1. Quote classics and tell stories.
When teaching a new class, combining with the content of the topic, introducing some stories about the history of mathematics and mathematicians or telling some vivid mathematical allusions can often stimulate students' interest in learning. For example, when teaching "the concept of irrational numbers", we can talk about the emergence of irrational numbers and the spirit of Herbs, the discoverer of irrational numbers, in order to cultivate students' moral character of fighting for truth. Talking about "circle", we can talk about the contribution of China ancient mathematicians Liu Hui and Zu Chongzhi to pi, and set up students' aspirations of loving the motherland and benefiting the nation.
2. Direct introduction method
At the beginning of the class, it is a common method to contact the theme of the teaching content and point out the focus and center of the problems discussed in this class, so that students can know as much as possible. For example, in the teaching of "the solution of quadratic equation in one variable" (the first class), after reviewing the basic knowledge of quadratic equation in one variable, you can directly ask the question: "How to solve the equation with shapes?" This paper introduces a special case of the unary quadratic equation "Ax2=B solution", and then introduces a new topic: "Direct Kaiping Method".
3. Review the past and introduce new methods
When teaching a new class, first review what you have learned before, and then ask questions on this basis, which can not only consolidate old knowledge, but also arouse students' enthusiasm for further study.
4. Case-finding method
It is an important way to explore knowledge and introduce topics to analyze and reveal the general laws of things with concrete examples in real life. For example, when explaining the "triangle mean value theorem", the following examples can be introduced first: In order to measure the width AB of a pond, someone takes a point C outside the pond, connects AC, BC and their midpoints D and E, and measures the length of de to get the width of the pond. This question will naturally arouse students' curiosity and stimulate their desire to explore knowledge.
5. Object intuitive method
In teaching, students can be guided to observe some physical objects, stimulate their intuitive thinking and lead to new topics. 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. Through practical operation, students will find that any three sticks can sometimes form a triangle, and sometimes they can't, revealing the relationship among the three sides of the triangle, and this new topic naturally comes out.
6. Cautious doubt method
To teach a new lesson, we should first ask some questions that can arouse students' doubts, guide students to eliminate doubts, and thus arouse their enthusiasm.
7. Comparison between old and new classes
When introducing the subject, adopting the method of analogy between old and new knowledge can not only make students understand new knowledge on the basis of further understanding old knowledge, but also leave a deep impression on mastering the logical relationship of theory. For example, when talking about the concept of logarithm, it can be introduced as follows: in the equation ab=c, A and B are known, and finding C is a power operation; If b and c are known, find a, which is a square root operation; If A and C are known, how to calculate B is a problem to be solved by the new discipline.
8. Inductive introduction method
Generally, new courses are introduced by summarizing the rules found in students' classroom exercises and answers. For example, in the "intersection" class, let students write all subsets of sets {3,5,8} and {3,7,8} on the blackboard and answer the questions: ① What are their non-empty proper subset? (2) Which of these sets are the common subsets of the original two sets? ③ Try to compare the similarities and differences of these common subsets ({3}, {8}, {3,8}) according to their elements. (4) According to the above, describe what set {3,8} is. After inspiring students to draw the conclusion that "{3,8} is a set composed of all common elements of {3,5,8} and {3,7,8}", the teacher immediately concluded that "set {3,8} is mathematically called set {3,5,8} and {
9. Demonstrate the import method
Teachers introduce new lessons with the aid of visual demonstration of teaching AIDS. For example, in the teaching of "ellipse", prepare a line before class, and let students try to draw a circle with this line after class. Then, the teacher tied an iron nail to each end of the string, and then tried to fix the iron nail on the blackboard (the distance between the two iron nails was less than the fixed length of the string), and tightened the string with chalk to make a circular curve motion around the two fixed points. Then chalk draws a closed curve (ellipse) on the blackboard. By comparing the similarities and differences between the two kinds of graphics, this paper analyzes the drawing process of the latter, and leads to a new lesson "Definition of Ellipse". This kind of guidance is intuitive and helpful to cultivate students' abstract thinking ability and imagination ability.
10. Comprehensive introduction method
In order to highlight key points and disperse difficulties, two or more basic knowledge are generally combined into new knowledge in teaching. For example, in the teaching of "the relationship between the root and coefficient of a quadratic equation", the classroom exercises are given at first: "We know the equation, ① find the second root,; ② Find the value of+sum; ③ Try to compare the relationship between+and the coefficient of the known equation. " In this way, students naturally introduce new courses through practice, comparative analysis and teacher's guidance.