How to do well the teaching of senior high school mathematics concept course under the new curriculum standard, senior high school mathematics

It has been some time since the implementation of the new mathematics curriculum in senior high school, and we have finally changed from a bystander of the new curriculum to a witness of "knowing the true face of Lushan Mountain". For a long time, due to the influence of exam-oriented education, many teachers pay more attention to solving problems than concepts in teaching, resulting in the phenomenon that mathematical concepts are out of touch with solving problems. Some teachers only regard the mathematical concept as a noun, but fail to see that its essence is a mathematical concept and a method to deal with problems. After teaching a "concept class", the rest is to solve problems quickly, which causes students to have a vague knowledge of concepts and can't understand and use them well, which seriously affects the quality of students' problem solving. On the other hand, in some places in the new textbook, the requirement for concept teaching is to know, which overestimates students' understanding ability and is also a reason why students can't solve problems. How to do well the teaching of mathematical concept course under the new curriculum standard.

First, understand the concept in the process of experiencing the mathematical concept.

The introduction of mathematical concepts should proceed from reality, create situations and ask questions. Through examples obviously related to concepts and intuition, let students perceive concepts and form perceptual knowledge in the experience of specific problems. Through the observation and analysis of a certain number of perceptual materials, the essential attributes of perceptual materials are extracted. For example, in the teaching of the concept of "out-of-plane straight line", teachers should first show the background of the concept, and then ask the question of "what is an out-of-plane straight line" for students to discuss with each other and try to describe it. After repeated revisions and supplements, they can define it concisely, accurately and rigorously. On this basis, students can find out the out-of-plane straight line in the classroom or cuboid, and finally draw the figure of the out-of-plane straight line with the plane as the background. Through the above process, students have a clear understanding of the concept of non-planar straight line, and also experienced the experience of the occurrence and development of this concept.

Second, understand the concept on the basis of excavating its connotation and extension.

The introduction of new concepts is the inheritance, development and perfection of existing concepts. Because some concepts are rich in connotation and extensive in extension, it is difficult to reach the goal in one step, and efforts should be made at three levels to gradually deepen and improve them. For example, the definition of trigonometric function has gone through the following three gradual deepening processes: (1) the definition of acute trigonometric function described by the ratio of the sides of a right triangle. (2) The definition of acute trigonometric function expressed by the coordinates of points. (3) Definition of trigonometric function with arbitrary angle.

Derived from this concept are: ① symbols of trigonometric functions in each quadrant. ② trigonometric function line. ③ Basic relations of trigonometric functions with the same angle. ④ Images and properties of trigonometric functions. ⑤ Three solving functions

The inductive formula of numbers, etc. It can be seen that the definition of trigonometric function is the most important in trigonometric function teaching and the cornerstone of the whole triangle part. It runs through all parts related to trigonometry and plays a key role.

Third, grasp the concept on the basis of finding the connection between the old and new concepts.

Many concepts in mathematics are closely related. It is helpful for students to master the essence of concepts to be good at discovering and analyzing their connections and differences in teaching. For another example, the concept of function has two definitions, one is given from the viewpoint of movement change in junior high school, and the other is given from the viewpoint of set and correspondence in senior high school. 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. Careful analysis of the definitions of the two functions is only based on different starting points, 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.

Fourth, consolidate concepts in the process of solving problems with mathematical concepts.

After the formation of mathematical concepts, it is an important part of mathematical concept teaching to explain the connotation of concepts, understand the "prototype" of concepts, guide students to use concepts to solve mathematical problems, and discover the role of concepts in solving problems. By thinking about the problem, let students devote themselves to the exploration of new concepts as soon as possible, and let students have inner experience and creation in the process of participation. In addition, the teacher's analysis through counterexamples and misinterpretations is also conducive to students' consolidation of concepts. At present, the shortage of class hours is a prominent problem in the teaching of new mathematics curriculum, which will seriously affect the teaching of mathematical concepts. Even so, I think it is worthwhile to spend more time on concept teaching, because only by understanding and mastering concepts can we better help students implement the "two basics", better help students understand mathematics, understand the thought and essence of mathematics, further develop students' thinking and improve their ability to solve problems.

In short, in concept teaching, according to the specific requirements of the new curriculum, we should creatively use teaching materials, optimize the concept teaching design, grasp the concept teaching process, and really let students have inner experience and creation in the process of participation, so as to understand the essence of mathematical ideas and concepts.