The mathematics teaching model of middle school, which adapts to the new mathematics curriculum concept, requires that the mathematics teaching activities should be based on students' cognitive development level and existing knowledge and experience, and teachers should stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematics activities, and help them truly understand and master basic mathematics knowledge and skills, mathematics ideas and methods in the process of independent exploration and cooperative communication, so as to gain rich experience in mathematics activities. Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning. " The new requirement of "Standard" for mathematics teaching activities is a challenge to traditional mathematics teaching. Fundamentally speaking, this challenge is to change the teaching mode from "exam-oriented education" to "quality education". I. Overview of Middle School Mathematics Teaching Mode Mathematics teaching mode refers to a relatively stable "style" teaching environment created in the teaching process in order to complete certain mathematics teaching tasks and achieve certain teaching objectives under the guidance of certain teaching ideas. For a long time, due to the influence of "exam-oriented education", the "exam-oriented teaching" mode aimed at imparting knowledge and coping with exams is quite common in middle school mathematics teaching in China, which greatly hinders the cultivation of middle school students' innovative spirit and practical ability. The Outline of National Basic Education Curriculum Reform points out: "Change the tendency that the curriculum pays too much attention to imparting knowledge, and emphasize the formation of active learning attitude, so that the process of acquiring basic knowledge and skills becomes the process of learning to learn and forming correct values". It is also pointed out: "Teachers should actively interact with students and develop together in the teaching process, handle the relationship between imparting knowledge and cultivating ability, pay attention to cultivating students' independence and autonomy, guide students to question, investigate and explore, learn in practice, and promote students to learn actively and individually under the guidance of teachers." Gradually realize the changes in the presentation of teaching content, students' learning methods, teachers' teaching methods and teacher-student interaction. It is not difficult to see that the single "exam-oriented teaching mode" aiming at exam-oriented education can no longer meet the needs of the reform and development of basic education. Therefore, exploring the teaching mode of cultivating students' innovative spirit and practical ability is the inevitable development trend of mathematics teaching reform to meet the needs of quality education. Only by constructing a mathematics teaching model that adapts to quality education can quality education not only stay in ideas, but also really guide mathematics teaching practice. Middle school mathematics teaching mode is the intermediary and bridge between teaching theory and teaching practice, and it is a "strategy system" and an "easy-to-operate implementation procedure" that embodies teaching theory to guide teaching practice. For example, the teaching mode of "speaking, listening, reading, taking notes (recording, reciting) and practicing" embodies the ancient teaching thought of our country, which is teacher-centered and aims at imparting knowledge. A few words highly summarized the teaching "strategy system" and "operation implementation procedure". For another example, Kailov's five-link teaching model of "organizing teaching-reviewing old lessons-teaching new lessons-consolidating exercises and assigning homework" is still widely adopted today because it is enduring and deeply rooted in people's hearts. In just 20 words, it embodies the essence of Kailov's teaching thought and is easy to operate. It can be seen that once a certain teaching mode is mastered, it provides a relatively stable structure, procedures and steps for applying a certain teaching theory to guide teaching practice. Once a teacher has mastered a certain teaching mode, he can better complete the teaching task and achieve the expected teaching goal. It is true that due to the different teaching purposes, students' psychological development level and teaching environment, it is necessary to adjust the teaching mode appropriately or adopt the corresponding teaching mode. Because mathematics teaching mode can express some education, teaching theory or educational thought in a simplified form, its function or function can be reflected in the following aspects: 1. Popularizing and optimizing modern mathematics teaching mode usually summarizes and standardizes some excellent teaching methods, makes them more mature and perfect, and rises to an effective theoretical system with strong practicality and unique personality characteristics. The teaching theory constructed by this teaching mode is not only concise and centralized, but also feasible, typical and effective. Excellent mathematics teachers' personal teaching experience, through the integration of various mathematics teaching theories and mathematics teaching reform experiments, is transformed into general theories through accumulation, processing and sublimation, not limited to simple teaching methods or personal teaching experience. It has a certain theoretical form and is a relatively stable comprehensive teaching system. In teaching practice, many mathematics teaching workers have summed up a lot of teaching experience, and after gradual generalization and systematic arrangement, a teaching model has been formed, which can be further promoted to the theoretical level. In addition, various modern mathematics teaching theories have guided the teaching practice, formed corresponding teaching modes, and enriched and developed mathematics teaching theories. For the mathematics teaching theory formed in this way, it is convenient for teachers to grasp and understand its essence intuitively and quickly, and it is convenient for popularization and optimization. Different from the general teaching theory, it is difficult for teachers to understand and master. 2. As a simplified form of teaching theory, the teaching mode of consultation and explanation function can explain the basic characteristics of teaching theory through concise language or symbolic graphics. It becomes a scheme easily accepted by practical workers and directly translates into teaching actions. On the one hand, the consulting and explaining function of teaching mode improves the practical value of educational theory and is convenient for front-line mathematics teachers to master in mathematics practice. At the same time, the teaching mode has become the "interpreter" and "propagandist" of teaching theory, which makes its inherent teaching theory consciously accept the guidance of modern teaching theory and directly applies the most advanced mathematics teaching theory to teaching practice, effectively overcoming the blindness of teaching practice and enhancing the effectiveness of teaching practice. On the other hand, it has played the role of consulting and explaining the teaching model. Mathematics teachers can directly apply it to teaching practice by understanding the theoretical points and grasping the operational essentials of the mathematical model. Different teaching modes are selected pertinently, and the teaching efficiency of mathematics classroom is improved through the reasonable application of teaching modes, so as to improve teachers' enthusiasm for learning modern teaching theory and improve teaching ability. 3. The demonstration and guidance of mathematics classroom teaching mode is the overall consideration of mathematics classroom teaching structure. In a sense, teaching mode is not only the product of teaching reform, but also directly promotes the development of teaching reform. Through the experiment of mathematics teaching reform, various types of classroom teaching mode systems are gradually established, and a classroom teaching mode library similar to the question bank is established. On the one hand, this will make mathematics teaching gradually move towards the road of scientific development; On the other hand, if we strengthen the teaching research of mathematics teaching mode in the teaching of mathematics pedagogy in normal universities and in the process of teacher training, we can greatly improve the effectiveness of the training of normal students and in-service teachers, and directly provide some teaching plans for mathematics teachers to choose and refer to, so that they can learn from them quickly, be familiar with teaching and ensure the teaching quality as soon as possible. The teaching mode of six kinds of mathematics courses in functional middle schools "six kinds of mathematics courses" in middle schools refer to six kinds of concepts, rules, examples, exercises, summaries and comments; Teaching "mode" refers to the mode or style with more general application significance formed when teaching the basic laws of these courses.

basic content

1. Concept class

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 commonness (the law of solving such problems) through personality (typical examples), which is the fundamental symbol of the quality of the example class.

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 commonness and individuality 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.