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How to understand the function is the main line of learning in the field of mathematics and algebra in junior high school.
The curriculum standard highlights the viewpoint that function is the main line of algebra content in junior high school, and focuses on intuitive research. On the basis of solving specific problems, students experience the intuitive essential characteristics of functions and understand the relationships and changes between variables. Therefore, function, as an important mathematical model to study the phenomenon of movement change, occupies an important position in junior high school mathematics and is the main line of learning in the field of junior high school mathematics and algebra. On the one hand, in the primary school stage, the standard puts forward the learning task of "exploring laws", which is actually the primary stage of function learning. On the other hand, function is a very important learning content in the field of mathematics number and algebra in junior high school. The course of number and algebra in junior high school includes four aspects: number, algebra, equation and inequality, variable and function, which are relatively independent and interrelated. Without the concepts of rational number, real number and algebraic expression, it is impossible to learn the relevant knowledge of equations and functions; Equations and inequalities are special cases of functions, which shows the important role of functions in junior high school mathematics and algebra courses. Function uses images to express quantitative relations, which is intuitive and vivid. The image of function allows students to understand the relationship between number and shape. Many algebraic methods are used in solving function problems, such as collocation method and formula method in solving the maximum value problem of quadratic function, transforming it into function problem in solving practical problems, and using the idea of classified discussion in scheme selection. These are important algebraic thinking methods in junior high school mathematics, which are of great significance to improve students' mathematics learning ability. Using functional thinking method can not only solve mathematical problems, but also solve many practical problems in real life, such as profit maximization, area maximization, scheme selection, etc., which precisely reflects the requirements in curriculum standards. Mathematics comes from life and serves life. It can embody many mathematical thinking methods, such as the combination of numbers and shapes, model thinking and transformation thinking. It can be said that function is a main line running through junior high school mathematics and algebra learning.