How can we learn junior high school mathematics well? 1. Prepare carefully before class.
In class the day before, you should browse the content of tomorrow's study. You should understand the related concepts, properties, theorems and examples if you can understand them, and make a mark if you can't understand them. To understand the new lesson when the teacher is speaking, it is best to do the corresponding exercises and exercises first. In this way, when the teacher talks about the new lesson, it will be targeted, which knowledge points should be carefully explained by the teacher and which knowledge can be relatively relaxed.
At the same time, if everything is done in front of the teacher, you will not be so nervous in class, and you can also spend some time thinking about the problems that you didn't notice in the preview process. You can also choose to do exercises. If you have done it, you can perform it on the blackboard. If you can't do it, you can ask your teacher or your classmates. For example, if you preview the lesson of absolute value, you can first find out what absolute value is and what its nature is. How to use these attributes? For what? Absolute value? In this concept? Distance? If you are not sure, circle it and listen to the teacher carefully in class.
2. Listen carefully in class
Keep up with the teacher's thoughts in class, actively cooperate with the teacher's teaching, raise your hand and speak enthusiastically, and be diligent in thinking. Is the purpose and method of the teacher's thinking questions the same as his own, is the teacher's thinking good or his own? Through comparison and targeted selection, it will be of great help and gain for future study. And make good class notes, write down the knowledge points you don't understand, and ask the teacher or classmates after class. Don't ignore the problems you don't understand. The accumulated problems will inevitably affect your future study. At the same time, we should also write down the properties and theorems that are not in the textbook, and write down important topics to provide a basis for future study and review.
3. Review in time after class
Read the knowledge learned that day carefully from beginning to end to see if you have made the knowledge points clear. If you don't understand the knowledge points, you can ask your teacher or classmates. The knowledge points in the textbook should be compared horizontally and vertically. Have a deeper understanding of this knowledge point. In particular, many examples and exercises in teaching materials contain important mathematical thinking methods and ideological essence, so we should pay attention to summing up, refining and using them flexibly in review.
For example, a rope with a length of 18cm is used to form an isosceles triangle. (1) If the waist is twice as long as the bottom, what is the length of each side? (2) Can an isosceles triangle with a side of 5cm be formed? Why? (The example on page 64 of the second volume of the seventh grade of People's Education Edition. ) This question contains the classification idea of mathematics. For another example, after learning the solution of binary linear equations, we should compare it with the solution of univariate linear equations we have learned before. And connect it with quadratic function, so that we can understand the difference and connection between them.
Step 4 check the problem carefully
Before you do your homework, you should carefully examine the questions and see clearly what the questions require and what the conditions are. What is the relationship between conditions and requirements?
For example, a+b=-8, ab=8, and simplified bb+aa =
If you don't carefully examine the questions, the following misunderstandings will appear:
b a b+ a a b = b a a b+ a b a b a b = a2+B2 ab a b =(a+b)2-2ab ab a b =
(-8)2- 16 8 8 = 12 2
However, through careful examination and careful analysis, a+b
The original formula =-BAAB- Ababou =-(a+b) 2-2 abab =-(-8) 2-1688 =-122.
5. Finish homework on time after class
Homework is an important part of after-class review, because the homework assigned by the teacher is not random, but targeted, mainly aiming at the key and difficult points of the knowledge learned that day. Therefore, homework should not be sloppy, be serious, and write neatly. After finishing your homework, you should check it carefully to see if there are any mistakes or thoughtlessness. And reflect: what have I learned through my homework?
Step 6 distract your mind
After doing the examples and exercises in the textbook, we should consider whether these questions are solved by one question or asked by many questions. So as to spread their own thinking and make their knowledge comprehensive. The depth of knowledge is broad enough to make full preparations for future exams, which is of great help to future studies.
Example: Topic (No.2 on junior high school geometry 187) The side length of a square is a, draw a semicircle in the square with the side length as the diameter, and find the area of the enclosed figure (shaded part).
Idea 1: the area of a square minus two semicircles equals the area of two notches, so the area of a square minus twice the area of two notches is the area of the shadow part.
Solution: S shadow =a2-2[a2-? (a ^ 2)2 =(？ 2 - 1)a2
Idea 2: subtract the square area from the area of four semicircles, which is the area of the shadow part.
Solution: S shadow =4 2 (a 2 )2-a2= (? 2 - 1)a2
Idea 3: The area of the semicircle minus the area difference of delta △AOB is 4 times, which is the area of the shadow.
Solution: s shadow =4[? (a ^ 2)2 ^ 2-S△ABC]=(？ 2 - 1)a2 .
Another example: If the base angle of an isosceles triangle is 65? What is its vertex angle? Make appropriate changes to the conditions and conclusions of this question and do a variety of questions to get the following question group.
If the vertex of an isosceles triangle is 65? What is its base angle?
If the internal angle of an isosceles triangle is 65? What are the other angles?
If the internal angle of an isosceles triangle is 95? What are the other angles?
(4) If the internal angle of an isosceles triangle is A? What are the other angles?
Through the change of a problem, let students find out the law of solving such problems in solving problems, thus simplifying complex problems.
In a word, good habits are a good start. Junior high school students have just entered the middle school stage, so it is more urgent to cultivate their good habits of learning mathematics. Erasmus tells us:? One nail squeezes out another nail, and one habit needs to be replaced by another. ? In other words, to overcome the habit of learning mathematics in primary school is to form a good habit of learning mathematics in middle school.