Talking about concepts well is the basis of talking about mathematics well. The main steps and requirements are:

(1) Introduction

(2) Definition

Students or teachers should define this concept. Definition should conform to the principle of definition, and pay attention to cultivating students' ability to define concepts step by step.

(3) Analysis

(4) Application

(5) Summary: Systematically summarize the related issues and precautions of the concept.

2. Regular courses

Laws here refer to theorems, axioms, inferences, formulas and rules. Law is the most basic and main content of mathematics. The so-called learning mathematics is mainly about learning laws. The main steps and basic requirements of teaching rules are:

(1) development law

(2) Prove the law

(3) Analysis law

Note: the form should be flexible and diverse, and the service for the application should be highlighted.

(4) Extended law

The general form of law (generally not beyond textbooks); Especially the special form of law (commonly used, requiring special memory and mastery).

(5) Application of law

This is the purpose of learning the law.

Attention: pertinence, gradient, flexibility and variability (such as a changeable topic).

(6) Summary

Systematically summarize the relevant issues of law, and form a relatively perfect understanding structure and matters needing attention.

3. Example class

Example classes are classes that reveal concepts and apply rules. It is different from ordinary exercises, and its core is to reveal the law of solving problems. It is an important way to cultivate ability and develop intelligence. The sample class should do the following:

(1) Preparation before class

For example, preparation before class is of special significance, and the following must be done:

(1) the choice of examples.

Examples should be typical (easy to reveal the law) and targeted (aimed at the problems existing in students or the need to consolidate and deepen basic knowledge, skills and mathematical methods), which is basic. We should also pay attention to inspiring more solutions, less but better.

② Reasonable arrangement

We should use the most typical and easiest examples to reveal the application law; The problem of consolidating and deepening the application of law should be from easy to difficult, gradient and related.

(2) classroom implementation (basic steps):

Objective: To point out what problems should be solved in this example class, so as to concentrate students' energy and improve the cooperation between teachers and students.

(2) Reveal the law: that is, reveal the essence of * * * through personality (typical cases) (the law to solve such problems), which is the fundamental symbol of the quality of example classes.

Note: it is best to guide students to sum up the rules themselves; Students must understand why this kind of problem has such a law of solving problems to prevent rote learning.

③ Consolidation exercises

④ Nodules

Further summarize the basic points of the law and matters needing attention in application, as well as the uniqueness and personality of this problem-solving law and the learned problem-solving law, so that the problem-solving law forms a network.

4. Exercise class

Exercise class is a student-centered exercise class under the condition that students basically master the law of knowledge application. It can be divided into autonomous exercises and guided exercises.

(1) Preparation before class

① Selected exercises: The exercises should be targeted and general, which is the foundation. Secondly, we should pay attention to flexibility, novelty, inspiration and comprehensiveness, which is the basis and key to a good exercise class.

Appropriate arrangement: from easy to difficult, systematic, phased and moderate gradient.

(2) Classroom implementation (basic steps)

Explain the purpose: let students know what problems to solve through practice, let students practice consciously and purposefully, and prevent them from doing problems blindly.

② Students' practice.

(3) Patrol guidance: This is the key point of a good exercise class. Please pay special attention to:

④ Nodules

Step 5 comment on the class

This course is offered after independent practice or test. The purpose is to analyze and solve the problems in the "three basics" and learning methods and attitudes reflected by students in the test paper.

(1) Preparation before class

① Good test questions: Without good test questions, there will be no good lectures and evaluation. The test questions should be comprehensive (including the basic contents of the "three basics"), typical and targeted, with a certain number of comprehensive, flexible and independent topics.

2 Be optimistic about the test paper: there are various forms, but we must fully grasp the students' "three basics", learning methods and attitudes reflected in the test paper.

③ Completes typicality: First, the typicality of the problems existing in the "three basics" and the optimal solution; Second, it is a typical example of learning attitude and methods, and it is the most basic material for a good lecture and evaluation.

Choose the right material: there are often many things to comment on, so we must pay attention to the choice, highlight the key points and solve the main problems.

(2) Classroom implementation

① Outline: achievements and main problems (laying the foundation for typical analysis); Praise the students with good learning attitude, rapid progress and the best grades by name, and don't mention the decline of academic performance by name, especially the students with bad learning attitude (try to reduce the time).

(2) Typical analysis: This is the fundamental sign of class evaluation. Analysis of "three basics" typical problems, we should pay attention to:

The problems existing in basic knowledge must be made clear to all students, which are caused by mistakes in concepts, formulas, rules, theorems, axioms, memory and understanding; Make a mountain out of a molehill, break the wrong root;

The problems existing in basic skills and problem-solving thinking methods should be clearly explained to all students because of insufficient knowledge, understanding and mastery of mathematical ideas, methods and problem-solving laws of such problems; We should avoid focusing on the theme or downplaying it.

For those with particularly big problems, students can practice after class as similar questions after evaluation.

Announce the answer: There are various forms, but all students must know the correct answer to each question.

6. Summary class

Summing-up class is to string together the learned knowledge structure or application law, make it systematic, form a better cognitive structure, and facilitate memory, understanding and application.

(1) two types.

(2) Summarize the requirements. Be scientific and comprehensive, and highlight key points; Highlight knowledge or thinking structure (this is the fundamental point); It should be targeted (mainly aimed at the problems existing in students).

(3) Precautions. Generally, it is a combination of summary exercises, but summary should be the core; It is necessary not only to highlight the links between various parts and form a good knowledge structure, but also to pay attention to solving the main problems existing in many parts, and the priority depends on specific problems.

The above is the teaching mode of six kinds of courses.

It should be noted that "Model" is a reference outline for teachers to deal with teaching materials and choose teaching methods. It can be refined, some steps can be omitted and some steps can be added.