In fact, the construction of mathematics foundation is much easier than other disciplines. Because the starting point, derivation process and application cases of formula theorem are very clear, as long as we start with the mathematical formula and find the starting point and process of its formula, we can win the basic knowledge.
First, the key methods to consolidate the foundation
Students with poor foundation, in particular, must honestly start from textbooks and do not need quick success. They want to review a chapter and master a chapter.
The specific method is to look at the formula first, understand and remember it, then look at the exercises after class, think about how to solve it with questions, not calculate, just think, and then look through the textbooks to see how the formula theorem is derived, especially the process and application cases.
Pay special attention to why these knowledge points are produced. For example, the mathematical meaning of set and mapping is to explain the relationship between two sets of data (elements). Functions are set-based. And the necessary and sufficient conditions arising from it.
Through this understanding, you will find that the foundation of mathematics can be mastered quickly. But remember, you must take it step by step, and don't worry.
For mistakes that are easy to make, we should take notes on the wrong questions, analyze the causes of the mistakes, and try to correct them; You can't do the problem blindly, you must do it on the basis of understanding the concept, because if you do it blindly, sometimes mistakes or misunderstandings will be consolidated and it will be more difficult to correct them.
For the typical problems in textbooks, we should deeply understand and learn to reflect after solving them: reflect on the meaning of the problems and prevent misunderstandings; Reflect on the process and prevent fallacies; Reflect on methods and strive for perfection; Reflecting on change and strategic positioning.
This can not only deeply understand this problem, but also help to expand the income of solving problems and jump out of the sea of questions!
Second, improve the application of basic knowledge.
While paying attention to the basics, we should also make a reasonable classification of high school mathematics. Classification is actually very simple, that is, it can be classified according to the big chapters of the textbook.
In the review process, students with high speed, large capacity and many methods, especially those with poor foundation, will be at a loss because they can't remember it after listening, but taking notes is an important link that can't be ignored, so you should remember the key ideas and conclusions, don't cover everything, and sort out your notes after class, because this is also a process of re-learning.
Let's talk about doing problems again. Everyone thinks that doing problems is the main theme of review, but it is not. No matter what level students are, thinking through questions is the main theme of reviewing mathematics.
Looking at the questions is mainly to look at the questions that can't be done, the questions that are wrong, especially the step that stuck you. Why write this question and this step in the answer, and why use this formula?
This formula is based on those conditions. What problem does it seem to solve? This is the direction of thinking. Many students have this problem. If you can't do the problem, you are often stuck in one step. As long as this step is solved, it will be solved later.
This is because the main points of application have not been found.
In fact, math problems are not difficult. All given conditions can be used to draw a useful conclusion. This is the key to solving problems, and this is the form of solving math problems.
The night before, a classmate asked me why I couldn't do problems, especially series problems. Here I will cite the problem of sequence to explain how to solve the problem and how to look at it.
For example, many series require common terms. As we all know, the way to find the general term is nothing more than Sn+ 1-Sn, or:
Sn-Sn- 1, or find the first term and its tolerance or common ratio. This is the basic idea. Then the condition given by the topic may be a complex function formula, but as long as the direction remains unchanged, the topic can be guaranteed to be worked out.
As we all know, two points determine a straight line, so mathematics is also two conditions that determine a formula.
Third, reasonable and effective targeted exercises.
Practice should be targeted and synchronized. If you see a problem and do it, you will often fail to consolidate it, with low efficiency and poor effect. Must learn to finish within a time limit, so as to improve efficiency, enhance the sense of urgency, and not form a procrastination style;
Treat the problem correctly, even if you can't do it, you should know that the gains at this moment are not necessarily small, because the relevant knowledge and methods have been consolidated in essence and achieved a certain purpose, so you can't affect your confidence. When you encounter a problem, you should think of yourself first. If you really don't have a clue, you should ask your classmates or teachers in time to prevent problems from accumulating and reduce your enthusiasm for learning.
Fourthly, the cultivation of mathematical thinking.
In the usual teaching, many students understand it at first sight, but they will do it at first sight, but they are wrong when they do it. What is the reason? This is because it has not reached its due level of thinking.
Because learning has three levels of ability:
First, "understanding", as long as the teacher explains clearly, the topic is chosen properly, and the students participate seriously, there is generally no problem, which is the lower level of thinking;
The second is "meeting", that is, being able to imitate on the basis of understanding, which needs to be reflected in appropriate practice, and thinking has reached a higher level;
The third is "enlightenment". When we realize the truth of solving problems, we can sum up the rules of solving problems, and we can flexibly apply them to other problems, so as to grasp the thinking method of solving problems in essence. This is the height of thinking and the goal we pursue.
Therefore. In the review process, we should base ourselves on the foundation, and then learn to think, especially learn to look at the questions according to the previous methods. Finally, it is to consolidate the practice and not blindly do the questions.
Fifth, improve problem-solving skills
When doing a problem, the first foothold is the problem itself, not the knowledge point, and the math problem is very logical. Do what the topic tells you to do, don't be self-righteous, apply it out of thin air, and see clearly what to ask, what the conditions are, what formulas can be listed for these conditions, or what unknowns should be set.
These questions should start from these angles. What conditions can these angles meet? This is the basic skill of doing problems. Most top students think so. Instead of directly applying knowledge points, unless you simply examine simple knowledge points.
Once the foundation is solid, you can do some difficult problems properly. If not, it depends on the question type. As I said before, the key to reading the topic is the step that sticks to you, not blindly reading the knowledge points. Look at the answer without thinking, 100 times or not.