1. In the fields of "number and algebra", "space and graphics" and "statistics and probability", what do you find to be the connection points of primary and secondary school knowledge? Answer: (1) "Number and algebra" is the basic content of mathematics in primary and secondary schools. In primary school, we mainly study natural numbers, positive decimals (positive fractions) and other numbers. Combined with the specific situation, we can understand the meaning of the four operations. The "number operation" in primary schools is so important that it occupies most of the current primary school mathematics teaching. The algorithm of elementary school lays a good foundation for junior high school mathematics learning. In middle school, in addition to the concept of number extended to rational number and real number, it is more important to have formula operation, which is consistent with the operation law when learning rational number and real number operation in primary school, thus showing the importance of this part. In addition, from primary school to middle school, I began to learn the operation of numbers and letters, and on this basis, I learned the operation and relationship of algebraic expressions, resulting in equations, inequalities, functions and so on. , which constitutes the basic part of "number and algebra" in junior high school mathematics. Finally, it is a leap in mathematical thinking from the special and concrete number of primary school mathematics to the abstract algebraic expression of middle school. (2) Space and Graphics is closely related to human existence and residence, and it is an important learning content to cultivate students' initial innovative spirit and practical ability. Compared with its mathematical content, it is more intuitive and vivid, and it is easier to abstract mathematical concepts, theories and methods from real situations. In primary school, the field of space and graphics mainly includes the preliminary knowledge of cognition, measurement, graphics and transformation, graphics and position. The main means of cognition is intuitive perception. Learning focuses on the calculation of length, area and volume, and less on the content of three-dimensional space. Because the teaching content is simple, it is difficult for students to effectively develop spatial concepts and spatial imagination. On this basis, junior high school has added graphics and coordinates, graphics and proof. This paper mainly uses deductive reasoning method to prove the properties of plane graphics according to the extended axiom system. Through the necessary demonstration of the basic nature of basic graphics, students can understand the necessity of proof, understand the basic process of proof, master the format of comprehensive proof, and feel the axiomatic thought initially, so that students can gradually transition from intuitive perception to logical demonstration, gradually understand the necessity of reasoning and learn how to reason. (3) Because the contents of "Statistics and Probability" are involved from primary school to early school, following the requirements of new curriculum and teaching reform, students are required to master the relevant contents of statistics and probability step by step and apply them to solve some practical problems. Therefore, in teaching, primary school students can experience the statistical process of data, learn some simple methods of collecting, sorting and describing data, answer some simple questions according to the statistical results, and initially feel the uncertainty and possibility of events. And can make simple judgments and predictions according to the results of data analysis; In the middle school stage, students should actively participate in the whole process of data statistics on the basis of primary school experience and preliminary understanding of statistics and probability, and in this process, use the language unique to statistics and probability to communicate and make simple reasoning, so that students can understand the idea of statistics, master some commonly used data processing methods, make appropriate choices and judgments, and solve some simple practical problems with preliminary statistical knowledge. 2. What are the main difficulties you encounter in teaching each part? Choose a specific content, what specific teaching methods did you use to solve it? Question 1: Answer: (1) In the teaching of Number and Algebra, the rational number operation in the seventh grade is the foundation, which has great influence on the operation of the following formulas, such as the operation of merging similar terms, the multiplication of polynomials, the operation of fractions, the quadratic root, etc. However, the introduction of difficult negative numbers has a great influence on students' operation. In the rational number operation of senior one, subtraction is mainly converted into addition and division into multiplication, so the addition rule and multiplication rule are the most important. In teaching, it is mainly to teach students to understand the law and master the steps of doing problems. The first step is to determine the sign of sum (or product), and the second step is to calculate the absolute value of each number. However, many students often make mistakes in determining the sum (or product) symbol. In short, the first difficulty is the operation of negative numbers in the process of solving problems. The second difficulty breaks through the place where students are prone to difficulties: "the development of letters representing numbers." The number represented by letters has duality, that is to say, the number represented by letters is both definite and arbitrary. To regard letters as the abstraction of "numbers" and understand the arbitrariness of letter values, it requires students to change their understanding from arithmetic method to algebraic method. A remarkable sign of the development level of students' mathematical ability is their level of using "letters represent numbers". Therefore, in junior high school mathematics teaching, we must conform to students' original cognitive structure and follow the principle of spiral rise, so that students can gradually realize the great "second leap" from "number" to "shape". (2) In the mathematics teaching of statistics and probability in junior middle school, it is a brand-new challenge for students to establish "random concept", and random phenomenon is an important research object in probability statistics. Especially if students lack rich experience in random phenomena, it is often difficult for schools to establish random concepts. Therefore, we should pay attention to creating situations in teaching. In a large number of experiments, let students experience the process of exploring random phenomena, conduct experiments by themselves, collect experimental data, analyze experimental results, and compare the results with their own guesses, thus enriching students' understanding of the meaning of probability and forming random concepts. But the learning process is more complicated, the operation is more difficult, and learning is more laborious and time-consuming. (3) The concept of "space and graphics" is abstract and difficult to understand; It is difficult to adapt from "number" to "shape"; The reasoning is logical and difficult to start. Generally speaking, we think that there are three kinds of geometric languages, namely, graphic language, written language and symbolic language. Many students are not very flexible in the conversion of the three languages, which brings difficulties to examining and doing problems. The concrete manifestations are as follows: ① it can't be expressed in correct geometric language; (2) The required geometry will not be drawn correctly; According to the meaning of the question, we can't use the corresponding knowledge we have learned to analyze and explore ways to solve the problem; ④ The process of geometric proof is unclear and the logic is chaotic. The second question: A: Let me talk about the specific teaching methods in the field of number and algebra. The content of number and algebra plays an important role in compulsory education and mathematics courses and has important educational value. Let me talk about the specific teaching methods in the field of Number and Algebra: (1) In teaching, students should be guided to contact with specific and interesting things around them, and feel the meaning of numbers through observation, operation, problem solving and other rich activities, and realize the role of numbers in expression and communication, so as to initially establish digital consciousness. (2) By solving practical problems, we can further cultivate students' sense of numbers, stimulate students' interest in learning, realize that numbers are mostly used in life, and enhance students' understanding of the meaning of operation, so that students can experience the quantitative relationship from the abstraction and realize the benefits of learning knowledge to solve problems. (3) Try to create conditions, organize students to investigate, collect and put forward practical problems in life or production, and try to solve them with what they have learned.