The first chapter is the concept of set and function.
1. Curriculum standard requirements:
In this chapter, set is studied as a language, which makes students feel the simplicity of expressing mathematical content with set.
Sex and accuracy help students learn to describe mathematical objects in set language and develop their ability to communicate in mathematical language.
Function is the core concept of high school mathematics. This chapter regards function as an important mathematical model to describe the changing law of the objective world, and emphasizes the combination with practical problems, so that students can feel the process and method of using the concept of function to establish a model, thus developing their understanding of variable mathematics.
1. Understand the meaning of sets, understand the "subordinate" relationship between elements and sets, and master some special symbols of number sets.
2. Understand the representation of set, choose natural language, graphic language and set language (enumeration or description) to describe different specific problems, and feel the significance and function of set language.
3. Understanding the meaning of inclusion and equality between sets can identify subsets of a given set and cultivate students' logical thinking ability of analysis, comparison and induction.
4. Be able to understand the meaning of complete works and empty sets in specific situations.
5. Understand the meaning of the union and intersection of two sets, find the union and intersection of two simple sets, and cultivate students' thinking ability from concrete to abstract.
6. Understand the meaning of the complement of a subset in a given set, and you will find the complement of a given subset.
7. venn diagram can be used to express the relations and operations of sets, and the role of intuitive graphs in understanding abstract concepts can be realized.
8. Learn to describe functions with sets and corresponding languages, and understand the meaning of function symbol y=f(x); Understand the three elements of function composition and the concept of mapping; Empirical function is an important mathematical model to describe the relationship between variables, and the role of empirical correspondence in describing the concept of function; Can find the domain and range of some simple functions, and skillfully use interval representation.
9. Understand some basic representations of functions (list method, image method and analysis method) and make appropriate choices in actual situations; I can draw some simple function images by sketching.
10. Through concrete examples, we can understand the simple piecewise function and apply it simply.
1 1. Combining with the familiar concrete function, we can understand the monotonicity, maximum (minimum) value and its geometric meaning of the function, and the meaning of parity and periodicity. Through the image of the concrete function, we can initially understand the central symmetric figure and the axisymmetric figure.
12. Learn to use the image of the function to understand and study the properties of the function and experience the mathematical method of combining numbers with shapes.
13. Through practical work, students can get a preliminary understanding of major historical events and important figures that have had a significant impact on the development of mathematics, and learn about functional examples in life.
Two. Writing intention and teaching suggestions
1. The textbook does not involve set theory, but only studies set as a language. Students are required to express related mathematical objects in the most basic set language, so as to realize the simplicity and accuracy of set language and develop the ability to communicate in mathematical language. The textbook strives to closely combine students' life experience and existing mathematical knowledge. By enumerating rich examples, students can understand the meaning of sets, understand and master the basic relations between sets and the basic operations of sets.
The textbook highlights the background teaching of the concept of function, emphasizing that starting from examples, students should have a full perceptual basis for the concept of function, and then abstract the concept of function with sets and corresponding languages, which is more in line with students' cognitive laws, conducive to cultivating students' ability of abstract generalization and enhancing their awareness of applying mathematics. In teaching, we should attach great importance to the background teaching of mathematical concepts.
2. Textbooks try to create situations and opportunities for students to express and communicate in set language, pay attention to expressing the relationship and operation of sets with venn diagram, and help students understand abstract concepts with intuitive charts. In teaching, we should fully embody this intuitive mathematical thought and give full play to the intuitive role of graphics in the teaching of subset and set operations.
3. The textbook pays attention to using the set viewpoint to study and deal with mathematical problems in the teaching of examples and exercises, which runs through the future mathematical learning.
4. In the arrangement of examples and exercises, the idea of classification in set is infiltrated, so that students can realize the wide application of classification in life and mathematics, which students lack in junior high school. In teaching, we must gradually infiltrate this kind of training from complexity to difficulty.
5. The textbook emphasizes understanding the three elements of a function from its essence, but does not advocate the complicated calculation of definition and range, especially the artificial over-training. Teachers should accurately grasp the requirements in this respect and prevent teaching from being set high.
6. Function representation is one of the main contents of this chapter. Different representations (list method, image method and analysis method) are emphasized in the teaching materials, with the aim of enriching students' understanding of functions and helping them understand the abstract concepts of functions. In teaching, we should not only give full play to the intuitive role of images, but also properly guide students to learn images from the perspective of algebra, so that students can deeply understand the important mathematical method of combining numbers with shapes.
7. The textbook takes mapping as a generalization of functions, adjusts the logical order, and embodies the special to general thinking law, which is beneficial for students to learn the continuity of function concepts.
8. The textbook strengthens the requirements of the integration of function and information technology, and draws the dynamic images of simple functions by computer, so that students can initially feel the important role of information technology in function learning.
9. In order to reflect the selectivity of teaching materials, the arrangement of exercises is more flexible, and teachers should make reasonable choices according to the actual situation of students.
Three. Suggestions on teaching content and class arrangement
The teaching time of this chapter is about 13 class hours.
1. 1 Set 4 class hours.
1.2 function and its representation of 4 class hours
Properties of 1.3 function 3 class hours
Practical homework 1 class hour
Review lesson 65438
The meaning and representation of the set 1. 1. 1
First, the teaching objectives:
Length knowledge and skills
(1) Understand the meaning of set and the relationship between elements and set through examples;
(2) Know the commonly used number sets and their special signs;
(3) Understand the certainty, mutual dissimilarity and disorder of elements in the set;
(4) Being able to express related mathematical objects in assembly language;
(5) Cultivate students' ability of abstract generalization.
2. Process and method
(1) Let students experience the process of abstracting and summarizing the same characteristics of a set from the examples of the set, and feel the meaning of the set.
(2) Ask students to summarize what they have learned in this section.
3. Emotions, attitudes and values
Let students feel the necessity of learning assembly and enhance their enthusiasm for learning.
Two. Teaching emphases and difficulties
Key point: the meaning and representation of set.
Difficulties: the proper choice of representatives.
Three. Learning methods and teaching tools
1. learning methods: students can read textbooks, study independently, think, communicate, discuss and summarize, thus better completing the teaching objectives of this course.
2. Teaching equipment: projector.
4. Teaching philosophy
(A) create a scene to reveal the theme
1. The teacher first asked: In junior high school, we came into contact with some collections. Can you give some examples of collection?
Guide students to recall, give examples and communicate with each other. At the same time, teachers evaluate students' activities.
2. Then the teacher pointed out: So, what does set mean? This is what we will learn in this class.
(2) Explore new knowledge
1. Teachers use multimedia devices to show students the following nine examples:
All prime numbers in (1) 1-20;
(2) four great inventions of ancient china;
(3) All permanent members of the Security Council;
(4) all squares;
(5) All overpasses completed before September 2004 in Hainan Province;
(6) To all points with the same distance on both sides of an angle;
(7) All real roots of the equation;
(8) All solutions of inequality;
(9) All senior one students enrolled in Guoxing Middle School in September 2004.
2. Teachers organize students to discuss in groups: What are the similarities and differences between these nine examples?
3. Choose a student from each group to publish the results of the group discussion. On this basis, teachers and students summed up the characteristics of nine examples and gave the meaning of the set.
Generally speaking, the sum of some specific objects is called a set. Every object in a set is called an element of this set.
4. The teacher pointed out that sets are usually represented by uppercase letters A, B, C, D, …, and elements are usually represented by lowercase letters …
(3) Questioning the defense, dispelling doubts and doubts, and developing thinking.
1. The teacher guides the students to read the relevant contents in the textbook and thinks: What are the characteristics of the elements in the set? And pay attention to personal assistance.