First, mathematical operations.
Operation is the basic skill to learn mathematics well. Junior high school is the golden age to cultivate mathematical operation ability. The main contents of junior high school algebra are related to operations, such as rational number operation, algebraic operation, factorization, fractional operation, radical operation, solving equations and so on. The lack of calculation ability in junior high school will directly affect the study of mathematics in senior high school. In the face of complex operations, we often pay attention to the following two points: ① emotional stability, clear arithmetic, reasonable process, even speed and accurate results; Have confidence and try to do it right once; Slow down and think carefully before writing; Less mental arithmetic, less skipping rope, and clear draft paper.
Second, the basic knowledge of mathematics
Understanding and memorizing the basic knowledge of mathematics is the premise of learning mathematics well. Understanding is to explain the meaning of things in your own words. The same mathematical concept exists in different forms in the minds of different students. Therefore, understanding is an individual's active reprocessing process of external or internal information and a creative "labor". The standards of understanding are "accuracy", "simplicity" and "comprehensiveness". "Accuracy" means grasping the essence of things; "Jane" means simple and concise; "All-round" means "seeing both trees and forests", with no emphasis or omission. The understanding of the basic knowledge of mathematics can be divided into two levels: first, the formation process and expression of knowledge; The second is the extension of knowledge and its implied mathematical thinking method and mathematical thinking method.
Memory is an individual's memory, maintenance and reproduction of his experience, and it is also the input, coding, storage and extraction of information. It is an effective memory method to try to recall with the help of keywords or hints. For example, when you see the word "parabola", you will think: What is the definition of parabola? What is the standard equation? How many properties does a parabola have? What are the typical mathematical problems about parabola? You might as well write down your thoughts first, and then consult and compare them, so that you will be more impressed. In addition, in mathematics learning, memory and reasoning should be closely combined. For example, in the chapter of trigonometric function, all formulas are based on the definition and addition theorem of trigonometric function. If we can master the method of deducing the formula while reciting it, we can effectively prevent forgetting.
Third, solve mathematical problems.
There is no shortcut to learning mathematics, and ensuring the quantity and quality of doing problems is the only way to learn mathematics well. The number of guarantees is: ① Choose the tutorial books or workbooks synchronized with the teaching materials. (2) After finishing all the exercises in a section, correct the answers. Never do a pair of answers, because it will cause thinking interruption and dependence on answers; Easy first, then difficult. When you encounter a problem that you can't do, you must jump over it first, go through all the problems at a steady speed, and solve the problems that you can do first; Don't be impatient and discouraged when there are too many questions you can't answer. In fact, the questions you think are difficult are the same for others, but it takes some time and patience; There are two ways to deal with examples: "do it first, then look at it" and "look at it first, then take the exam". (3) Choose questions with thinking value, communicate with classmates and teachers, and record your own experience in the self-study book. (4) guarantee the practice time of about 1 hour every day.
To ensure the quality is (1) the problem is not much, but the essence, learn to "dissect the sparrow". Fully understand the meaning of the question, pay attention to the translation of the whole question, and deepen the understanding of a certain condition in the question; See what basic mathematical knowledge it is related to, and whether there are some new functions or uses? Reproduce the process of thinking activities, analyze the source of ideas and the causes of mistakes, and ask to describe your own problems and feelings in colloquial language, and write whatever comes to mind in order to dig out general mathematical thinking methods and mathematical thinking methods; One question has multiple solutions, one question is changeable and pluralistic. ② Execution: Not only the thinking process but also the solving process should be executed. (3) Review: "Reviewing the past and learning the new", redoing some classic questions several times and reflecting on the wrong questions as a mirror is also an efficient and targeted learning method.
Fourth, mathematical thinking.
The integration of mathematical thinking and philosophical thinking is a high-level requirement for learning mathematics well. For example, mathematical thinking methods do not exist alone, but all have their opposites, which can be transformed and supplemented each other in the process of solving problems, such as intuition and logic, divergence and orientation, macro and micro, forward and reverse. If we can consciously turn to the opposite method when one method fails, there may be a feeling that "there is no way to doubt the mountains and rivers, and there is another village." For example, in some series problems, in addition to deductive reasoning, inductive reasoning can also be used to find the sum formula of general formula and the first n terms. It should be said that understanding the philosophical thinking in mathematical thinking and carrying out mathematical thinking under the guidance of philosophical thinking are important methods to improve students' mathematical literacy and cultivate their mathematical ability.
As long as we attach importance to the cultivation of computing ability, grasp the basic knowledge of mathematics in a down-to-earth manner, learn to do problems intelligently, and reflect on our mathematical thinking activities from a philosophical perspective, we will certainly learn mathematics well.