Many middle school students often sigh: I understand everything the teacher says, but I don't know where to start when I encounter a slightly more difficult problem. What's the problem? How can I learn math well? This is a question that they are puzzled by, and it is also a question that they are struggling to find an answer. In fact, the main problem is that students' ability to solve mathematical problems is poor, but in fact, their ability to learn mathematics is poor. Let me talk about how to improve students' ability to learn mathematics.

First, deeply understand the basic knowledge.

The level of mathematical ability depends on the amount of knowledge first. Without knowledge, there is no mathematical ability. Some students despise the study of basic mathematics knowledge. They can't even define some basic concepts. They are helpless in the face of some basic math problems, but they always think that they have no skills of one kind or another. I don't know if this is because they don't have the basic knowledge and methods. Improving students' mathematical ability must be achieved by solving problems. Problem solving is a process of reasoning with basic knowledge and basic theory until the problem is solved. Without basic knowledge and basic theory, nothing can be solved. If you encounter a problem, it is probably because you don't have the basic knowledge needed to solve it, or because you don't have a correct understanding of the basic knowledge you need.

As can be seen from the above analysis, the solution to the first problem depends on exploration, and the solution to the second problem depends on a deep understanding of arithmetic progression's basic knowledge.

Fourth, seriously understand the mathematical thinking method.

Mathematical thought is the essence of mathematics, which is contained in basic knowledge. Only when teachers constantly permeate relevant mathematical ideas in the process of imparting basic knowledge can students' basic knowledge achieve a qualitative leap. In the teaching of mathematical methods, teachers should consciously choose comprehensive test questions, regard the solution of test questions as the concrete application of a certain method and idea, and explain its essence, so that students can draw inferences from one example to another. Only in this way can we apply the mastered methods to the knowledge of each chapter. Mathematical thought belongs to the category of methods, but it is more the characteristics of ideas and viewpoints. They belong to high-level refinement and generalization. In middle school mathematics, * * *' s mathematical thoughts are: function and equation thoughts; The combination of numbers and shapes; Classification and integration thought; The transformation and transformation of ideas; Special and general ideas; Finite and infinite thoughts; Possibility and necessity, etc. The basic mathematical methods are: undetermined coefficient method; Alternative methods; Matching method; Reduction to absurdity; Digging and filling method, etc. The mathematical logic method or thinking method is: analysis and synthesis; Induction and deduction; Comparison and analogy; Concrete and abstract, and so on. These are the fundamental methods of understanding, thinking and analyzing when solving mathematical problems. The understanding and application of mathematical ideas and methods can reflect students' mathematical ability.

Analysis 1 fully considers the function image corresponding to the topic, and uses the idea of combining numbers and shapes to find the answer to the question, while analysis 2 establishes the functional relationship between distance d and angle θ, and uses the function idea to find the answer to the question, from which we can realize the power of mathematical thought in solving problems.

Fifth, exercise the ability to calculate.

The strength of problem-solving ability is also reflected in the level of computing ability. When analyzing the reasons why the problem can't be solved, it may be that we can't find a suitable algebraic deformation method, or we may not have the algebraic deformation ability needed to solve the problem at all. Deformation often goes hand in hand with logical reasoning and is often related to accumulation. It is a temporary performance of the usual training results.

This is a very difficult question. Through the above verification process, we can see that solving this problem requires solid basic skills and strong logical thinking ability, as well as skilled algebraic operation ability and superb algebraic deformation ability. Without these abilities, we can only look at the problem and sigh. Especially the subtle stroke in the underline. Without rich experience in solving problems and profound accumulation of solving problems, we can't think of this kind of deformation.

Problem-solving ability is a comprehensive expression of basic knowledge, basic skills, mathematical thinking, mathematical methods and mathematical ability. Weak links will lead to failure in solving problems. If you want to learn mathematics well, you must improve your ability to learn mathematics, and more importantly, you must work hard in the above aspects.