Compulsory Mathematics in Senior High School 1 teaching material analysis (Chapter 1 Collection) Mathematics is a scientific language and an effective tool to describe the laws of nature and society. Symbolization and formalization are prominent features of mathematics. In a sense, learning mathematics means learning a formal language with a specific meaning, and using this formal language to express, explain and solve various problems. Set theory was founded by German mathematician Cantor at the end of 19. Set language is the basic language of modern mathematics, which can be used to express mathematical content concisely and accurately. 1. The educational goal of this chapter is to make students feel the simplicity and accuracy of expressing mathematical content with set, help students learn to express mathematical objects with set language, and lay a foundation for future study. 1. Understand the meaning of set, understand the relationship between elements and set, and preliminarily master the representation method of set; 2. By understanding the meaning of inclusion and equality between sets, a subset of a given set can be identified; Understand the meaning of complete works and empty sets; 3. Understand the meaning of complement set and seek complement set; 4. To understand the meaning of intersection and union of two sets, it requires intersection and union of two sets; 5. Infiltrate mathematical thinking methods such as combination of numbers and shapes and classification; 6. Cultivate students' thinking ability in the process of guiding students to observe, analyze, abstract and acquire mathematical knowledge such as sets and the relationship between sets by analogy; 7. Through the study of this chapter, students can initially feel the simplicity and accuracy of expressing mathematical objects in set language, and appreciate the beauty of simplicity of mathematics. Second, the design intention of this chapter This chapter contains three parts: the meaning, expression and operation of set. The textbook first sets up the problem situation of "designing yourself", which makes students feel that the concept of set is around us and closely related to our lives. Guide students to understand the characteristics of sets through examples, and learn and understand the representation methods of sets from different angles; By observing specific sets, students can feel and summarize the inclusive relationship between sets from two aspects: "number" and "shape". Different from the traditional textbooks, the textbooks in this chapter make students feel and get the concept of complement of a set by observing specific sets, and then rise to the inside of mathematics, and understand "complement" as a kind of "operation" between sets. On this basis, through examples, let students feel and master two other "operations" between sets-intersection and union. The overall design idea of this chapter is from concrete to theory, and then back to concrete, spiraling up. This chapter makes full use of venn diagram and number axis to help students understand the meaning and operation of set vividly, which embodies the idea of combining numbers with shapes. The content of this chapter fully considers the cognitive laws of students. In the process of putting forward the concept of set, students are encouraged to give their own examples through narration. The whole design provides space and possibility for students and teachers to take active activities. This chapter has set up columns such as "thinking" and "reading", which provide a carrier for students to broaden their thinking and further study. For example, guide students to think about whether a B and B A can be established at the same time and explore the proof method of set equality. In order to meet the needs of students at different levels, this chapter has set up inquiry and expansion questions in exercises and review questions, for example, asking students to explore and prove C =(C) (C) and so on. This chapter focuses on the cultural value of mathematics. For example, Cantor, the founder of set theory, introduced the historical background and significance of infinite set through narration and reading to improve students' interest in learning and mathematics literacy. 3. As a mathematical language, the set of teaching suggestions in this chapter is an important tool in the follow-up study (such as expressing the definition and range of functions, the solutions of equations and inequalities, curves, etc. in the language of the set). In mathematics learning, a problem is often transformed into a simpler and clearer problem through semantic transformation. Therefore, in the teaching process of this chapter, we should be able to guide students to use natural language, graphic language and set language appropriately to express the corresponding mathematical content according to specific problems. It is necessary to make use of the mathematics content that students have learned and the examples in life, so that students can feel the benefits of using set language, and then develop their ability to communicate in mathematics language. The teaching time of this chapter is about 4 class hours. The specific distribution is as follows (for reference only): 1. 1 set and its expression: about 1 class, 1.2 subset, complete set, complementary set, about 1 class, 1.3 intersection set,. The summary and review of 8+0 class hours is about 1 class hour. Four. The Temple of Heaven was built in 1426, which is one of the existing exquisite ancient buildings in China. Through observation, we can find that such a magnificent building is composed of some basic spatial graphics. It and the introduction provide the main background of this chapter, arouse students' experience of life, and make them notice the close relationship between space graphics and our life in the real world, which is the growing point of knowledge and methods in this chapter. Solid geometry is a mathematical subject that studies the relationship between the shape, size and position of objects in three-dimensional space. Learning solid geometry is of great significance for us to better understand the real world and survive and develop better. The introduction further puts forward the central question of this chapter from the whole to the part: (1) What is the basic geometry of space? (2) How to describe and depict the shapes and sizes of these basic geometric figures? (3) What is the positional relationship between the basic elements that make up these geometric figures? It reveals the basic ideas of this chapter, provides a research topic for students' learning activities and points out the direction. The meaning of 1. 1 set and its representation 1. Teaching goal (1) Understand the meaning of set, and know the commonly used number set and its notation; (2) Understand the meaning of "belonging" relationship and set the equation; Understand the meaning of finite set, infinite set and empty set; (3) Master two representations of sets-enumeration and description, and correctly represent some simple sets. 2. The set of writing intention and teaching suggestions (1) is an original and undefined concept in mathematics. In the teaching material processing, students can feel the meaning of set through a large number of familiar examples, such as "family", "boy" and "girl", and initially understand how to describe objects in the language of set. With the introduction of the concept of set, students can freely give examples, such as "natural numbers" and "rational numbers", in addition to specific examples in textbooks. (2) The "certainty" mentioned in the descriptive concept of a set means that whether any element belongs to this set is certain. The difference and disorder of elements in a set can also be illustrated by students' examples. (3) The equality of sets (they contain the same elements) only requires understanding, not from the perspective of mutual inclusion of sets. (4) Enumeration and description have their own advantages. For example, 1, the textbook expresses the solution of one-dimensional linear inequality in the language of set, thus obtaining the descriptive definition of infinite set. In teaching, students are only required to make judgments and give some concrete examples. Through example 2, students can have a further understanding of empty sets, and in teaching, students can give examples by themselves. 1.2 subset complement 1. Teaching objective (1) to understand the meaning of inclusion relation between sets; (2) Understand the concepts and significance of subset and proper subset; (3) Understand the meaning of complete works and the concept and significance of supplementary sets; 2. Writing Intention and Teaching Suggestion (1) Starting from the analysis of specific sets, through the analysis of the relationship between sets and their elements, the concepts of subsets and proper subset are obtained. In teaching, we can start from the last section, let students give some examples of sets themselves, and guide students to analyze the relationship between them, especially the relationship between elements. Attention should be paid to using venn diagram to help the analysis from the perspective of "shape". A is thinking about 0? 1 B and b? 0? 1 A can be established at the same time, provided that A =B B. Both of them are established at the same time, which is a way to prove the equality of sets. In the teaching process, students can be guided to analyze by venn diagram, so that students can feel the equivalence of the simultaneous establishment of the two and the equality of the set. (2) Through observation and comparison, the differences and internal relations among subset, proper subset and complement are analyzed. At the same time, we should make full use of venn diagram to help students understand these different concepts from the perspective of "form". The textbook passed "Thinking" Example 2, with three sets in each group. The two sets A and B have no common elements, but their elements are only elements in set S. This kind of thinking lays a foundation for students to feel and understand the concepts of complementary sets and complete sets, and also lays a foundation for understanding complementary sets from the perspective of set operation. 1.3 intersection and union 1. Teaching objective (1) Understand the concept and significance of intersection and union; (2) Understanding the representation of intervals; (3) Master the terms and symbols about sets and use them to correctly represent some simple sets. 2. Writing Intention and Teaching Suggestion (1) Starting from the complement set, it is proposed that the complement set is an operation of a set, and then the concepts and meanings of intersection and union are obtained by studying the specific set relationship. In teaching, after putting forward the operation between sets, students can observe the relationship between sets through concrete examples and understand the meaning of intersection and union with the help of venn diagram. (2) The concepts of intersection and union can also be given at the same time, which is easy to learn; The operation of intersection and union can be understood through venn diagram sum number axis. The application of problem scenario set and the representation of the relationship between sets The review of this chapter mainly reflects and summarizes the learning content, knowledge growth process, important research methods and ideas of this chapter. It is a process from thick to thin. The block diagram shows a growing mathematical tree. This chapter mainly studies the preparatory knowledge of sets, including the related concepts of sets, the representation of sets, the relationship between sets and the operation of sets. Starting from the examples in life, this paper explores the method of describing mathematical objects with set language. With the collective language, we can express our ideas more clearly. Set is the foundation of the whole mathematics, and it is widely used in future study.