How to understand that functions are the main line of learning in the middle school mathematics and

How to understand functions is the main line of learning in the field of mathematics and algebra in junior high school Functions are the first formal study of the process of "change" in middle school mathematics, and it is an important mathematical model for the study of motion change. The specific learning requirements of the "New Standard" for the content of functions are as follows: explore the quantitative relations and change laws in simple examples, and understand the significance of constants and variables.

Combined with examples, understand the concept of functions and three notations, and give examples of functions. It can analyze the functional relationship in simple practical problems in combination with images. It can determine the value range of the function argument in a simple practical problem, and can find the value of the function.

Ability to describe the relationships between variables in simple practical problems using appropriate functional notation. Combined with the analysis of the functional relationship, the changes of the variables can be preliminarily discussed. On the one hand, at the primary school level, the "New Standards" puts forward the learning task of "exploring the law", which is actually the initial stage of function learning. On the other hand, in the mathematics curriculum at the junior high school level, the definition of functions only adopts the more intuitive "variable theory".

A change in one variable causes a change in another variable, without adopting an abstract "mapping theory"; At the same time, the basic characteristics of functions, such as the three elements of functions, the monotonicity of functions, and parity, are not systematically mentioned. Rather, it is only required to combine specific functions, effectively penetrate, and gradually reveal the intuitive and essential characteristics of functions—connections and changes; But at the same time, the "New Standard" also highlights the idea of functions as the main line of algebra content in junior high school. Therefore, functional learning is not a "new" content in junior high school, and it is necessary to pay attention to its continuity with primary school. At the same time, the learning at the junior high school level is not theoretical, but mainly based on intuitive research; However, it is necessary to introduce the connection between functions and equations, inequalities, etc. Therefore, function is an important mathematical model for studying the phenomenon of motion change, and it is the main line of junior high school algebra.

Because of the various knowledge learned later, functions are used the most, and many problems are inseparable from functions.

A lot of problems have different solutions, there are a lot of problems with functions will be very convenient, I just graduated from junior high school, in the third year of junior high school, we Jiangsu words to answer most of the questions is a combination of functions and what knowledge, learning functions is the foundation, all the books can be represented by the coordinates on the function, the teacher will emphasize.

Functions are learned every semester, and the high school entrance examination will take big questions with large scores.

The curriculum standards highlight the idea that functions are the main line of algebra content in junior high school, focusing on intuitive research, and on the basis of solving specific problems, students can experience the characteristics of the intuitive nature of functions and experience the connections and changes between variables. Therefore, as an important mathematical model for studying the phenomenon of motion change, function plays an important role in junior high school mathematics and is the main line of learning in the field of junior high school mathematics and algebra courses. On the one hand, at the primary school level, the "Standards" puts forward the learning task of "exploring the law", which is actually the initial stage of function learning.

On the other hand, functions are very important in the field of mathematics and algebra in junior high school. The number and algebra curriculum at the junior high school level roughly includes four major aspects: numbers, algebraic formulas, equations and inequalities, and variables and functions, which are relatively independent and interrelated. Without the concepts of rational numbers, real numbers, and algebraic formulas, it is impossible to learn the relevant knowledge of equations and functions; Equations and inequalities are special cases of functions, which shows that functions play an important role in the curriculum of number and algebra in junior high school.

The function uses an image to express the relationship between numbers, which is intuitive and vivid, and the image of the function allows students to experience the relationship between numbers and shapes. Many algebraic methods are used in solving function problems, such as matching methods and formula methods are used in solving the maximum value problem of quadratic functions, which are first transformed into function problems when solving practical problems, and the ideas of classification and discussion are used in scheme selection, which are important algebraic thinking methods in junior high school mathematics and play a significant role in the improvement of students' mathematics learning ability. By using the function thinking method, we can not only solve mathematical problems, but also solve many practical problems in real life, such as the problem of maximum profit, the problem of the largest area, and the problem of scheme selection, which precisely reflects the requirements of the curriculum standards, mathematics is the best in life, and serves life.

It can concentrate on many mathematical ideas and methods such as the combination of numbers and shapes, model ideas, transformation ideas, etc., and it can be said that functions are a main line throughout the learning of junior high school mathematics and algebra courses.