Mathematical concept learning method

The definition, theorem, concept, formula and law of mathematics are the framework of mathematical knowledge system, the basis of solving problems and reasoning. To truly understand its essence, generally speaking, we must do the following steps:

Step one: find out the ins and outs.

Any new knowledge will never be a tree without roots, it is always developed and summarized on the basis of old knowledge. Therefore, when learning new definitions, theorems, formulas and laws, understanding the origin and development of knowledge is of great significance for deepening the understanding of knowledge itself.

Step 2: Deliberating word for word and layer by layer.

Mathematical language has the characteristics of conciseness, abstraction and rigor. Therefore, when we study definitions, theorems and rules, we must fully and accurately understand their contents, which requires careful scrutiny of their literal expressions one by one. For example, the concept of the opposite number in the textbook is defined as follows: "Just like 6 and -6, there are only two numbers with different symbols. Suppose one of them is opposite to the other. " If we remove the sentence "like 6 and -6", it is easy to make our understanding deviate. For example, -(+2) and +(-2) also meet the condition of "only symbols are different". Is it the inverse number? Obviously not. There are many such descriptive concepts in junior high school mathematics learning. For descriptive concepts, we must grasp the whole concept, and don't take it out of context, which is prone to misunderstanding or ambiguity.

Step 3: Pay attention to the restrictions.

The restrictive conditions in formulas are an inseparable part of concepts and formulas, but they are often ignored by students and should be highly valued in learning. At the same time, analyzing the restrictive conditions can often help us understand the essential characteristics of concepts or formulas more deeply. For example, some of our students often regard plumb as vertical downward, and only two straight lines placed horizontally are regarded as parallel. This understanding of the concept has been replaced by the influence of life experience and narrowed.

Step 4: Identify by contact and comparison.

In mathematical knowledge, there are many summaries and related knowledge derived from the same basic concepts and methods, or seemingly identical but essentially different knowledge. The main way to learn this kind of knowledge is the practice of "finding contact and grasping contrast". For example, the concepts of "straight line, ray and line segment" are both related and different.

Master the example reading method

Grasping the examples in the textbook is a good learning method. The specific approach is:

First, reading before class: read the examples carefully, mark the places you don't understand, and listen carefully in class.

Second, class selection: listen carefully to the teacher's difficult points in the example and concentrate on picking the difficult points.

Third, thinking after class: after listening to the teacher's explanation, read and think after class. Think about why you didn't understand at that time and where the card was.

Fourth, cross-talk before the exam: Every time you review before the exam, you should not only remember the formulas and concepts, but also review the main examples of each chapter and string together the knowledge.

English is the most conscientious subject. If you make a contribution, you will get something. Opportunism is unacceptable.

"Four Ways" to Learn English

The first way to learn English is to read more, do more, recite more and accumulate more. Maybe some students will say, what is this method? But at present, many students can't learn English well because they have abandoned this most basic method.

First, read more books. In many questions, such as filling in the blanks, a sense of language is usually very important. The best way to improve the sense of language is to read more and read aloud, and stimulate the brain from both auditory and visual aspects. The effect is very good.

The second is to do more, that is, to cultivate the so-called problem consciousness. It is impossible to read without doing anything. When you do a certain amount of questions, you will naturally understand the intention of the questioner and be handy in the exam.

Third, recite more articles and words. Reciting classic articles can not only help you improve your sense of language, do objective questions well, but also help you cope with the composition easily and consolidate the words in the process of reciting articles, killing three birds with one stone. Why not? Words are the basis of learning English well. Simply memorizing new words is not only very difficult, but also difficult to understand the usage of words in specific contexts. Moreover, each word often has many translation items, sometimes with great differences. Simply memorizing words is not only confusing, but also inaccurate. Memorizing words in a specific context can improve the speed and accuracy of memory and know how to use them.

Finally, accumulate more. English learning is very slow. Pay more attention to accumulation at ordinary times and try to read and write every day. The effect of accumulated learning in this way is better than that of concentrated learning for a few days or a period of time. In the daily learning process, you will encounter many phrases and words that you didn't know before. Students should keep these contents in their notebooks and constantly review and consolidate them. After a knowledge point is recorded in the notebook, it is often necessary to review four or four.

In addition to normal English classes, you can spend some scattered time learning English every day, such as before lunch break or before going to bed at night, or take an English notebook with you and take it out when you are free. Over time, students feel that they can recite many English words easily without spending too much time.

Grab a book and attack grammar.

There are two cornerstones in learning English: vocabulary and grammar. To learn vocabulary well, of course, it is inseparable from reference books such as dictionaries. To learn grammar well, you should insist on using reference books. This reference book should be an authoritative grammar book, and it should be accompanied by a workbook. After choosing a grammar book, how should I use it in my daily study? The suggestions are as follows:

First, read through. It is very helpful to read through a concise English grammar book or even skim it. Because the grammar knowledge learned in middle school is scattered for six years, "I usually see only a few, but I don't see zero", so it is difficult to form a complete system in my mind. After reading through the grammar books, the scattered knowledge we usually learn can be systematized, which sublimates our deep understanding of the whole English grammar system.

Second, do exercises. Practice many times from beginning to end according to the assigned exercise book, so that you can often find your weak links in grammar. If you encounter difficulties in doing the problem, you'd better not look at the reference answers at the back, because the easy answers will be easily forgotten.

Third, for future reference. Take this grammar book with you and look it up as often as a dictionary. For example, if you can't understand a long and difficult sentence, you can look at the relevant chapters in the grammar book and analyze and judge, which requires you to clearly know the content and content of the grammar book and turn it out.

Dictionaries and grammar books are reference books for learning English. They can help us solve problems and are our silent teachers. Both are indispensable.