There are other ways to learn. According to different learning situations, the learning process is divided into four steps and five steps. Students can choose according to the characteristics of what they have learned, and even create their own learning steps, such as reading, listening, writing and practicing the four-word learning method, and then browse, ask questions, read, repeat and review the five-step learning method. Third, only by letting students know how to learn can they really master knowledge. If mathematical knowledge is regarded as a system, then the structure of mathematical knowledge has four elements, namely facts, reasons, uses and objects. Specifically, according to the different levels of knowledge structure, these four elements can be listed as follows:
Four things, facts, reasons, applications, materials, problems, topics, topics, topic methods, topic paths, questions, what, why, how to use, what inspiration, concepts, names, definitions, judgments, relationships, theorems, conditional conclusion proofs, applications, methods, formulas, expressions, deduction, calculation and connection.
In our opinion, no matter what level of knowledge we learn, we should master the corresponding four elements. If you only know "what" and don't know "why", you can't understand the principle of the conclusion. If you only know theoretical knowledge and don't know how to use it, it will become useless knowledge. If there is no clear thinking, the knowledge points are not closely linked and scattered, then the knowledge is not solid and the foundation is not solid, so it is difficult to innovate when learning new knowledge. Therefore, the four elements are indispensable. On the one hand, learners must walk in four steps and consciously master the four elements of each piece of knowledge. These four steps are: perception, understanding, application and systematization. Specifically, it is:
⑴ Perception (fact): Have a preliminary understanding of general conclusions and have an overall response to various attributes reflected by concepts, theorems and formulas. Perception is the beginning and foundation of mathematics learning. Only by knowing "what" can we further explore "why?" So as to understand and apply knowledge.
⑵ Understanding: In order to understand a mathematical conclusion, we must understand its principle and its context. Cognition is a kind of thinking process in which people gradually realize the various connections of things and find out their essential laws. It can be seen that only through understanding can the perceptual knowledge of things rise to rational knowledge. Connotation and extension of mathematical concepts, proof of theorems, derivation of formulas, explanation of conclusions, etc. Only by understanding can we really grasp the principle of mathematical facts.
⑶ Application: Application is the continuation and deepening of learning. On the basis of perception and understanding, students have mastered mathematical knowledge, but they should also apply knowledge to problem-solving and analysis, so as to deepen their understanding of what they have learned, make their study twice the result with half the effort, and master skills and improve their thinking ability through practical training. In mathematics textbooks, the summary of examples, the solution of exercises and the completion of extracurricular homework are all "practical" processes.
⑷ Systematization (event body): "event body" refers to "knowledge system". There are various connections between mathematics learning materials. If students understand the connection between old and new knowledge, they can do this and that. Mastering "things" has the following functions: knowledge structure is tight, memory is firm, thinking is flexible and diverse, which lays the foundation for learning new knowledge and is easy to produce new associations. Therefore, it is very important to systematize knowledge through summary.
Fourth, let students clearly learn a mathematical concept, theorem and formula from what aspects. In the process of learning mathematics, there are always a lot of concepts, theorems and formulas. How to really master them? Teachers should clearly point out what kind of process is needed, what requirements are to be met, and what aspects are generally to be understood and mastered.
Algebraic learning method.
(1) Copy the title, browse and set the target.
⑵ Read and record the key contents.
(3) Try to make an example. Do exercises quickly and summarize the questions.
5] Memory summary.
Four steps of geometry learning.
(1).( 1) Write the topic and browse the teaching materials; (2) Teach yourself and write the contents;
⑵. ① Read the teaching materials according to the catalogue, ② Teach yourself geometric concepts and theorems;
(3).① Reading examples to form ideas, ② Writing out the process of solving problems;
(4).① Do the problem quickly, ② Summarize the method of solving the problem.
Let students understand how to achieve efficient learning results. Super learning method, fast memory method, fast reading method and fast learning method are all learning methods with the purpose of "fast", so they can be called efficient learning method. The core of learning mathematics knowledge is memory, and being able to remember what you have learned quickly and firmly is the main symbol of good study and good grades. Therefore, exploring and mastering various quick memory methods should be the goal that every student must pay attention to summarize and pursue. Many books are introducing the fast memory method, the central idea is novelty and excitement, turning words into images (because the memory of images is 1000 times that of words), relaxing the brain and enriching associations. Memory is closely related to attention, observation, imagination and understanding. The cultivation of memory must be coordinated with other intellectual factors. Psychologists divide memory into four steps: memory, retention, recognition and reproduction, and we should also remember mathematical knowledge according to these four steps.
The Super Learning Method was invented by Bulgarian Dr. Rozanov. It has become an excellent learning method in the world because of its high efficiency and multiple functions. This learning method is being implemented all over the world, which is called the learning revolution. Super learning method can be used to learn the knowledge of any subject, especially the basic courses, which can help students remember everything easily. Super learning method can be roughly divided into two parts: one is to guide the spirit into a relaxed state, so that learners can maximize their learning efficiency in the alpha wave state; Secondly, in order to learn at a certain pace in this state, I try my best to write the textbook as an operable model. Super learning method requires students to have a preparation before learning: (1) to eliminate physical and mental tension (there are three methods: breathing, physical relaxation and psychological relaxation); ⑵ Enter the alpha wave state from the relaxed state (there are four methods: feeling calm reaction, visual image alpha wave enhancement, mind entering the alpha wave state, and recalling past success). After the above preparations are completed, you will enter the learning process, such as memorizing theorems and formulas. You can read aloud and take a deep breath alternately, and even play a special music rhythm to study in a pleasant atmosphere.
Speed reading is an efficient reading method for thinking and remembering, which was developed by two Soviet experts for several years. Speed reading method is not only used for Chinese reading, but also for mathematics learning.
Browsing textbooks also has important application value. The key points of fast reading are: (1) get rid of "argot", browse with your eyes and get information quickly; (2) broaden your horizons and let your eyes get more information; ⑶ Grasp the teaching materials as a whole and get important information. (4) In the fast reading training, attention, observation and memory can be improved, so that the mind is agile, the brain is flexible, and the learners become smarter and smarter.
Fast learning method is a new learning method in Japan, which enables people to master knowledge flexibly and quickly at a speed five times faster than the normal method. Everyone has this experience, an unforgettable event or a difficult math problem. If you consciously tell others a few times, you can greatly deepen your impression and make it easier to remember or organize. This experienced teacher probably knows best. In order to make it clear to the students, the teacher's brain is working nervously, and the knowledge he has talked about is strengthened and sorted out in this process, making it clear. The fast learning method is based on this principle. When learning in this way, you don't need to fully understand it first, but after you get the teaching materials, you can directly mobilize your existing knowledge according to the catalogue and tips and conduct a speculative "self-study". After writing, you can open the book and read it for the first time. The first reading can test the shortcomings of the first "self-study", and the fallacies and heresies will "jump to the page" and make you deeply understand. Then you can compile a refined and applicable "content list" in your own language and conduct a second "self-study" against it. This lecture will obviously feel more accurate and organized than the first one. Then read it through for the second time, and you will have a deeper feeling this time. When you teach yourself for the third time, you will speak more perfectly and richly, and many vague places will become clear. Finally, you can read it through, so that you can browse quickly and summarize it systematically, and feel that your knowledge has been clearly reflected in your brain. After three or four rounds of "self-study-through reading, intensive reading and rough reading", you can easily master the mathematics knowledge you want to learn.
The above four efficient learning methods can be understood in detail through other reference books, but learners can also explore and summarize through the above introduction, so as to make their learning effect better and better.