As the saying goes, "everything is difficult at the beginning." If you want to have a good math class, a good beginning is half the battle. The introduction of new courses is the forerunner of new course teaching. Ingeniously introducing a new depth can effectively organize the teaching of the new curriculum, focus students' attention on the learning of the new curriculum, create a suitable situation for the new curriculum, stimulate students' interest in learning, form an internal force to promote students' conscious and active exploration, and make students step into the realm of "happy learning" from "hard learning" and develop in quality, knowledge and ability. The following article will combine the author's teaching practice for more than ten years. Several common methods of introducing new courses into mathematics teaching.

First, the introduction method of straight to the point

Straight to the point is the direct guidance method. We are used to "cut to the chase" when talking and writing articles, so that the theme is prominent and the argument is clear. When some newly taught mathematical knowledge is difficult to attract people with the help of old knowledge, we can directly point out the topic and immediately arouse students' interest in learning. For example, when teaching sine and cosine in trigonometric functions, you can introduce it like this; What is the ratio of the opposite side to the hypotenuse and the ratio of the adjacent side to the hypotenuse of acute angle A in a right triangle? In this lesson, we will learn these contents-sine and cosine. This import is very simple. It not only clarifies the theme of this class, but also explains the background of this class.

Second, review the new introduction method of old knowledge

Reviewing old knowledge and learning new teaching methods can organically combine old and new knowledge, so that students can naturally gain new knowledge from reviewing old knowledge. For example, when teaching the concept of "fraction", students can be guided to review the concepts of algebra, polynomial and monomial, and then ask: If there are letters in the denominator, what are they? This naturally introduces the concept of "score", so that students can firmly grasp the essential characteristics of this concept. For example, when teaching the "Secant Theorem", first review the content and proof of the theorem of intersecting chords, that is, the product of the length of two straight lines divided by the intersection of two intersecting chords in a circle is equal, and then move the two chords to make their intersection outside the circle. There are three situations. In this way, students can easily understand the mathematical expression of the cutting line theorem and its inference. On this basis, guide students to describe the content of the theorem, and sum up that the * * * of the circular power theorem means that the product of line segments is equal. The difference is that the intersecting chord theorem is the line segment within the intersection point, while the secant theorem and inference are the coincidence of the two ends of the outer line segment and the tangent theorem. In this way, students can find a string of new knowledge from the review of old knowledge and master the proof method of line segment product equality. Reviewing the learned theories by reviewing the old ones can not only make students feel unfamiliar in the application process, but also contribute to the development of new courses and make the transition of new courses more natural.

Third, the analogy introduction method

Analogy guidance is a way of thinking that infers that new knowledge has the same or similar properties when both old and new knowledge have the same or similar properties and some properties of old knowledge are already known. When the new content is similar to the old knowledge learned before, we can introduce the new curriculum content by analogy to promote the transfer of knowledge. The new one is better than the old one. Natural transition, concise and lively, and can effectively mobilize the enthusiasm of students' thinking.

For example, when teaching "similar triangles property", we can take congruent triangles property as an example to make an analogy, that is, the corresponding sides, corresponding angles, corresponding line segments and corresponding perimeters of triangles such as gold are all equal. Then, what is the relationship between the corresponding edge, the corresponding angle, the corresponding line segment and the corresponding perimeter of similar triangles? This way. It is natural to get the nature of similar triangles by analogy.

Fourth, personally practice the introduction method.

Hands-on practice introduction method is a practical activity operation method, that is, according to the teaching materials of geometry knowledge, the introduction method of obtaining new knowledge by hands-on operation is adopted. In the classroom teaching. Teachers should create more activity situations so that students can explore, practice and innovate independently. Only in this way can students deeply understand mathematics knowledge and stimulate their interest in learning mathematics. Cultivate their practical ability and spirit of inquiry. For example, when teaching "the sum of the internal angles of a triangle is 180 degrees", let students cut the three internal angles of the triangle and put them together, thus summing up the property that the sum of the internal angles of the triangle is 180 degrees from students' practice. Another example. When teaching parallelogram. Let the students take out a piece of paper and cut out two congruent triangles. Let them overlap the equal sides of these two triangles to make a jigsaw puzzle. Students will get two kinds of figures, one is a general quadrilateral and the other is a parallelogram. Then observe the characteristics of its edges and corners. It is not difficult for students to get the characteristics of parallelogram through hands-on operation, practice and exploration, and this knowledge is obtained by students through active operation and personal experience. Not taught by teachers, nor taught by teachers, so that students can not only learn, but also learn and explore, so that students can enjoy the joy of discovering truth.

Five, the discovery of import method

The way to discover and guide people is to inspire students to discover certain laws from certain phenomena. Discovery lead-in method can improve students' interest in learning in the joy of discovery, and is also beneficial to students' understanding and memory of new knowledge. For example, when teaching "the relationship among three sides of a triangle", students can take out three sticks of different lengths to see if they can form a triangle. By observing the actual operation, students will find that. Take three sticks at random, sometimes you can form a triangle, sometimes you can't. So as to reveal the relationship between the three sides of the triangle. This new topic naturally leads to. In this way, the introduction of new curriculum will lead students' discovery from experiment to strict logical reasoning, which is a natural transition for teaching materials: for students, it will become a need and satisfaction for thinking. For those laws that are easy to find, this method can also be used to introduce new lessons.

Sixth, emphasize the introduction method

Emphasized lead-in is a way to emphasize the importance of what you have learned and lead in new lessons. This method can attract students' attention and attract their attention. For example, when teaching "function", it can be introduced as follows: equation is an important content of junior high school mathematics, occupying an important position, and function is an important content of junior high school mathematics. It occupies a relatively important position and is also the basis for further study in the future. So, starting today, let's learn functions. For another example, when teaching "circle", it can also be introduced that the shape of three wings is the focus of plane geometry, and the circle is the focus of plane geometry. It plays an important role in the senior high school entrance examination questions and is also the basis for further study in the future. So ... starting today, we will learn about circles.

There are many ways to introduce new courses. Either method should be based on students' life experience and existing knowledge background, aiming at stimulating students' curiosity and interest in learning and arousing students' thirst for knowledge. In this way, students will not be bored with mathematics, and their interest and self-confidence in learning mathematics will be greatly increased. In this way, students' mathematical thinking ability, ability to analyze and solve problems will be improved, and students will have good feelings and attitudes towards mathematics. In fact, as long as we carefully consider how to introduce new courses, we can come up with one or even more methods to guide courses, so as to cultivate students' interest, stimulate their curiosity and ignite the sparks of students' thinking.