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 should grasp the following steps: step one: make clear the context.
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 methods are as follows: First, reading before class: read the examples carefully, mark the places you don't understand, and pay attention 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.