The focus of preparing for the math exam is to consolidate the foundation and master the ideas, methods and skills of solving problems. Therefore, review can be divided into two stages. First, review the knowledge points one by one and consolidate the basic stage; The key points of this stage are: comprehensive review and implementation of double basics; Standardize problem solving and train thinking; Master methods and use ideas; Pay attention to operation and improve ability; Master skills and improve speed. The second stage is to select exercises and improve problem-solving skills. In the process of reviewing knowledge points one by one, we should pay close attention to textbooks, deeply understand and master various mathematical concepts, theorems, properties, formulas and laws, as well as the internal relations and laws among various parts of knowledge, and make induction and analogy to achieve communication and series connection, thus forming a reasonable cognitive structure and knowledge network. The selection of review questions should closely follow the outline and be typical; Comprehensive. It should be conducive to the mastery and consolidation of "double basics" and the improvement of ability. At the same time, exploring "multiple solutions to one problem" and "multiple solutions to one problem" is an important way to cultivate creative thinking and comprehensive application ability.
Specifically, the review of basic knowledge, skills and methods should be based on consolidation, proficiency and comprehensiveness.
(1) Compare similar and confusing basic knowledge horizontally, so as to achieve the purpose of accurately understanding and mastering knowledge.
(2) Do a good job of checking and filling the gaps in basic knowledge in time, find out the weak links in your knowledge and skills by doing relevant exercises or wrong questions in the test paper before practice, and then review and consolidate them in a targeted manner.
(3) Consolidate basic knowledge, skills and methods through comprehensive exercises. We should attach importance to the relationship between mathematics and production and life and related disciplines, and improve the comprehensive application ability of mathematics. Familiar with the characteristics, common solutions and requirements of various types of questions.
The improvement of ability should be realized through the comprehensive application of mathematical knowledge, mathematical ideas and methods, as well as the training of analyzing and solving problems.
(1) It is necessary to explore the internal relationship between knowledge and form a knowledge network. Based on high school mathematics as a whole, the horizontal connection between chapters is excavated to form a horizontal knowledge network.
(2) Pay attention to the mastery and application of basic mathematics ideas and methods. When doing every comprehensive problem, we should consciously use mathematical ideas to promote the transformation from known to unknown, from complex to simple, and find out the channel from known to unknown, so as not to be blind.
(3) Through problem-solving practice, improve the comprehensive application of mathematical knowledge to analyze and solve problems. When solving comprehensive problems, we should first understand the concepts and related knowledge of various knowledge points involved in the problem, recall the conventional solutions to solve (prove) such problems, and determine the key and difficult points to solve (prove). Then, we should focus on exploring ways to solve the difficulties.
Respondents added 2009-11-0510: 07 1. Everyone can learn math well.
It is an indisputable fact that mathematics is boring, abstruse and abstract for many people, but it does not mean that it is difficult to learn. A famous mathematical figure once said, "Mastering mathematics means being good at solving problems, but it does not depend entirely on the number of problems solved, but also on the analysis, exploration and thorough research before solving problems." In other words, solving mathematical problems is not to regard yourself as a problem-solving machine or a problem-solving slave, but to strive to be the master of problem-solving. It is to absorb the methods and ideas of solving problems and exercise your own thinking. This is the so-called "math problem should examine the ability of candidates." So how to "analyze and explore", "think deeply and study hard" before and after solving the problem? In fact, everything in the world is interlinked. I wonder if students like Chinese? If you want to write an excellent composition, you must be careful, creative and have a writing outline. This kind of creativity must come from your own life, your own personal experience, feelings and ideas, and you can never write a good article by making it up. Then to solve a math problem, we should also examine the problem and find out what the problem is known. What are you waiting for? This is called "targeted". "De" means opening the channel between "known" and "to be sought", that is, "creativity", that is, using one's existing mathematical knowledge and problem-solving methods to communicate this connection, or breaking the problem into parts, or turning it into a familiar problem. This "creativity" is a long-term accumulation of mathematical thinking, a summary of one's own experience in solving problems, and a feeling after solving problems. So the summary after solving the problem is the most important. I remember that since primary school, the Chinese teacher always asked us to tell the central idea of an article after reading it. what is the purpose? When we finish a math problem, we should also think about and summarize its central idea: what knowledge points are involved in the problem; What problem-solving methods or ideas are used in solving problems, so as to "communicate" with the proposer and reach the realm of "understanding". Of course, the summary after solving problems should also be considered: whether there are other solutions to the problem; Whether it can be popularized to solve similar problems. Only by "drawing inferences from others" can we really "touch the analogy". In short, any study should not be greedy for perfection, but should strive for perfection.
2. Pay attention to improving study habits
1. Three bad habits in the process of mastering knowledge
Ignoring understanding, rote memorization: thinking that everything will be fine as long as you remember formulas and theorems, while ignoring the understanding of the process of knowledge deduction, it is not only difficult to extract applied knowledge, but also lose the absorption of ideas and methods involved in the process of knowledge deduction. For example, this is the fundamental reason why the trigonometric formula "often remembers and often forgets, but can't remember repeatedly", and then there is no sense of solving problems with trigonometric transformation.
Emphasis on conclusion over process: the characteristic of mathematical proposition is the causal relationship between conditions and conclusions. Ignoring the mastery of conditions will often lead to wrong results, even correct results and wrong processes. If you can't see when and how to discuss it in your study. One of the reasons is that the preconditions of mathematical knowledge are vague (such as monotonicity of logarithmic function, properties of inequality, summation formula of proportional series, maximum theorem, etc.). )
Ignore reviewing in time and strengthen understanding: Everyone knows the simple truth of "reviewing the past and learning the new", but few people persistently apply it in the learning process. Because under the careful guidance of the teacher, the content of each class seems to be "understood", so I can't bear to spend eight to ten minutes reviewing the old knowledge of the day. I don't know that "understanding" in class is the result of the joint efforts of teachers and students. If you want to "know" yourself, you must have a process of "internalization", which must extend from classroom to extracurricular. Remember, there must be a process of "understanding" from "understanding" to "meeting", and no one can forbid it.
2. Four kinds of bad mentality in the process of solving problems
Lack of accumulation of typical topics and methods that have been learned: some students have done a lot of exercises, but the effect is little and the effect is not good. The reason is that they are forced to do problems passively in order to complete the task, lacking the necessary summary and accumulation. On the basis of accumulation, we can strengthen the "theme" and "sense of theme", gradually form a "module", and constantly draw intellectual nutrition from it, thus realizing the mathematical thinking method hidden in the model. This is the process from quantitative accumulation to qualitative change, and only "accumulation-digestion-absorption" can "sublimate".
When solving new problems, there is a lack of exploration spirit: "learning mathematics without doing problems is equivalent to entering Baoshan and returning to empty space" (Chinese). In the society we are facing, new problems appear constantly and everywhere, especially in the information age. Learning mathematics requires constant exploration in problem-solving practice. Fear of difficulties and excessive dependence on teachers will form the habit of not learning actively over time. We adopt the method of "thinking before speaking, doing before commenting" in classroom teaching, precisely to stimulate learners' enthusiasm for active exploration. It is hoped that students will enhance their self-confidence, be brave in guessing, actively cooperate with teachers, and make mathematics classroom teaching a communication process of learners' thinking activities.
Ignore the standardization of problem-solving process and only pursue the answer: the process of mathematical problem-solving is a process of transformation, and of course it is inseparable from standardized and rigorous reasoning and judgment. In solving problems, jumping too much, scribbling letters and drawing by hand, it is difficult to produce correct answers with such an attitude towards slightly difficult problems. We say that the standardization of problem-solving process is not only the standardization of writing, but also the standardization of "thinking method". Students should learn to constantly standardize their own thinking process and strive to solve problems perfectly.
Do not pay attention to arithmetic, ignore the choice and implementation of operation methods: mathematical operation is carried out according to rules, and the general rules and methods must of course be firmly grasped. However, the relativity of stillness and the absoluteness of motion determine that the general methods to solve mathematical problems cannot be fixed. Therefore, when using generality, generality and general principles to solve problems, we should not ignore arithmetic, but pay more attention to guessing and inference, and choose reasonable and simple operation methods. The method of solving problems without thinking must be improved. Replacing "doing" with "seeing" or "thinking" is the root cause of poor computing ability and complicated calculation.
3. Review and consolidate three misunderstandings.
It is believed that doing more problems can replace reviewing comprehension: it is necessary to learn mathematics well and do a lot of supporting exercises. But just practicing without thinking, thinking and summing up may not have a good result. Students who only bury themselves in solving problems and don't think upward, although they have done a lot of problems, it is difficult to keep the knowledge they have learned at random. Only by rolling summary can knowledge be "preserved" forever and a leap in knowledge level can be achieved. The exercises in our usual review, midterm and monthly exams are precisely to guide students to review and understand in a multi-level, all-round and multi-angle way, so that knowledge can be networked. Therefore, in the review process, good thinking and diligent summary are necessary, and also an effective way to accumulate knowledge and methods.
Do not pay attention to the connection between knowledge and the systematization of knowledge: the proposition of mathematics in college entrance examination often examines students' comprehensive application ability at the intersection of knowledge. If we only rely on a single knowledge to master it, we will not fully understand the relationship between knowledge and knowledge system, which will inevitably lead to superficial understanding and poor comprehensive ability, and of course it is difficult to achieve good results. The "before and after" and "summary of problem-solving rules" in our usual teaching are aimed at strengthening the connection between knowledge, hoping to attract students' enough attention.
Not good at correcting mistakes that have been made: the process of correcting mistakes is the process of learning and progress, and human society is also developing in the process of fighting against mistakes. Therefore, being good at correcting mistakes and summing up experiences and lessons in time is also an important part of learning. Some students often stop at "√" and "×" in the homework corrected by the teacher, or even turn a blind eye; Just ask the test scores, and don't care or seldom care why they are "wrong". Note: Memories, whether sweet or bitter, are always beneficial and beautiful, and always encourage yourself to face the future with more confidence! The process of correcting mistakes is the process of learning and progress.