I. teaching material analysis

1, textbook content

This lesson is the first lesson of the simple nature of function 2. 1.3 in Chapter 2 of Function Concept and Basic Elementary Function Ⅰ published by Jiangsu Education Press. This lesson mainly studies the definitions of increasing function and subtraction function, and applies the definitions to solve some simple problems.

2. The position and function of teaching materials.

The property of function is the cornerstone of studying function, and the monotonicity of function is the first property to be studied. Through the study of this lesson, students can understand the concept of monotonicity of function, master the steps to prove monotonicity of function, and use monotonicity knowledge to solve some simple practical problems. Through the above activities, they can deepen their understanding of the nature of functions. The monotonicity of function is not only the continuation and expansion of the concept of function that students have learned. It is also the basis for further research on monotonicity of exponential function, logarithmic function and trigonometric function. In addition, it is also widely used in the size of comparison numbers, qualitative analysis of functions and related mathematical synthesis problems. It is one of the core knowledge that plays a connecting role in the whole senior high school mathematics. From a methodological point of view, this teaching process is also permeated with mathematical thinking methods such as exploration and discovery, combination of numbers and shapes, induction and transformation.

3. Teaching objectives

(1) Knowledge and skills: enable students to understand the concept of monotonicity of functions and master the monotonicity of discriminant functions.

Methods;

(2) Process and method: Starting from real life problems, guide students to explore the concept of monotonicity of function independently, apply the definitions of visualization and monotonicity to solve the problem of monotonicity of function, let students understand the mathematical thinking method of combining numbers and shapes, and cultivate students' ability to find, analyze and solve problems.

(3) Emotion, attitude and values: let students experience the scientific function, symbolic function and tool function of mathematics, and cultivate students' good mathematical thinking quality of intuitive observation, exploration and discovery and scientific demonstration.

4. Key points and difficulties

The concept of monotonicity of teaching focus (1) function;

(2) Using the definition of monotonicity to judge the monotonicity of some functions.

Knowledge formation of monotonicity of teaching difficulty (1) function;

(2) Using the definition and monotonicity of function image to judge and prove the monotonicity of function.

Second, the analysis of teaching methods and the guidance of learning methods.

This lesson is an abstract mathematical concept lesson, so we should pay attention to the teaching methods:

1. Introduce topics through real life problems that students are familiar with, create situations for concept learning, narrow the distance between mathematics and reality, stimulate students' thirst for knowledge and arouse their enthusiasm for participation.

2. In the process of using definition to solve problems, we should stick to the key sentences in the definition and complete all kinds of difficult breakthroughs one by one through the participation of students, so as to solve all kinds of problems.

3. While encouraging students to participate, the leading role of teachers can not be ignored, which is embodied in asking questions, commenting and standardizing writing. Students should be taught clear thinking, rigorous reasoning and successful written expression.

4. Modern teaching methods such as projector and multimedia are adopted to increase teaching capacity and intuition.

In legal research:

1, which allows students to question, try, summarize, summarize and apply problems, and cultivate students' ability to discover, study and solve problems.

2. Let students intuitively enlighten their thinking with graphics, and complete the leap from perceptual knowledge to rational thinking through the construction of positive and negative examples.

;