Three cores that should be mastered in learning mathematics well
1. Core concepts
Paying attention to the investigation of concepts is the characteristic of mathematics examination questions in Beijing college entrance examination. According to the test instructions and the characteristics of the test questions, special attention should be paid to the following concepts when reviewing:
(1) necessary and sufficient conditions;
(2) Function: the essence, expression, nature (mainly monotonicity) and viewpoint of function;
(3) Number sequence: the viewpoint of function (function whose domain is countable), and the concepts of conjecture and arithmetic (ratio) number sequence are summarized;
(4) Probability statistics: random events, addition and multiplication formulas, classical (geometric) probability, estimation of population with samples, etc.
(5) Geometry related concepts: three views, spatial angle, linear programming, definition and properties of straight lines and circles, conic curves, etc.
2. Core thinking
(1) extreme principle;
(2) the viewpoint of movement change;
(3) experiment and guess;
(4) structure;
(5) If it is difficult, it will be reversed.
3. Core methodology
(1) matching method, undetermined coefficient method, method of substitution method, function image making method, maximum (minimum) value method;
(2) The image and properties of sine function and the application of sine and cosine theorem;
(3) The proof of parallelism and perpendicularity of spatial geometric elements, and the method of finding spatial angle by using spatial vectors;
(4) the solution of probability and the method of estimating the population with samples;
(5) The application of derivative sum function: the method of solving equation (zero point) and inequality problem;
(6) Analytical method to solve the conic problem.
Methods and suggestions for learning high school mathematics well.
First, gradually form? Give priority to me? learning model
Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration; Correctly treat difficulties and setbacks in learning, persevere in failure, be neither arrogant nor impetuous in victory, and develop good psychological qualities of initiative, perseverance and resistance to setbacks; In the process of learning, we should follow the cognitive law, be good at using our brains, actively find problems, pay attention to the internal relationship between old and new knowledge, not be satisfied with the ready-made ideas and conclusions, and often think about the problem from many aspects and angles and explore the essence of the problem. Must pay attention to learning mathematics? Live broadcast? You can't just read books without doing problems, and you can't just bury your head in doing problems without summing up the accumulation. We should be able to learn from textbooks and find the best learning method according to our own characteristics.
Second, develop good study habits.
1, develop a good personality. It is necessary to establish correct learning objectives, cultivate strong learning interest and tenacious learning perseverance, and have sufficient learning confidence.
2. Develop good test habits and improve reading ability. Examining questions is the key to solving problems. Mathematical problems are composed of written language, symbolic language and graphic language. We carefully scrutinize word for word, looking for a breakthrough point, thus forming a solution to the problem.
3. Develop good problem-solving habits and improve thinking ability. Cultivating and standardizing problem-solving habits is an effective way to improve the expression ability of words, symbols and graphics, and mathematical language is the basis for developing thinking ability. Therefore, only by laying a good foundation can we gradually improve our thinking ability.
4. Develop the good habit of calculus and checking, and improve the calculation ability. Students should use their brains and study hard, not only by writing, but also by oral calculation and mental calculation. For complex calculations, they should be patient, master arithmetic and pay attention to simple methods. Improve computing power, computing speed and accuracy.
5, develop the habit of induction and summary, improve the ability of generalization. After learning each section and chapter, we should summarize according to the logical relationship of knowledge, so that the knowledge we have learned will be systematic, organized and thematic, which will play a very good role in further deepening the accumulation of knowledge, using knowledge flexibly and improving our ability.
6. Improve self-regulation ability. Adapt to the new learning environment and the teaching methods of teachers in various subjects as soon as possible. We should base ourselves on our own reality, optimize our learning strategies and standardize our learning behavior in order to learn well and quickly.
Third, take some concrete measures according to your own learning situation.
Take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extracurricular knowledge that teachers expand in class. Write down the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future. Establish a mathematical error correction book. Write down error-prone knowledge or reasoning in case it happens again. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply 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. Recite some mathematical rules and small conclusions, so that your usual operation skills can reach the level of automation or semi-automation proficiency. Regularly sort out the knowledge structure, form a plate structure and implement it? Integral container? , such as tables, make the knowledge structure clear at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Several kinds of problems boil down to the same knowledge method. Read math extracurricular books and newspapers, participate in math extracurricular activities and lectures, do more extracurricular math problems, increase self-study and expand knowledge. Review in time, strengthen the understanding and memory of the basic concept knowledge system, carry out appropriate repeated consolidation, and eliminate learning without forgetting. Learn to summarize and classify from multiple angles and levels.
Such as: ① classification from mathematical thoughts, ② classification from problem-solving methods, ③ classification from knowledge application, etc. , so that the knowledge learned is systematic, organized, thematic and networked. Do you often do something after you finish the problem? Reflection? Think about the basic knowledge used in this problem, what is the mathematical thinking method, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem are used to solve other problems. Whether it is homework or exams, we should put accuracy first and general methods first, rather than blindly pursuing speed or skills. This is an important problem to learn mathematics well.
Four, timely understand and master the commonly used mathematical ideas and methods.
To learn high school mathematics well, we need to master it from the height of mathematical thinking methods. Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts. With mathematical ideas, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In terms of specific methods, commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and special, finite and infinite, abstraction and generalization. When solving mathematical problems, we should also pay attention to solving the problem of thinking strategy, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics include: controlling complexity with simplicity, combining numbers with shapes, advancing forward and backward with each other, turning life into familiarity, turning difficulties into difficulties, turning retreat into progress, turning static into dynamic, and separating and combining.