First of all, master the concept.
Because definitions, theorems and formulas are accurate abstractions of quantitative relations in the objective world, the abstract process is also a process discovered and proved by predecessors. Students in grade three should pay attention to reviewing the introduction method of predecessors' roads, which can teach us how to be abstract and objective and cultivate our ability of observation and inquiry. We should seriously engage in discovery activities, study the discovery process and draw our own conclusions. Stimulate curiosity and make the mind enter a positive state of preparation.
The study of the concept is to eliminate doubts and doubts and verify its correctness. Where there is doubt about this concept, let's try it. Through self-verification, memory will be accurate.
Second, master the formula.
The derivation of research theorems and formulas is a way to make junior high school students' understanding rise from perceptual to rational, and it is also a thinking mode of calculation in proof. There are many methods to deduce the theorem of mathematical formula, which is the basic method of mathematical demonstration. Special attention should be paid to the derivation of theorems and formulas with typical significance in thought, method and skill. Studying the derivation process of a formula and theorem is no less than doing several exercises.
The proof of theorem is very simple, but it is important to discover your feelings from the process of proof, think about its enlightenment, learn its methods and problem-solving skills, and then apply these skills to solving problems, and you will become smarter. There are often several different ways to deduce formulas and theorems, and only one is introduced in textbooks, leaving room for students to think independently. After studying all the methods, we can see: first, the simplest and most intuitive is the situation in the textbook; Secondly, the methods and conclusions of examples and exercises are often the basis for demonstrating new problems.
Third, in-depth analysis
Many junior high school students feel that "there are many concepts, but they are a bit messy". It is not surprising to feel this way, because many mathematical concepts are easily confused. From the perspective of epistemology, it is not enough to truly understand a concept by introduction and deduction, but also by identification and analysis to clarify confusion, clarify connotation and extension, and deepen understanding.
Some similar concepts can only be found in comparison, and the key is to grasp the differences. By comparison, we can not only know the same attributes between concepts, but also know their different attributes, so that we will not be confused when using them. Definitions, theorems and formulas can generally be expressed by mathematical symbols. Although several quantities contained in relational expressions have a fixed relationship, they do not necessarily have a unique fixed form. More conclusions can be drawn through reasonable changes in form.
Some formulas are established under certain conditions. If the situation changes, wrong conclusions may be drawn. Therefore, in order to use the formula correctly, it is necessary to understand the context of the conditions. When there are many conditions in the formula, it is necessary to find out the reasons of these conditions and avoid the cross error between the conditions. The concept of mathematics must be firmly remembered. Only by remembering can we talk about calculation, application and demonstration, otherwise we can't have the ability to solve problems.
Students in grade three should pay attention to cultivating strong interest, actively spreading their thinking wings and giving full play to their subjective initiative when learning mathematics.