1, the thinking method of establishing a model (modeling thinking for short)

Modeling is not only one of the important thinking methods in elementary mathematics, but also one of the important thinking methods in advanced mathematics. It can be used to quickly abstract some research objects or practical problems into mathematical problems and then solve them.

In calculus, a lot of knowledge and problems contain this way of thinking, especially abstracting the functional relationship between variables in practical problems, and then solving practical problems by solving functional problems (that is, establishing functional models).

2. The thinking method of combining numbers and shapes.

Number and shape are two basic objects of mathematical research, which are closely related and have their own characteristics. The thinking method of combining numbers and shapes is to make full use of the intuition and standardization of numbers, study mathematical objects and solve mathematical problems through the transformation of the relationship between numbers and shapes. Because calculus is about functions,

Function intuitively reflects its nature through its image, so the thinking method of combining numbers and shapes is embodied in the whole learning of calculus knowledge. Therefore, in the whole teaching process, we should pay attention to the characteristics of teaching materials and guide students to capture the numerical information in knowledge and problems in time.

3. The transformation of thinking methods.

When studying a problem, the thinking method of transforming one research object into another under certain conditions is called transformation thinking method. This way of thinking is widely used in the derivation of formulas and theorems and the solution of mathematical problems, and it is an extremely important way of thinking.

4, the corresponding way of thinking

As we know, a lot of knowledge in mathematics contains corresponding ideas. For example, the point real number on the number axis; Points and ordered number pairs on the coordinate plane: independent variables and function values in functions; Angular radians) and real numbers: there is a certain correspondence between equations and curves, which reflects the corresponding thinking methods.

5. The thinking method of classified discussion.

The thinking method of classified discussion is more common in mathematics. It is a way of thinking that divides mathematical objects into asymmetric objects according to their different attributes. In the teaching of calculus, the idea of classification is revealed in time.

Helping students master and use the thinking method of classified discussion is helpful to deepen understanding and digest knowledge, so as to master its essential laws.