Reflection on the Teaching of Comprehensive Problems of Function Nature
The following are some of the main points of the reflection on the teaching of the comprehensive problem of function properties:
** 1. Introduction of Function Concepts **
1. ** The importance of connecting with existing experience **
- Before the teaching of function properties, the introduction of function concepts needed to consider the students 'existing knowledge and experience. For the introduction of the concept of functions in high school, students could use the function definition based on the relationship between variables that they were familiar with, such as abstracting the concept of functions from examples in life and mathematics. Doing so would help students develop their abstract knowledge of functions from the three perspectives of variable dependence, real number set correspondence, and function image geometry intuition. The concept of function in junior high school (In a changing process, there are two variables, x and y. For every definite value of x, y has a unique definite value corresponding to it. x is an independent variable, and y is a function of x) provides the foundation for the learning of the concept of function in senior high school. Teaching should pay attention to the connection between the two.
2. ** The Meaning of Function Notation **
- The representation of functions (image method, tabulation method, analytical method, etc.) had their own characteristics, which needed to be discussed in the study of function concepts. Different expressions could be converted to each other, but some functions could only be expressed in specific expressions. In teaching, students should be guided to choose the appropriate representation according to the specific problem. This would help students understand the concept of function from many aspects, establish a connection between mathematical expression and abstract definition, and thus better understand the nature of function.
** 2. Function Nature Teaching **
1. ** Fundamental understanding of function properties **
- The nature of a function was the invariable and regular nature of change. Students should be taught to understand this nature. There was no need to worry about letting the students discover the properties of the function on their own. It was feasible to use the method of "demonstration + imitation." The main point was to let the students understand the accuracy of using letters, unequal equations, logical symbols, and so on.
2. ** Function Monotonicity Teaching **
- ** Concept Formation **
- It was difficult to extract a logical description such as "arbitrary"(x1
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