Function thought is one of the important thoughts that run through the whole senior high school mathematics curriculum. In order to better understand the high school mathematics curriculum, it is necessary to understand the development of function thought in the primary and secondary school mathematics curriculum.
In high school, I learned more knowledge. We use more abundant examples to guide students to realize that function is an important mathematical model to describe the laws of daily life and other disciplines. Function model should occupy a very important position in high school mathematics. In any life scene, such as post office, gas station, airport, etc. We will find many functional relationships that describe the law. In other disciplines, such as physics, chemistry, biology, geography, society, economy and other disciplines, functional relationships describing laws abound.
We might as well use some specific function models to understand functions, such as piecewise functions, simple power functions, exponential functions, logarithmic functions, trigonometric functions and so on. Combining these functions, we introduce some basic properties that describe the change of functions, such as monotonicity, periodicity and parity.
In the high school mathematics curriculum, through the study of functions, the idea and definition of mapping are gradually formed. Function is the correspondence between two groups of real numbers, and mapping is the correspondence between two groups of real numbers. Mapping can help us better understand the "bridge relationship" between two objects. The idea of mapping and the idea of function are essentially the same, but the two objects they contact are different. In the process of applying the idea of function (mapping) to solve problems, we can deepen our understanding of the bridge function of function.
The thought of function plays an important role in the study of other parts of mathematics.
In senior high school curriculum, functions and sequences, functions and derivatives and their applications, functions and algorithms, and functions and random variables in probability are closely related. It is a very important starting point to understand these contents with the idea of function (mapping). On the other hand, through the study of these contents, the understanding of function thought is deepened.
Function is a basic mathematical model to describe the objective world. Therefore, the learning of function should be organically combined with the experience, feeling and application of function to solve the problem. Students should be guided to think about the application of functions, especially the application of functions in daily life and other disciplines. The idea of mathematical modeling can permeate into teaching.
Understand the thought of function when learning related contents of function knowledge. In fact, in the whole high school mathematics curriculum, we need to constantly experience and understand the "benefits" brought by "function thought".
To sum up, the thought of function is a main line of high school mathematics curriculum, which links many contents of high school mathematics curriculum from one angle. With this main thread, we can weave the knowledge of mathematics together, so as to master the knowledge more firmly.