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 grasp 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, it is of great significance to understand the ins and outs of knowledge for deepening the understanding of knowledge itself.
Step 2: Deliberating word for word and layer by layer.
Mathematical language is concise, abstract and rigorous. Therefore, when we study definitions, theorems and laws, 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 defined in the textbook: "Like 6 and -6, there are only two numbers with different symbols, so we say that one of them is the opposite number of the other." If we remove the sentence "like 6 and -6", our understanding will easily be biased. For example, -(+2) and +(-2) also meet the condition of "only symbols are different". Is it a reciprocal? 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 leave the described examples out of context, causing 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 easily 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, when we understand the concepts of vertical and parallel, some of our students tend to regard the vertical downward as vertical, and only two straight lines placed horizontally as parallel. This concept was replaced by the influence of life experience, which narrowed the connotation of the concept. It is also an interference of non-essential factors, which should be eliminated consciously as far as possible in learning.
Step 4: Identify by contact and comparison.
In mathematical knowledge, there are many summaries derived from the same basic concepts and methods and their related knowledge 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". Such as "straight line, ray, line segment", they are both related and different.
Master the example reading method
It is a good way to learn by grasping the examples in the textbook and not relaxing. 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, pick in class: listen carefully to the teacher's examples and concentrate on "picking" the difficulties.
Third, thinking after class: after listening to the teacher's explanation, reading and thinking after class. Think about why you didn't understand at that time and where the card was.
Fourth, pre-test string: Every time you review before the test, you should not only remember the formulas and concepts, but also review the main examples of each chapter to string together the knowledge.
In addition, try to avoid mistakes in the exam and recommend an article:
"Twenty Cross Formula" to Prevent Errors
It is often seen that after the math exam, many students shout: I have done this problem long ago, but unfortunately I made a mistake here and forgot there. I am also annoyed sometimes, why teachers often talk about topics and students often make mistakes. Calm down and think about it. It is no wonder that students or teachers may remind you when you usually do the questions. During the exam, one person and one table are very serious, and the examination room is very serious. When the atmosphere is tense, candidates will inevitably make mistakes in the math exam. How to minimize mistakes and maximize your own level? Besides keeping a normal mind, what other good test-taking skills are there? I occasionally get a beautiful name: "20-character formula", so I can always remind myself during the exam.
The content of my so-called "twenty-cross formula" is: "A single cell has a special knot. Look up the box letters, guess for yourself, ask the name, and install the correct page." Students can remember homophones or memorize them in less than three minutes. Ladies and gentlemen, this is not a secret martial arts story, but dealing with junior (senior) middle school math exams can effectively improve scores and reduce unnecessary mistakes. It is not illegal to write on the draft with a pencil as soon as the test paper and draft are issued. It's really effective to have a look from time to time when you encounter difficulties in the exam. Let me explain these 20 words one by one.
1. "Single" is the unit. In the math exam, especially in the fill-in-the-blank and calculation questions, you should write the unit. It is not uncommon for students to be deducted for forgetting to write, and there are also mistakes in writing units, such as the square meters of the area being wrongly written as meters.
2. "Grid" is a format. Some students have no format for solving problems, so they can deduct them if they want.
3. "A" is the English letter A, and the quadratic term coefficient a of the general quadratic equation and the quadratic term coefficient a of the general quadratic function are not zero. However, students often ignore the range of letters.
4. "Special" is the special value method. Some math problems confuse students. If you use the special value method, you can sometimes get an effect of four or two kilograms, which is also in line with the dialectics of "general-special-general"
5. "knot" is the conclusion. The answers to application questions, the conclusions of short-answer questions and the conclusions of drawing questions are often forgotten.
6. "standard" is the standard. From elementary school to junior high school, the final conclusion loses points because it does not reduce points. It is not uncommon for the coefficient before the root of a single or quadratic square to be written with a fraction and the denominator to have a root sign or denominator. These nonstandard conclusions should be avoided.
7. "Inspection" refers to inspection. The discriminant of the roots of the three most common problems in junior high school mathematics, students often ignore the test when doing this kind of filling, selecting, calculating and proving, which leads to unnecessary loss of points.
8. "Square" is the idea of equation. If we use equation thinking to solve many problems in middle school mathematics, we can really solve them.
9. "Shape" is the combination of number and shape. Many problems can be easily solved by the combination of numbers and shapes, especially the travel problem and quadratic function in traditional application problems. Sometimes it's better to draw a sketch and try.
10. A function is a function. At present, there are many math application problems in the senior high school entrance examination, which can be modeled by function thought. This is also one of the difficult contents for students.
1 1. "From" indicates the value range of the function independent variable. I once made up a jingle about the value range of function independent variables: algebraic expressions take all real numbers, the denominator of fractions is not zero, and even roots are not negative, so practical problems should be considered. The formula here refers to the right-handed algebraic formula in the resolution function. In the examination, when using function method to solve practical problems, the range of independent variables is often omitted, which leads to losing points.
12. "Quantity" is a measure. In some geometric fill-in-the-blank questions or multiple-choice questions, it is really difficult to calculate the size or numerical relationship between angles and line segments. You might as well measure it with a protractor or ruler. However, if the original picture is not accurate, you'd better draw one yourself.
13. "Guess" is not a guess. Although some fill-in-the-blank questions and multiple-choice questions are difficult, it is also a waste to leave them empty. What a pity. Here, you might as well guess one, and the multiple-choice question has a quarter probability of being correct. Why not? 14. "fen" is the idea of classified discussion. At present, there are more and more classified discussion questions in the senior high school entrance examination, and students often miss one or several of them. I often remind students to be more careful to prevent one from leaking out.
15. Time is time. Watch the time. General fill-in-the-blank questions and multiple-choice questions are controlled within half an hour, and the rest are done in turn. Difficult questions are skipped and left to the end. It is forbidden to spend a lot of time by hard attack. Finally, you must leave about 15 minutes to check the whole article, but you must not look at your watch too often. You should look at general or one kind of questions at a time.
16. "Ask" means to ask the teacher if you can't see clearly or have questions, or if you have any requirements. I am too timid to ask. If there is a mistake in the test paper, it is too late to regret it. We should also advocate "not ashamed to ask questions" here.
17. "Name" is "name". Because some candidates are nervous, they will miss their names and admission ticket numbers. Isn't that a waste of time? Such a reminder is certainly useful.
18. "Packaging" is the binding line. In the past, when candidates did negative papers, they often did them in the binding line, so the correct questions were deducted from the binding line. In fact, the test paper can be folded along the binding line, and the answer should be within the binding line, thus avoiding such a situation.
19. "quasi" is the admission ticket. Don't forget to write the admission ticket number except the answer. Don't forget to take the joint exam when you enter and leave the examination room. Otherwise, the admission ticket for the next exam will be gone, and you won't be so anxious that you are sweating all over.
20. "Pages" means waiting for the curly hair to come down, counting how many pages there are and how many big questions there are. Then you can allocate time and adjust the speed of solving problems. I used to hear that candidates regret for life because they missed one or several pages, which is a lesson from the past and a lesson from the future.
Since last June 165438+ 10, I have been asking students this question in all kinds of math exams. By the time of the final exam, only two of the 105 students I taught forgot to take the root equation. Because these two people even forgot to write the formula. Looking back at the monthly exam on June 5438+ 10, more than 20% students didn't take the radical equation, and all the other questions were wrong. It seems that this trick really works. Recently, students' unnecessary mistakes have been greatly reduced in the review of the third grade exam. I will write it today and discuss it with you. If you are interested, don't try it. The above 20-word formula is also very effective for solving problems in high school! Because the cross formula is also practical in many places in high school.