How to learn mathematics, problems that should be paid attention to: 1. Feel mathematics with your heart, appreciate mathematics and master mathematical thoughts. A mathematician once said: Mathematics condenses the greatest ideals with the smallest space.
2. Pay attention to the understanding of mathematical concepts. The biggest difference between high school mathematics and junior high school mathematics is that there are many concepts, which are abstract and easy to learn? Smell? Very different from the past, the solution usually comes from the concept itself. When learning a concept, it is not enough to know its literal meaning, but also to understand its hidden deep meaning and master various equivalent expressions. For example, why the images of functions y=f(x) and y=f- 1(x) are symmetrical about the straight line y=x, but the images of y=f(x) and x=f- 1(y) are the same; Another example is why when f(x- 1)=f( 1-x), the image of function y=f(x) is symmetrical about y, while y=f(x- 1-x) and y=f( 1-x).
3. Do you want to keep two words in math learning? Rigorous innovation? The so-called rigor means that when training at ordinary times, you can't be sloppy. If you are right, you must admit it. If you are wrong, you must find the reason and correct it. You must not take it? I think so, right? Mentality, muddle through. As for innovation, the requirements are higher. If you can solve this problem, will you use another simpler and more effective method? This requires a solid basic skill. At ordinary times, we see some people never use conventional methods to do problems, and always love to create some methods by themselves. Folk prescription? Solving the problem, although sometimes it can make him run into some good methods, I don't think it is advisable. Because you must learn to use conventional methods first, then you can innovate, and your innovation is meaningful, and those are always one-sided? Pursuit? People with new methods, their thinking is like castles in the air, which is bound to be a flash in the pan. Of course, we must have a sense of innovation, but innovation is conditional and must have a solid foundation, so I want to advise those who are not strong and always like to use it? Folk prescription? Students, it's time to wake up and stop drilling into that poor dead end!
4. Establish a good habit of learning mathematics, which is a stable and lasting conditioned reflex and natural need consolidated through repeated practice. Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. In addition, we should ensure that there is a certain amount of self-study time every day, so as to broaden our knowledge and cultivate our ability to learn again.
5, listen more, do more, think more, ask more: this? Dos? It is the key to cultivate mathematical ability. Listen. Right here? Study? , is it? Practice? (do exercises or other questions in the textbook), that is, apply what you have learned to solving problems. ? Listen. With what? Work? Difficulties are inevitable, so it depends on the situation? Think? Kung fu has survived, or will it be solved if you can't figure it out? Ask? Consult classmates, teachers or reference books, and be sure to solve the problem until it is solved. This is the so-called learning: ask questions while learning.
6. Perseverance and perseverance: basically, we must have an understanding that mathematical ability is the result of long-term efforts and cannot be achieved overnight. You may spend a day or a night memorizing a text, and you will get high marks when you recite it in the exam the next day. You may also spend a week or two studying math hard, but you may not do well in the math exam in the end. At this time, you should not be discouraged or feel sorry for the time you have spent, because what are you planting? Because? What will you get? Fruit? As long as you continue to work hard and persevere, you will finally prove that your efforts have not been in vain!
About mathematics learning methods: 1. 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 theory of psychology and the characteristics of mathematics, 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. But for a long time? Teaching instead of learning? Most students have not paid 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.