1 How to improve junior high school students' math scores
Deeply understand the concept.
Concept is the cornerstone of mathematics. Learning concepts (including theorems and properties) requires not only knowing why, but also knowing why. Many students only pay attention to memorizing concepts and ignore their own background, so they can't learn math well. For every definition and theorem, we should know how it comes from and where it is used on the basis of remembering its content. Only in this way can we make better use of it to solve problems.
Look at some examples.
Careful friends will find that after explaining the basic content, the teacher will always give us some extra-curricular examples and exercises, which is of great benefit. The concepts and theorems we learn are generally abstract. In order to make them concrete, we need to apply them to the theme. Because we have just come into contact with this knowledge, we don't have enough skills to use it. At this time, examples will be of great help to us, and we can put the existing concepts in our minds in the process of reading examples.
You can't just look at the fur, not the connotation.
When we look at the examples, we really want to master their methods and establish a wider way to solve problems. If we look at something, we will lose its original meaning. Every time we look at a topic, we should clarify its thinking and master its thinking method. If we encounter similar topics or the same type of topics again, we will have a general impression and it will be easy to do, but we must emphasize one point unless we are very sure.
We should combine thinking with observation.
Let's look at an example. After reading the questions, we can think about how to do it first, and then compare the answers to see what our ideas are better than the answers, so as to promote our improvement, or our ideas and answers are different. We should also find out the reasons and sum up experience.
2 How to learn junior high school mathematics well
Basic knowledge of mathematics
Understanding and memorizing the basic knowledge of mathematics is the premise of learning mathematics well. Understanding is to explain the meaning of things in your own words. The same mathematics has different forms in different students' minds. Therefore, understanding is an individual's active reprocessing process of external or internal information and a creative "labor". The standards of understanding are "accuracy", "simplicity" and "comprehensiveness". "Accuracy" means grasping the essence of things; "Jane" means simple and concise; "All-round" means "seeing both trees and forests", with no emphasis or omission. The understanding of the basic knowledge of mathematics can be divided into two levels: first, the formation process and expression of knowledge; The second is the extension of knowledge and its implied mathematical thinking method and mathematical thinking method.
Memory is an individual's memory, maintenance and reproduction of his experience, and it is also the input, coding, storage and extraction of information. It is an effective memory method to try to recall with the help of keywords or hints. For example, when you see the word "parabola", you will think: What is the definition of parabola? What is the standard equation? How many properties does a parabola have? What are the typical mathematical problems about parabola? You might as well write down your thoughts first, and then consult and compare them, so that you will be more impressed. In addition, in mathematics learning, memory and reasoning should be closely combined. For example, in the chapter of trigonometric function, all formulas are based on the definition and addition theorem of trigonometric function. If we can master the method of deducing the formula while reciting it, we can effectively prevent forgetting.
Mathematical thinking
The integration of mathematical thinking and philosophical thinking is a high-level requirement for learning mathematics well. For example, mathematical thinking does not exist alone, both of them have their opposites, and they can be transformed and supplemented each other in the process of solving problems, such as intuition and logic, divergence and orientation, macro and micro, forward and reverse. If we can consciously turn to another method when one method is blocked, there may be a feeling that "mountains and rivers are full of doubts and there is no way to go." Understanding the philosophical thinking in mathematical thinking and carrying out mathematical thinking under the guidance of philosophical thinking are important methods to improve students' mathematical quality and cultivate their mathematical ability.
As long as we attach importance to the cultivation of computing ability, grasp the basic knowledge of mathematics in a down-to-earth manner, learn to do problems intelligently, and reflect on our mathematical thinking activities from a philosophical perspective, we will certainly learn mathematics well.
Three methods of learning junior high school mathematics well
Careful friends will find that after explaining the basic content, the teacher will always give us some extra-curricular examples and exercises, which is of great benefit. The concepts and theorems we learn are generally abstract. In order to make them concrete, we need to apply them to the theme. Because we have just come into contact with this knowledge, we don't have enough skills to use it. At this time, examples will be of great help to us, and we can put the existing concepts in our minds in the process of reading examples.
You can't just look at the fur, not the connotation. When we look at the examples, we really want to master their methods and establish a wider way to solve problems. If we look at something, we will lose its original meaning. Every time we look at a topic, we should clarify its thinking and master its thinking method. If we encounter similar topics or the same type of topics again, we will have a general impression and it will be easy to do, but we must emphasize one point unless we are very sure.
We should combine thinking with observation. Let's look at an example. After reading the questions, we can think about how to do it first, and then compare the answers to see what our ideas are better than the answers, so as to promote our improvement, or our ideas and answers are different. We should also find out the reasons and sum up experience. Examples of various difficulties are taken into account.
Looking at the examples step by step is the same as the following "doing the questions", but it has a significant advantage over doing them: the examples have ready-made answers and clear ideas, and we can draw conclusions as long as we follow their ideas, so we can look at some skillful and difficult examples that are difficult to solve by ourselves without exceeding what we have learned, such as the competition questions with moderate difficulty.
4 junior high school mathematics learning methods
Mastering preview methods and cultivating mathematics self-study ability
Preview is a learning method to learn new knowledge in textbooks before class. To learn junior high school mathematics well, we must first learn to preview new mathematics knowledge, because preview is the premise of listening to classes well and mastering classroom knowledge, and it is an indispensable link in mathematics learning. Preview can adopt the preview method of "one batch, two batches, three trials and four points". "One stroke" is to circle knowledge points and basic concepts. The "second batch" and "third test" are just trying to do some simple exercises to test the effect of your preview. "Four points" is to list the main points of this knowledge you have previewed, and to distinguish which knowledge you have mastered through previewing and which knowledge you can't understand through previewing, and you need to learn further in classroom learning.
Mastering classroom learning methods and improving classroom learning effect
Classroom learning is the most basic and important link in the learning process, and we should adhere to the "five arrivals", that is, listening, watching, speaking, thinking and reaching;
Handwriting: it is to write down the main points and thinking methods of the lecture simply and clearly, so as to review, digest and rethink, but the lecture should be the main part, supplemented by records;
Listening: Listen to the teacher attentively, how to analyze and summarize. In addition, listen to the students' answers to see if they are enlightening, especially the questions that they didn't understand beforehand;
Mouth-to-mouth: actively cooperate with teachers and classmates to explore, dare to ask questions and express opinions, and not follow suit;
Eye-catching: look at the teacher's expression, the meaning expressed by gestures, the teacher's demonstration experiment and the content on the blackboard, look at the textbook content that the teacher asks to read, and connect the knowledge in the book with the knowledge that the teacher said in class;
Heart orientation: that is, we should think carefully in class, pay attention to understanding new knowledge in class, and think positively in class. The key is to understand and be able to integrate and apply flexibly. It is necessary to grasp the key words and understand the new concept spoken by the teacher from another angle.