First, the basic links and principles of mathematics learning

Students' study at school is carried out under the guidance of teachers. Classroom learning generally includes four links: first, listening to the teacher's class, which is part of the lecture; In order to digest and master the knowledge taught in class, you need to do exercises, which are part of your homework. In order to further consolidate the knowledge learned and understand its internal relations, it is necessary to remember and summarize, which is part of the review. In order to study more actively in the next class, it is necessary to read the new lesson in advance, which is part of the preview. Each part of these four links has its independent significance and function, and each part is interrelated, influenced and restricted. These four links form a small cycle, that is, the learning cycle. The learning cycle is the trajectory of a learning wheel running for one week. People who are good at learning should find its starting point, end point and intermediate links from the printing of a wheel running for one week, form a four-link stereotyped learning cycle, form a learning system, and let each link fully play its role, so as to achieve good learning results.

The basic process of mathematics learning

When students learn new knowledge independently, they will generally go through the following five basic steps.

The first step is to develop knowledge, things or numbers.

Preliminary perception of line.

For example, examine the conditions and processes of things and their existence and evolution; Participate in the demonstration, operation, existence, change and development of the learned knowledge, and then have a preliminary feeling about the learned knowledge.

Contact and preliminary understanding of new knowledge-building perceptual knowledge

Developing new knowledge representation in associative form

Exploring the Internal Relationship between Old and New Knowledge —— Second Perception

Abstract generalization of the essential characteristics of new knowledge-the transformation to rational knowledge

New knowledge in memory-Gong Gu

Applying new knowledge-transforming knowledge into ability

Paying attention to the research on the basic process of students' learning mathematics is of great significance to improving teaching methods, strengthening the guidance of learning methods and improving teaching quality.

Principles and basic methods of mathematics learning

According to the characteristics of psychological theory and mathematics, analytical mathematics learning should follow the following principles: dynamic principle and gradual principle. The principle of independent thinking, the principle of timely feedback, and the principle of integrating theory with practice, and thus put forward the following mathematics learning methods:

1. Combination of seeking advice and self-study.

In the process of learning, we should not only strive for the guidance and help of teachers, but also rely on teachers everywhere. We must actively study, explore and acquire, and seek the help of teachers and classmates on the basis of our serious study and research.

2. Combination of learning and thinking

In the process of learning, we should carefully study the contents of textbooks, ask questions and trace back to the source. For every concept, formula and theorem, we should understand its context, cause and effect, internal relations, and mathematical ideas and methods involved in the derivation process. When solving problems, we should try our best to adopt different ways and methods, and overcome the rigid learning methods of books and machinery.

3. Combine learning with application and be diligent in practice.

In the process of learning, we should accurately grasp the essential meaning of abstract concepts and understand the evolution process of abstraction from actual model to theory; For theoretical knowledge, we should look for concrete examples in a wider scope, make them concrete, and try our best to apply theoretical knowledge and thinking methods to practice.

4。 Broaden your horizons, accept the appointment, and return to the appointment from Bo.

Textbooks are the main source of students' knowledge, but they are not the only source. In the process of learning, in addition to studying textbooks carefully, we should also read relevant extracurricular materials to expand our knowledge. At the same time, study hard on the basis of extensive reading. Master its knowledge structure.

5. There are both imitation and innovation.

Imitation is an indispensable learning method in mathematics learning, but it must not be copied mechanically. On the basis of digestion and understanding, use your brains and put forward your own opinions and opinions, instead of sticking to the existing framework and existing model.

6. Review in time to enhance memory.

What you learn in class must be digested on the same day, reviewed first and then practiced. Review must be carried out frequently, and after each unit, the knowledge learned should be summarized and sorted out to make it systematic and profound.

7. Summarize the learning experience and evaluate the learning effect.

Summary and evaluation in learning is the continuation and improvement of learning, which is conducive to the establishment of knowledge system, the mastery of problem-solving rules, the adjustment of learning methods and attitudes and the improvement of judgment ability. In the process of learning, we should pay attention to summing up the gains and experiences of listening to lectures, reading books and solving problems.

Further, there are learning methods involving specific contents, such as: how to learn mathematical concepts, mathematical formulas, rules, mathematical theorems and mathematical languages; How to improve the ability of abstract generalization, calculation, logical thinking, spatial imagination, problem analysis and problem solving; How to solve mathematical problems; How to overcome mistakes in learning; How to get the feedback information of learning; How to evaluate and summarize the problem-solving process; How to prepare for the exam? Further research and exploration of these problems will be more conducive to students' learning mathematics.

Many outstanding educators and scientists in history have a set of learning methods suitable for their own characteristics. For example, the learning method of Zu Chongzhi, an ancient mathematician in China, can be summarized in four words: seeking the past and the present. Search is search, absorbing the achievements of predecessors and studying extensively; Refining is refining, comparing and studying various ideas, and then digesting and refining by yourself. The famous special scientist Einstein's learning experience is: by self-study; Pay attention to autonomy, get to the bottom of it, imagine boldly, try to understand, attach importance to experiments, get through mathematics and learn philosophy. If we can dig out and sort out more learning experiences of these educators and scientists, it will be a very valuable asset. This is also an important aspect of the study of learning methods.

Although the problem of learning methods has always been concerned by educators, many good learning methods have been put forward. However, due to the influence of "teaching instead of learning" for a long time, most students do not pay attention to their own learning methods. Many students have not yet formed effective learning methods suitable for them according to their own characteristics. Therefore, as a conscious student, while learning knowledge, we must master scientific learning methods.