Methods and Skills of Solving Mathematics Problems in Junior High School —— A pair of commonly used formulas
For example, the multiplication formula and trigonometric function formula in mathematics, commonly used numbers, such as the square of 1 1~25, the trigonometric function value at a special angle, the chemical properties, valences and chemical reaction equations of commonly used elements in chemistry, etc. It should be memorized, which is very beneficial to improve the calculation speed when needed.
In short, learning is a deepening cognitive process, and solving problems is only an important part of learning. The more familiar you are with the content of learning, the more familiar you are with the basic ideas and methods of solving problems, the more numbers and formulas you recite, the more you can organically combine the part and the whole to form a jumping thinking, and the speed of solving problems will be greatly accelerated.
Learn to draw in solving math problems in junior high school.
Learn to draw when solving math problems. I hope the students can learn to draw well.
Drawing is a process of translation. When reading a topic, if you can draw an analysis chart of your understanding of mathematics (or other disciplines) according to the meaning of the topic, the topic will become vivid and intuitive. In this way, abstract thinking in solving problems becomes thinking in images, thus reducing the difficulty of solving problems. Some topics, as long as the diagram is analyzed, the relationship will be clear at a glance. Especially for geometry problems, including analytic geometry problems, if you can't draw pictures, sometimes you can't start at all. Therefore, it is very important to keep in mind the basic drawing methods of various questions, the image and significance of various functions, and the evolution process and conditions to improve the speed of solving problems.
Pay attention to drawing as accurately as possible when drawing. Accurate drawing sometimes allows you to see the answer at a glance, and then further calculation can confirm it; On the other hand, inaccurate drawing sometimes leads you astray.
Investigation on the Methods of Solving Mathematics Problems in Junior Middle School
For a specific exercise, the most important part of solving the problem is to examine the problem.
Carefully examine the questions. The first step of examination is examination, which is a process of obtaining information and thinking. Read the questions slowly, think while reading, pay special attention to the inner meaning of each sentence, and find out the implied conditions. What are the known conditions once reading is over? What is the conclusion of the solution? What conditions are still missing? Can you deduce them from the known conditions? In your mind, this information should have formed a network, you have a preliminary idea and solution, and then you can calculate and verify according to your own ideas. Some students have not developed the habit of reading and thinking, and they are very anxious. As soon as they were anxious, they began to solve the problem. As a result, they often miss some information and spend a long time trying to solve it, but still can't find the reason. They think quickly but slowly. Many times students come to ask questions, and I watch them with him. Halfway through, he said, "Teacher, I can."
Therefore, we should pay special attention to the actual problem-solving and carefully examine the questions.
The problem-solving method of junior high school mathematics increases the difficulty of exercises, and the process of people understanding things is from simple to complex, from the outside to the inside step by step.
Increase the difficulty of practice
We should make it easy first and then difficult, and gradually increase the difficulty of practice. A person's ability is also gradually increased through exercise. If more simple problems are solved, the concepts are clear and the formulas, theorems and solving steps are familiar, jumping thinking will be formed when solving problems, and the speed of solving problems will be greatly improved. When you get into the habit and encounter general problems, you can also maintain a high speed of solving problems. However, some of our students don't pay much attention to these basic and simple exercises and think it is unnecessary to spend time solving these simple exercises. As a result, the concept is unclear, formulas, theorems and problem-solving steps are unfamiliar, and there is nothing to be done when encountering a slightly more difficult problem, let alone the speed of solving problems.
In fact, the labor intensity and efficiency of solving simple exercises are not necessarily lower than solving a complex problem. For example, it is certainly much easier for a person to carry a small bag of rice to the fifth floor than to carry a big bag of rice to the fifth floor. However, if the person carrying the rice only goes up once, and the person carrying the bag has to go up and down 50 times, or even 100 times, then the person carrying the bag is more labor intensive than the person carrying the rice. So in the same time, solving 50 simple problems and 100 simple problems may take more manpower than solving a difficult problem. For another example, if the weight of this bag of rice is 100 kg, it is too heavy, which exceeds the ability of the rice delivery person, so that the rice delivery person has made great efforts, but failed to carry it to the fifth floor. Although the labor intensity is great, it is in vain. Bag carriers can only carry 100 kg of rice to the fifth floor once, 15 times. The labor intensity may not be great, but the efficiency is self-evident. It can be seen that solving a difficult problem is not as good as solving 30 slightly simple exercises, and the gains may be even greater.
Therefore, when studying, we should first solve those seemingly simple but important exercises according to our own ability, so as to continuously improve the speed and ability of solving problems. With the improvement of speed and ability, gradually increasing the difficulty will achieve twice the result with half the effort.
Methods and skills of solving problems in junior high school mathematics II. Cultivating junior high school mathematics problem-solving thinking
Cultivate and exercise junior high school math problem-solving methods and skills: do more targeted and appropriate synchronous exercises, step by step, and cycle by cycle. When learning mathematics, you must do problems and do them properly. The purpose of doing the problem is first to master and consolidate the knowledge learned; Secondly, initially inspire the flexible use of knowledge and cultivate the ability of independent thinking;
The third is to integrate and communicate different junior high school mathematics knowledge. When you do the problem, you should carefully examine the problem and think carefully. How should we do it? Is there a simple solution? Think and summarize while doing, and deepen the understanding of knowledge through practice.
Attach importance to classroom efficiency
In junior high school math class, I think the most important thing is only one word: follow.
1, with books
Always know what knowledge points the teacher explained.
2, with the teacher
Follow the teacher's blackboard writing and explanation, take some notes, and take notes as simply and quickly as possible. (Later perfect)
3. Think.
Keeping up with thinking is undoubtedly the most important thing. Keep up with your thinking, that is, you understand. Listen carefully to the teacher's analysis process, follow the teacher's ideas, and explore new methods appropriately. Personally, thinking is the most important. After all, there is a big difference between coming up with it yourself and the teacher pointing it out to you.
4. The combination of numbers and shapes. The combination of number and shape means that the problem of number can be solved through the analysis of figure, and the problem of shape can also be considered through the study of logarithm.
5. Change the way of thinking. Transforming thinking means that when solving practical problems, it is often necessary to transform unfamiliar topics into familiar topics, sum up the laws of things from special to general, and make appropriate changes.
6. The idea of category theory and the idea of situation theory is the way of thinking that when a problem cannot be done in a unified way, the problem to be studied needs to be divided into several situations to be studied separately.
7, function and equation thinking method, function and equation thinking is to learn to think with variables and functions for some mathematical problems, and learn to transform the unknown and known relationships.
The methods and skills of solving problems in junior high school mathematics must be previewed before three classes.
The degree of preview varies from person to person, but the minimum requirement is to know: what is the content of this class, what is the focus, what is the difficulty, what is not understood, this part of knowledge will have some connection with what you have learned in the past, whether you have mastered the basic content in the past and so on.
Listen carefully
Everyone knows this, but we can be very sure that many people can't do it at all!
The quality of class attendance has a great influence on the whole study. If the learning efficiency in class is low, it may take many times after class, but it may not be able to make up for it.
Therefore, the quality of lectures can really reflect a person's learning ability-at least, it reflects whether a person can learn.
Finish your homework carefully.
This is a cliche.
But what is "earnest"?
I think the most important thing is to review the textbook before doing your homework, and then do it. In the process of doing it, keep your mind "online". In addition to doing the problem itself, we should also think about what this problem is about, where it is easy to make mistakes, what needs attention, and how to study knowledge points.
The necessary brush questions and summary.
There is nothing to say when brushing the questions. If you want to learn beginners well, apart from individual talents, you can't do problems for the vast majority of students.
Take mathematics in Grade One as an example: For most students, the ability to calculate rational numbers is directly related to their practice.
However, light brush practice is obviously not enough, and efficient learning methods cannot be separated from "summary", and the two most important parts are:
(1) wrong topic sorting;
(2) comb the knowledge points.
These two tasks are really complicated to do, but they are of great positive significance to improve students' grades and master knowledge!
Ask if you don't understand.
I can guarantee that more than 90% of the students know that they should "ask if they don't understand" in their studies, but they can never do this.
Many children will feel ashamed to ask their teachers questions. At that moment, they will think, "Will the teacher laugh at me for being stupid?" "Will the teacher criticize me for not listening well in class?" ……
If they will take other measures, such as asking their classmates, asking their parents or surfing the Internet, they are most afraid of letting go of these questions, so they will miss the opportunity to save and fill the knowledge loopholes again and again, and then the problems will snowball. ...
So don't worry, expect to worry about this and that. It's better to find the textbook for next semester now and preview it first!