1. How to preview?
(1) Preview content
Before learning a new lesson, we should preview the textbook. What aspects should be previewed in senior high school mathematics? Preview concepts. Find out the key words in the definition, further think about the function of these key words, and try to understand the concept completely if you remove them.
Preview theorem. Find out the conditions and conclusions of the theorem. Analyze the application environment of the theorem and the types of proof questions, especially pay attention to the rigor of the conditions. What will happen if the conditions weaken?
Preview formula. It is necessary to master the structural characteristics and use conditions of the formula, understand the solution object of the formula, and think about whether the formula can be deformed. What are the new functions after the transformation?
Preview examples. Think about what knowledge points are examined in the example and what problem-solving methods and skills are used in the example.
After previewing, you should list some knowledge points that are worth mastering in this lesson, how much you understand, which knowledge points are difficult, and list several problem-solving methods and skills in this lesson.
(2) Preview method
Preview the new lesson is not a cursory tour, we should pay attention to the following points:
Reading. Read it roughly first to understand the main idea of the textbook. Then read carefully according to the characteristics of the topic. Mathematics textbooks can be divided into concepts, laws (including laws, theorems, inferences, properties, formulas, etc. ), diagrams, examples, exercises, etc. For example, when reading examples, students are required to: distinguish the steps of solving problems and point out the key points; Find out the basis of each step and get into the habit of asking why each step has a basis; Compare the characteristics of the examples in the same section and try to understand the intention of choosing examples; Analyze the standard format of problem-solving examples and do the problems according to the format of examples.
Mark. Different problems encountered in the preview should be marked with different symbols. For example, type "*" and "?"in key places. Next to the problem. For conclusions that need to be understood, you can add "-"at the bottom of the text, add ""after key words and phrases, and so on. It should be noted that when painting, you should have a focus, not everything. There are too many symbols, and the result is very confusing.
Batch. Preview often has its own views, ideas and experiences, so we should lose no time to write them aside. For example, it is easier to understand the proof of a theorem in another way: "Three points on a straight line without * * * determine a plane." It has two meanings: three points on a straight line without * * can be used as a plane, and only one plane can be used, that is, "it exists and is unique."
Writing includes several aspects. Write the general idea: the general idea of each chapter or unit or paragraph can be written on the edge of the book. Write a summary: write the feelings and experiences of previewing a part; Writing experience, summing up and expanding will always be beneficial to a certain part of learning. The feelings and experience of solving problems, the understanding and expansion of knowledge should be written out, which is conducive to future study, review and reflection.
2. How to attend classes and review
In class, we should focus on solving the problems in preview, regard the teacher's questions, pauses, demonstrations of teaching AIDS and models as enjoying music, answer the teacher's questions in class in time, keep the synchronization of thinking and teacher's explanation, and pay attention to transforming the teacher's evaluation of your questions into the motivation for learning. How did this method come about? Listen attentively, devote yourself to classroom study, listen attentively, and listen to how the teacher lectures, analyzes and summarizes. In addition, listen to the students' questions and answers to see if it is enlightening to you. Listen, read textbooks and blackboard writing, watch the teacher's expressions and gestures, and accept the teacher's thoughts vividly and profoundly. Think hard, keep up with the teacher's lecture ideas, and analyze how the teacher grasps the key points. Solve the problem. Under the guidance of the teacher, take the initiative to answer questions or participate in discussions. In addition, we should pay special attention to the hints in the teacher's lecture. Teachers often give some language, tone and even some action tips for some key and difficult points in lectures.
Pay attention to do some effective work:
One is to take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extra-curricular knowledge supplemented by teachers during lectures. Notes are not records, but simple and concise records of the main points and thinking methods in the above lectures for review, digestion and thinking.
The second is to establish a mathematical error correction book to record the error-prone knowledge or reasoning to prevent it from happening again. Efforts should be made to find, analyze, correct and prevent mistakes. We should be able to understand the right things from the opposite side. Guo Shuo can get to the root of the error, so as to prescribe the right medicine; Answer questions completely and reason closely.
Third, timely summary review, retrospective review: First, combine books and notes to recall what the teacher said in class, such as the ideas and methods of analyzing problems (you can also write them in a draft book while thinking). Then, open your notes and books, compare what you don't remember clearly, and make up, so as to consolidate the content of the class that day and check the effect of the lecture that day.
① Knowledge network of this unit (chapter);
② The basic ideas and methods of this chapter (which should be expressed in the form of typical cases);
(3) Self-experience, the content of this chapter, you should record the typical problems you did wrong, analyze the reasons and correct answers, and record the most valuable thinking methods or examples in this chapter, as well as the unresolved problems you have, so as to make up for them in the future.
(4) Doing a certain amount of exercises, that is, whether it is homework or exams, we should put accuracy first and general methods first, instead of blindly pursuing speed or skills. This is also an important issue for learning mathematics well.
There are wonderful ways to learn mathematics in senior high school.
3. How to improve learning efficiency
(1) Pay attention to improving thinking ability.
Some students usually study hard and do a lot of math problems, but they don't understand the main idea. In order to "prevent leakage", almost every sentence in every reference book is regarded as the focus. What is more sad is that in the process of repeated work, they never put their lengthy thinking in order, and some questions asked by teachers and classmates are often "low-level", just turn your head a little! The result of not paying attention to cultivating the feeling of solving problems is that the grades will never go up, which is the result of "reading more and more books" Mathematics problem-solving is often flexible, and everyone has his own way of thinking to solve mathematics problems, which improves learning efficiency.
Think more, enjoy more and gain more. In the usual study, you must leave quite a few topics for yourself to fully think about, especially the more difficult ones, even if you think for an hour or even longer. To solve difficult problems, as long as you think fully, even if you don't do it, the whole thinking process is valuable. Because difficult problems are often comprehensive and powerful, it requires the solver to keep divergent thinking. So problem solvers often have a long exploration process. In the whole process of exploration, students are constantly looking for breakthroughs, constantly hitting a wall, constantly adjusting their thinking offensive and making progress. At the same time, students make a lot of attempts on the knowledge and skills they have learned, which has a good review effect. Students also test their mastery of relevant knowledge by doing problems, so as to set appropriate goals for future study.
Thinking more is a good way to cultivate a person's comprehensive ability in mathematics, but some students often ignore the calculation ability and practice. Although calculators can be used in some exams, calculators cannot complete algebra, analysis and trigonometry. Sometimes students are right in solving problems, but it is a pity that they make mistakes in calculation. Some students in high school are not good at analyzing geometry. One of the important reasons is that the calculation of analytic geometry is very large. If the method is not used properly, the calculation will be more complicated and error-prone. Therefore, students must have excellent computing skills. At the same time, they should pay attention to induction when thinking about problems, let concepts return to nature and tap your learning potential.
(2) Mastering mathematical thinking methods
Mathematical thought is the soul of mathematics, and mathematical method is the behavior of mathematics. The process of solving problems by mathematical methods is the process of accumulating perceptual knowledge. When this quantity accumulates to a certain extent, it produces a qualitative leap and rises to mathematical thought. If mathematical knowledge is regarded as a magnificent building built with clever blueprints, then mathematical methods are equivalent to architectural means. This blueprint is equivalent to mathematical thinking. Correct use of mathematical ideas and methods to learn mathematics or solve problems is conducive to the comparison and classification of knowledge. Only in this way can you learn knowledge systematically and flexibly, and truly integrate what you have learned into your own knowledge structure and become your own wealth.
Mathematics is a science about thinking, and the process of learning mathematics is the process of the formation and development of mathematical thinking. Senior one is a transition from intuitive image to abstract experience, and students must attach importance to and pay close attention to training.
For example, when studying Function, a textbook for senior one, we can use quadratic function, an elementary function that students are familiar with and have a certain foundation, to develop it step by step. First, draw the image of the following function, and observe the range of the function from the image:
①y=x2-2x
②y=x2-2x，x∈[0，+∞)
③y=x2-2x，x∈(-∞，4)
④y=x2-2x，x∈[0，4]
⑤y=x2-2x，x∈[2，4]
⑥y=x2-2x，x∈[- 1，0]
We can think like this: the choice of images in different domains, the difference of the same function value domain in different domains, and further observe the monotonicity of the function from the images, and learn to use monotonicity to find the range of the following functions:
⑦y=x2-2x，x∈[a，a+ 1]
⑧y=(x-a)2- 1，x∈[2，4]
This not only helps us to learn the concept and nature of functions, but also helps us to learn important mathematical ideas such as the combination of numbers and shapes, transformation and transformation, and helps us to cultivate innovative consciousness, thus improving students' thinking ability.
Mathematical thoughts and methods are abstractions and generalizations of mathematical knowledge at a higher level, which are contained in the process of occurrence, development and application of mathematical knowledge. A math educator once said: "The math knowledge that students learned in junior high school or senior high school has little chance to be applied after entering the society, so this kind of math as knowledge is usually forgotten in less than a year or two after leaving school. However, no matter what occupation they are engaged in, the mathematical spirit and mathematical thinking method engraved in their minds have played a long-term role in their lives and work. " The track of theoretical research and talent growth shows that mathematical thinking method plays an important role in cultivating people's ability and improving people's quality.