In the actual teaching process, due to the influence of the old textbooks, some teachers continue to deepen and supplement the content while teaching according to the knowledge system and requirements in the new textbooks, and unconsciously return to the old textbooks in terms of knowledge and methods to deal with problems, thus losing the significance of pruning and strengthening the work with the new textbooks, changing the true colors of the new textbooks, such as the chapter on trigonometric function teaching, and only giving several limited inductive formulas. It also points out the steps to turn any angle into an acute angle and find the trigonometric function. Although we don't have to simplify it completely in its order, we can see from these steps that these formulas are enough for us to use. If the teacher supplements other inductive formulas and uses a large number of formulas flexibly, it will be very troublesome to memorize, which will increase the learning difficulty of students invisibly.
On the other hand, the way to deal with problems should not be limited to the old methods in the past, but should be updated according to the contents of new textbooks. Because of the deletion and increase of content, the new textbook will inevitably have many differences and unique features, such as introducing vectors as tools, which injected new vitality into the solution of mathematical problems.
If you don't change your view of knowledge in the process of using new textbooks and still crawl on the original content, it will inevitably lead to the failure to implement the spirit of curriculum standards, making it difficult for students to learn well, and "popularizing mathematics" can only become empty talk.
Second, the knowledge connection should be smooth.
Students think that an important reason why mathematics is difficult to learn is the mental hole caused by the fault of knowledge connection, which is mainly reflected in the following aspects.
First, the influence of the deletion of junior high school content on senior high school mathematics learning. After the deletion of junior high school mathematics textbooks, some teachers are unfamiliar with the new junior high school textbooks. On the basis of the old textbooks, they use the knowledge deleted from the old textbooks in the new teaching process, which causes the burden of students' study. For example, the center of gravity theorem has been deleted from the new textbook of junior high school, and the current textbook of senior high school only appears in the form of exercises in the chapter of plane vector, which can be found in many textbooks. Its connection with solid geometry and analytic geometry was almost deified, and the teachers explained it with relish. For another example, the cubic formula has been deleted from the new junior high school textbook, and it has not been introduced into the senior high school textbook. However, in the teaching set and inequality, teachers unconsciously put it into the teaching content, which will inevitably lead to difficulties for students to understand and use.
Second, teachers' improper handling of teaching materials makes it difficult for some students to accept them. Teachers exceed students' existing knowledge system when they choose to understand knowledge, which makes the level requirements of curriculum standards not fully reflected, and the unconscious deepening and horizontal connection make it difficult for students to accept. For example, in the chapter of function, the solution of range is greatly reduced. If students are told the solution of the range of values in some form at the beginning, it will be difficult for students to accept it, resulting in some students falling behind and unable to continue their studies.
Therefore, when teaching, teachers must understand students, find the nearest development field, let students transition from the existing knowledge level to the new knowledge system, incorporate new knowledge into the original cognitive structure, improve the original cognitive structure, and realize the smooth connection of knowledge.
Third, training should be moderate.
Mathematics education has many characteristics, but its main feature is the solid "two basics" (basic knowledge and basic skills) teaching. According to Mr. Zhang Dianzhou, the basic theoretical characteristics of China's "double-base" teaching include four aspects: first, memory leads to understanding; second, speed trumps efficiency; third, the rigorous formation of reason; and fourth, repeated dependence on variants. Therefore, mathematics learning is the combination of learning and practice, and practice is an indispensable and important process of mathematics learning. If a large number of repeated exercises will make students feel bored, thus losing interest in mathematics learning. Therefore, in order to implement students' "double basics", the number and difficulty of selected mathematics problems should be appropriate and well grasped, so that more students can feel the fun of learning mathematics and keep their interest in learning mathematics. Teachers can choose appropriate questions for students to practice and make them flexible and diverse.
In addition, high school mathematics teaching should prevent the phenomenon of "de-theming", that is, in teaching, the essence and connotation of mathematics are less, and the so-called situational and life-oriented games are more. One-sided emphasis on exploration and cooperation allows students to pursue the external performance of teaching, rather than thinking deeply about the concept and content of mathematics. Although the classroom is lively, but the thinking depth of students' participation is not enough, mathematics itself is attractive, and mathematics teaching should be attracted by the essence of mathematics.
(Editor Li Chuang)