematical thinking.
This requires us to understand the basic definitions in textbooks, master the mathematical formulas and theorems in textbooks, and understand the problem-solving ideas of examples in textbooks. Only by mastering the basic mathematical concepts skillfully can we draw inferences from others, make our mathematical knowledge comprehensive and improve our mathematical achievements.
Second, we should develop good study habits.
Mathematics study habits include classroom habits, homework habits and exam habits. Let's talk about these three habits in detail:
First, classroom habits
Classroom learning is the main position of learning activities, and classroom efficiency will directly affect the learning effect. Therefore, we should do "four meetings" in class, that is, thinking, asking questions, taking notes and discovering.
Thinking: Just follow the teacher's thinking, so that math knowledge is more organized and easier to accept.
You can ask questions: learning is the process of finding and solving problems, so if you have questions, you can get more math knowledge.
Note-taking: The process of taking notes on topics is a process involving hands, eyes and brain, which will deepen the mastery of knowledge and improve classroom efficiency.
Will "discover": through the summary of mathematical problems, find the law, so as to get twice the result with half the effort.
Second, work habits.
Many students feel that they have learned in class, so they "mix" in their math homework, which leads to weak basic knowledge and vague basic concepts.
The core of good homework habits is "independent completion and initiative". Every day's homework should be completed today, and the homework of that day must be completed on the same day, so as to consolidate classroom knowledge and ensure memory efficiency in the first time. In addition, homework should be done independently, and "plagiarism" is a common problem for many students. Once you get into the bad habit of plagiarism, your math scores will plummet; Even if you encounter problems, please ask your classmates or teachers for help and discuss with you. Only in this way can we deepen our impression and learn better and better.
Third, test habits.
Examination is an important part of study. Through the examination, we can summarize the learning achievements at a certain stage and find the problems in learning. In mathematics, the longest mistake students make is "carelessness". Of course, carelessness is not as simple as it seems, for many reasons. You can talk about the topic of "carelessness" in detail later. If you want to develop good test habits, you should start with four processes: careful review, careful examination of questions, careful thinking and careful summary, so that every test becomes a ladder of progress.
Third, we should talk about skills when doing math problems.
Many education experts and math teachers don't recommend "sea tactics". Is the sea tactics desirable? In fact, "crowd tactics" is also a learning method, just need to add two words: "choose carefully" and "summarize well"
Be selective in the process of doing the problem. Think about what knowledge points this problem mainly talks about and whether you have encountered similar problems before. Only by carefully selecting and doing representative questions can we strengthen our understanding and mastery of knowledge points.
Many students only know how to do problems, but don't know how to summarize them, which can't reflect any learning effect. Therefore, it is very important to summarize after doing the questions. Only by summing up carefully can we accumulate experience in doing problems and achieve ideal results.
Fourth, we must work hard.
"No pains, no gains", achieving good results is not only "cleverness", but also hard work. Many students have poor grades, not because they are not smart, nor because they have the wrong methods, but because they can't bear hardships. "Bao Jianfeng comes from sharpening", and students with good grades regard learning as an interest, not a task. Therefore, if you want to learn math well, you must be prepared for a long-term attack. Only hard work can yield something.
Methods and skills of improving math scores
First, we should learn to read textbooks thoroughly.
To thoroughly understand the textbook, we should start from the following four aspects: to find out how many chapters there are in the textbook, and what each chapter mainly talks about, that is, to be familiar with the knowledge framework; What are the basic questions of each chapter? List the knowledge framework and basic questions as an outline and read them repeatedly; Familiarize yourself with and supplement the above outline by doing the questions.
Second, be good at summing up.
It should be summarized from the following three aspects: (1) summarize the solutions, paying special attention to the phenomenon of multiple solutions to one problem and multiple solutions to one problem; (2) Summarize the big questions. Summarize the problems first, and then summarize the methods; (3) summarize the mistakes. If you have any questions, please ask your teacher or classmate immediately. After a period of training, I am not as confused as a headless fly when I pick up the topic again.
Third, rational use of examples.
Examples play an important role in junior high school mathematics learning. We should make examples play a greater role in the following two aspects.
1, after-class analysis, seeing examples and understanding the examples in class does not mean that you have the ability to solve problems and transfer knowledge. After class, we need to re-examine and analyze the examples from a new angle. Due to the mastery of new knowledge, the expansion of knowledge and the guidance and teaching of teachers, we have different understandings of difficulties when we look at examples and enter a higher level. You will have a deeper understanding of the application of basic knowledge, the choice of analysis and reasoning methods. If you don't look at the examples after class, your thinking will stay at a shallow level, and you can't complete the transformation process from shallow to deep, from the outside to the inside.
2. Examples of homework reasoning. Doing problems is the most important and effective way to use knowledge to solve problems and improve ability, and it is also the key to learn mathematics well. When doing homework, we must first identify the examples, that is, what kind of examples this problem belongs to in this chapter; Secondly, we should recall how the teacher solved the problem in class, then analyze several methods to solve the problem, and finally make clear which method is the easiest. If you can't remember clearly or forget the examples you have learned before, you should take time out to read, analyze and remember.
Fourth, learn to use the wrong books.
1, check the answer, put a red cross on the wrong question, write the correct answer next to it with pens of different colors, and then do this question until you get the correct answer.
2. Set up a wrong question book, copy every wrong question on it, and have a look before each exam. Extract the abstract error reasons from the wrong questions, extract the characteristics of * *, and summarize them into the rules that should be paid attention to in the future. Take a look before the exam.
For example, nail the finished papers together, and then mark the wrong topic on the head of each paper. In this way, when you open the paper, you will know which questions are wrong, so you don't have to waste time wandering around.
Another example is to arrange the wrong questions according to the chapters where the knowledge points are located, which is convenient for analyzing the reasons for the mistakes. Also, you can add your own comments after each wrong question and write down the reasons for your mistakes. Look at your notes before the exam, it will be very rewarding.
How to remedy the poor math foundation in junior high school
1 summarize the law Many math problems have obvious laws, and the exploration of this law can only rely on ourselves. What the teacher can teach you is just the trick of finding the law. Many students and parents are curious about how to explore the law. The town teacher has no better suggestions except a lot of practice.
On the premise of remembering the formula clearly, do the questions properly. Don't blindly do a lot of questions, and then forget the last one. In fact, it was a waste of time, and then the grades didn't improve. I don't know if you have heard the saying, whether to do a problem or not, it is not to do more things, but to do fine things. As long as you master one type of question skillfully, you will still encounter the same type of question in the future.
Mathematics learning from quantitative change to qualitative change is inseparable from doing problems. It is difficult for most students to draw inferences from each other. Since we can't do it, we need to make up for it with many problems, but we can't do it blindly. First, the problem should be from easy to difficult; Second, the question should be given to the topic before the limited time model test; Third, the problem should be sorted out; Fourth, we must analyze the problem; Fifth, the question should be guessed.
4 check the wrong questions and get into the habit of checking the wrong questions after writing. During the exam, let the children write down the number of wrong questions they have checked out. Teachers and parents can give certain rewards according to the children's examination results to encourage children to check carefully.
Five Ideas of Solving Problems in Junior Middle School Mathematics
In addition to a good foundation, problem-solving efficiency is also an important factor affecting junior high school math scores. Therefore, mastering the correct problem-solving ideas is also the key to learning mathematics well. The following are five ways to solve problems in junior high school mathematics. Let's learn them together.
1, the idea of function and equation
The idea of function and equation is the most basic idea in middle school mathematics. The idea of function is to analyze and study the quantitative relationship in mathematics from the point of view of movement change, establish the functional relationship or construct the function, and then analyze and solve the related problems by using the image and nature of the function. The idea of equation is to analyze the equivalence relation in mathematics, construct an equation or an equation, and analyze and solve problems by solving or using the properties of the equation.
2. The combination of numbers and shapes.
Numbers and shapes can be changed under certain conditions. For example, some algebraic problems often have geometric background, and we can solve the related algebraic triangle problems with the help of geometric features. Some geometric problems can often be solved by algebraic methods through quantitative structural characteristics. Therefore, the idea of combining numbers and shapes plays an important role in solving problems.
3. Type of problem solving
① "Variable cell number": it means that with the help of a given figure, after careful observation and research, it can reveal the quantitative relationship contained in the figure and reflect the inherent properties of the geometric figure.
(2) "From number to shape": according to the conditions of the topic, draw the corresponding figure correctly, so that the figure can fully reflect its corresponding quantitative relationship and prompt the essential characteristics of numbers and formulas.
③ "number-shape transformation": observing the shape of the figure, analyzing the structure of the number and formula, causing association, transforming each other in time, abstracting into intuition, and prompting the implied quantitative relationship.
Classified discussion thinking
The idea of classified discussion is very important because it is logical, because it covers a wide range of knowledge points, and because it can cultivate students' ability to analyze and solve problems. The fourth reason is that it is often necessary to discuss various possibilities in practical problems.
The key to solve the problem of classified discussion is to break the whole into parts and reduce the difficulty of local discussion.
Common types
1 type: discussion caused by mathematical concepts, such as the positional relationship between real number, rational number, absolute value, point (line, circle) and circle;
The second category: discussions caused by mathematical operations, such as whether both sides of inequality are multiplied by a positive number or a negative number;
The third category: the discussion caused by the restrictive conditions of properties, theorems and formulas, such as the discussion caused by the application of the root formula of the quadratic equation of one variable;
The fourth category: the discussion caused by the uncertainty of graphic position, such as the discussion caused by related problems in right, acute and obtuse triangles.
The fifth category: classification discussion caused by the influence of some letter coefficients on the equation, such as the influence of the number of letters in quadratic function on the image, the influence of quadratic term coefficient on the image opening direction, the influence of linear term coefficient on the vertex coordinates, and the influence of constant term on the intercept.
The idea of classified discussion is a way of thinking to classify mathematical objects and seek answers. Its function is to overcome the one-sidedness of thinking and consider problems comprehensively. Classification principle: classification is neither heavy nor leakage.
4. Transformation and regression of ideas
Transformation and transformation is one of the most basic mathematical ideas in middle school mathematics and the core of all mathematical thinking methods. The combination of number and shape embodies the transformation of number and shape; The idea of function and equation embodies the mutual transformation between function, equation and inequality; The idea of classified discussion embodies the mutual transformation between the part and the whole, so the above three ideas are also the concrete manifestations of transformation and transformation.
Transformation includes equivalent transformation and non-equivalent transformation, and equivalent transformation requires the necessary cause and effect in the process of transformation; There is only one case of unequal conversion, so the conclusion should be tested, adjusted and supplemented. The principle of transformation is to turn unfamiliar and difficult problems into familiar, easily solved and solved problems, and to turn abstract problems into concrete and intuitive problems; Turn complex problems into simple ones; Turn the general into a special problem; Turn practical problems into mathematical problems and so on, so that problems can be easily solved.
Common conversion methods
① Direct transformation method: directly transform the original problem into a basic theorem, a basic formula or a basic graphic problem;
(2) method of substitution: using "method of substitution" to transform formulas into rational formulas or algebraic expressions into idempotents, and to transform complex functions, equations and inequalities into basic problems that are easy to solve;
③ Number-shape combination method: study the relationship between quantity and spatial form in the original problem, and obtain the transformation path through mutual transformation;
(4) Equivalent transformation method: the original problem is transformed into an equivalent proposition that is easy to solve, so as to achieve the purpose of reduction;
⑤ specialization method: transform the form of the original problem into a specialized form, prove the specialized problem, and make the conclusion suitable for the original problem;
⑥ construction method: "construct" a suitable mathematical model to turn the problem into an easy-to-solve one;
⑦ Coordinate method: Using coordinate system as a tool to solve geometric problems by calculation method is also an important way of transformation method.
5, special and general ideas
This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions. Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.
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