The concept of number. Function is one of the most important basic concepts in middle school mathematics. Throughout middle school algebra. Since the first letter represents numbers, variables are introduced, which makes mathematics change from the calculation of static numbers to the change of quantity. Moreover, variables are interrelated, interdependent and restrictive, and this dependence between variables produces functions. Junior high school has initially discussed the concept of function, the expression of function relationship and the drawing of function image. High repetition function is a re-understanding of the concept of function, which is to understand the definition of function by using the idea of set and correspondence, so as to deepen the understanding of the concept of function. Functions are closely related to other knowledge in mathematics, and are interrelated and transformed with equations, inequalities and other knowledge. The study of functions is also the basis for further study of mathematics. In middle school, we should not only learn the concepts, properties, images and other knowledge of functions, but more importantly, the idea of functions should penetrate into the whole process of mathematical research more widely.
Function is the main content of middle school mathematics and plays a connecting role. Function is also the hinge of the connection between elementary mathematics and advanced mathematics. Especially in today's deepening application consciousness, the essence of function is to reveal the interdependence and mutual restriction of quantity in the objective world. Therefore, the re-understanding of the concept of function has an irreplaceable position and important practical significance. This section is more content, divided into two classes. The content of this lesson is: the concept of function, the three elements of function, the solution of definition domain and value domain of simple function, interval representation and so on. (The content of the second lesson is: review of the concept of function, definition of more complex function and solution of value domain, piecewise function, function image, etc. )
Analysis of learning situation
Students have learned the concept of function in junior high school before learning this section, and know that function can be used to describe the dependence between variables. However, the expression of the concept of function itself is abstract, students' understanding of dynamics and statics is still weak, and they lack a certain understanding of the essence of the concept of function, so it is difficult to further learn the images and properties of function. The junior middle school defines the function from the angle of action change. Although this definition is intuitive, it does not fully reveal the essence of the concept of function. For example, for functions
From the point of view of movement change, it is not easy to explain and seems far-fetched. But it is very natural to explain it with sets and corresponding viewpoints. Therefore, it is necessary to understand the function and re-understand the concept of function with the idea of set and correspondence. Because of the abstraction of mathematical symbols, students will be discouraged, thus affecting their enthusiasm for learning mathematics. Although senior one students have been exposed to the concept of function in junior high school, there are still some obstacles in the process of relearning functions. One of the reasons is that they don't understand the newly introduced function symbol "y=f(x)". Teachers should consciously explore the aesthetic factors of functional symbols in teaching and enlighten the truth with beauty. In the teaching process of this class, teachers should provide students with practical opportunities, create familiar problem situations for students, and guide students to observe, calculate and think, so as to understand the essence of the problem and summarize the conclusions.