Since the 1950s, China's middle school mathematics syllabus has been revised many times, but all of them have the same guiding ideology, that is, to do well the three basics. It is emphasized that a correct understanding of mathematical concepts is the premise of mastering the basic knowledge of mathematics. At present, the outstanding problem in China's mathematics teaching is to ignore the correct understanding of the mathematical foundation, that is, the mathematical concept. On the one hand, textbooks underestimate students' understanding ability, and in order to "reduce the burden", dilute or even avoid some basic concepts that are difficult to understand; On the other hand, the exam-oriented strategy of "sea tactics" makes teachers have insufficient time and energy to study how to make students deeply understand basic mathematical concepts. It is said that the burden is reduced, but in fact the pressure on teachers and students has increased.
Without "process" teaching, because of the lack of mathematical thinking method as a link, the relationship between concepts can not be understood, and it is difficult to establish the relationship between concepts, which leads to the lack of integrity of students' mathematical cognitive structure.
Second, we should adopt different methods for different concepts.
Some only need to implement concept teaching in example teaching. For example, the concept of relevance is descriptive, and there is no need to pursue formal rigor. It is suggested to adopt case teaching method. Compared with the functional relationship, it highlights two essential characteristics of the relationship: relevance and uncertainty.
Some first introduce the background of the concept, and then let students perceive the concept and extract the essential attributes through the obvious and intuitive examples related to the concept.
Some should contact other concepts and use multimedia and other auxiliary facilities for intuitive teaching.
Third, grasp the concept between the old and new concepts.
Many concepts in mathematics are closely related, such as parallel line segment and parallel vector, plane angle and space angle, equation and inequality, mapping and function, opposite event and mutually exclusive events. In teaching, we should be good at discovering and analyzing their connections and differences, which will help students grasp the essence of concepts. For another example, the concept of function has two definitions. One is the definition given by junior high school, which is from the point of view of motion change, and the corresponding relationship is to correspond each value of independent variables with a unique function value; The other is the definition given by high school, which is based on the viewpoint of set and correspondence, in which the correspondence is to correspond each element in the original image set with the only determined element in the image set.
The definition given by junior high school in history comes from physical formula, and function is an important mathematical model to describe the dependence between variables. Functions can be represented by images, tables, formulas, etc. Therefore, high school uses sets and corresponding languages to describe functions, which captures the essential attributes of functions and is more general. Experts in New Oriental Youneng Middle School believe that the definitions of the two functions are exactly the same as the range of values, and the essence of the corresponding relationship is the same, but the starting point of narration is different, so the definitions of the two functions are essentially the same. Of course, it is not easy to really know and understand the concept of function, which requires a long process of repeated contact.