Students only learned arithmetic numbers (integers, fractions, decimals) in primary school, and these numbers are all derived from objective reality. After entering junior high school, they introduced a new number-negative number (the meaning of negative number was also introduced in the experimental textbook of the second new curriculum standard), and the range of number expanded to the rational number domain, and the operation of number changed from four operations of addition, subtraction, multiplication and division to power and square accordingly. In order to make a good transition between knowledge, first, we should dilute the concept. For example, when talking about the concept of algebra, let students understand all kinds of algebra first, and then summarize the concept of algebra. Second, let students master four arithmetic operations skillfully, and then understand the law of symbols, so that the operation of rational numbers can pass easily.

2. Numbers and formulas

In the knowledge of "rational number" in the first chapter of grade seven, the concept of algebraic expression was introduced, and then the operation of rational number expression was learned. This transition from counting expression to general abstract algebraic expression with letters is a major turning point in mathematics, and it is of great significance to realize the leap from concrete to general and from concrete to abstract. In this transition, the concept of algebraic expression is the key, which makes students clear that "expression" also has some properties of numbers and the meaning of letters representing numbers. For example, use -a to represent the inverse of a; Use letters to express the conclusion of finding the absolute value of a number; Laws of subtraction and division of rational numbers expressed by letters. Doing so can make the explanation of the problem more concise and in-depth, and at the same time consolidate, strengthen and improve the previous knowledge of numbers and algebra.

3. From arithmetic method to solving application problems with column equations.

Most of the application problems in primary schools are solved by arithmetic, and the unknowns are put in a special position, and the unknowns are solved by known quantities. After entering junior high school, I used column equations to solve application problems, expressed the unknown quantity with letters, and put it in the same position as the known quantity, trying to find out the equivalence relationship, list the equations and find out the unknown quantity. Because of this, generally speaking, the equation of series is more direct and natural than the equation of series, so it has more advantages. At first, students were used to solving application problems with arithmetic, and did not pay attention to the study of solving application problems with equations. At this time, teachers should consciously choose some application problems that are simpler than arithmetic as examples, and compare and explain them in two ways, so that students can gradually realize the advantages of solving application problems with equations. For students' homework, some application problems also need two methods to solve, so as to stimulate students' enthusiasm for learning, and at the same time, we should pay attention to the flexible use of knowledge and cultivate students' ability to analyze and solve problems.

4. Statistics and probability

Statistics and Probability has infiltrated some preparatory knowledge in the first two issues, and has been expanded and improved to varying degrees in the third issue. For example, the fourth chapter "Data Collection and Arrangement" in the first volume of the seventh grade is the opening chapter of the third issue of "Statistics and Probability", which plays a connecting role. On the one hand, strengthen the contact with the first two issues, and at the same time pay attention to laying a good foundation for the later study. For the collection and arrangement of data, the mathematics curriculum standard adopts a spiral arrangement of three periods. The first phase requires "learning some simple methods of data collection and collation", the second phase requires "further learning methods of data collection and collation", and the third phase requires "understanding the necessity of sampling and the idea of estimating the population with samples". According to this feature, the teaching materials in this chapter pay special attention to the connection with the first two sections, and write new contents on the basis of systematically combing the relevant contents in the first two sections. For example, the design of questionnaire, the use of sampling survey to collect preliminary knowledge of data, the use of frequency distribution table to sort out data. , so that the three learning periods become a whole.

In short, after entering junior high school, students' learning tasks, pressure for further studies and living environment have changed greatly, especially the mathematics knowledge they want to learn has made a leap in abstraction and rigor. As mathematics teachers in primary and secondary schools, we should seriously analyze and study related issues, earnestly strengthen mathematics teaching and research among local primary and secondary schools, and make some useful explorations to do a good job in the connection of mathematics teaching in primary and secondary schools and improve teaching quality, so that our students can develop continuously, harmoniously and healthily from primary school to middle school and even higher-level schools.