We must consciously understand the concept in the way that Teacher Li said in our usual study.
1, grasp the essence of the concept. Each concept has a definite meaning, that is, the special nature that distinguishes it from other concepts.
For example, the concept of "equation" is "equation with unknown number", which clearly points out the difference between equation and algebra; Algebraic expression is "a formula for connecting numbers and letters representing numbers with algebraic operation symbols", so the essence of algebraic expression is a "number", and the equation we have learned is to connect two algebraic expressions with an equal sign, and its essence is to express a "relationship". Only when the letters take a certain value can the algebraic expressions on both sides of the equal sign be equal, and this "certain value" is still unknown.
2. Conditions for understanding concepts. Definition is a sentence to judge a thing, which consists of two parts: topic setting and conclusion. Therefore, we need to analyze the conditions in the definition. Can we reduce or increase the conditions? For example, a quadratic function is a function with the shape y = ax2 bx c (a≠0). If the condition of a≠0 is removed, the coefficient of the quadratic term can be equal to 0, and this function is not necessarily a quadratic function, but also a linear function. This is where we often make mistakes in doing problems, because without the condition of a≠0, it is not the concept of quadratic function.
3. Learn to use definitions in the right and opposite ways.
All mathematical definitions are true propositions, and its inverse propositions are also true propositions, which means that the definitions are reversible. The reversibility of concept definition plays an important role: it can be used to judge whether something conforms to this concept; The nature of this concept can be obtained by using the definition in reverse. Only by learning to use definitions sequentially and reversely can we use definitions flexibly to solve practical problems.
4. Deeply understand the meaning of mathematical concept symbols.
Mathematical symbols are an expression of mathematical concepts, which are simple and clear, and easy to remember and use. For example, the absolute value "|a|" of a has geometric meaning besides algebraic meaning, indicating the distance from the point with coordinate A on the number axis to the origin; -Is it negative? The letter a stands for real number, and -a is the antonym of a, which is also a real number.