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How to carry out hierarchical teaching in junior high school mathematics
1 Introduction

In China, Shanghai took the lead in proposing hierarchical teaching reform and conducted relevant experimental teaching. This method gives full play to the advantages of class teaching system, overcomes the disadvantages of sameness, gives full play to students' personality, realizes the goal of teaching students in accordance with their aptitude and improves teaching efficiency. People pay more and more attention to the layered teaching method. Specifically, stratified education can be realized from the following aspects.

2 How to realize stratified education

2. 1 stratified comprehensive level of all students.

On the premise of fully understanding the actual situation of students, teachers divide all students into three grades: A, B and C according to their intelligence level, learning initiative, mastery of basic knowledge, usual performance and examination results. A-level students have solid basic knowledge and active thinking. B-level students have medium basic knowledge and good thinking level. C-level students have weak basic knowledge and average thinking level. What we should pay attention to here is that stratification should allow students of different levels to connect flexibly and make students full of confidence and hope from stratification. After a period of study, students at all levels re-adapt through various forms of testing and evaluation. In this way, A-level students, while feeling glorious, will always be soberly aware that they may fall into the other two levels and continue to work hard. Students of Grade B and Grade C will follow the example of students at the next level and constantly improve their grades, so that students at all levels can encourage each other and make progress together.

However, students' ideological burden and parents' doubts should be fully considered when they are stratified. After stratification, it will have a certain impact on the psychology of C-level students and their parents. Students mainly feel inferior, and parents feel humiliated. It can be seen that it is very important to do well the work of students and parents before the stratified teaching experiment. Patiently explain the advantages and benefits of hierarchical teaching to students and parents, so that students and parents can eliminate their concerns, and remind students and parents to make certain mental preparations.

2.2 According to the syllabus, the teaching objectives are stratified.

Classroom teaching is mainly based on the syllabus. Teachers can divide the teaching objectives of each lesson into three different development levels according to students' cognitive ability and the knowledge structure of teaching materials, and achieve different teaching objectives for students at different levels. For example, when teaching "Double Angle Formula", A-level students are required to derive the formula, which can be used flexibly in specific complex questions. Students of Grade B are required to understand the derivation process of the formula and deeply understand the formula from the process of understanding the formula derivation. C-level students should not only remember formulas, but also solve simple trigonometric functions.

Of course, under this teaching organization mode, the difficulty of classroom teaching organization and implementation will increase, which will put forward higher requirements for teachers, but it will play a positive and good role in teachers' own professional development. 2.3 The teacher's lesson preparation content is hierarchical.

On the basis of students' stratification, different teaching schemes are made for students of different levels. For A-level students, it is necessary to put forward higher requirements, in addition to completing the exercises specified in the textbook, choose some books and books on mathematics competitions in an appropriate amount to exercise students' divergent thinking. Students are also required to summarize the types of exercises, write out the experience of solving problems, and learn deeply through summary. For B-level students, while consolidating the basic knowledge of mathematics, we should focus on improving their mathematical thinking ability and strive to make it possible for some B-level students to transform into A-level students. For C-level students, it is mainly to improve their enthusiasm for learning mathematics and their confidence in learning mathematics well. Through the careful guidance of teachers and the training of a large number of basic questions, we can improve our mathematics foundation and gradually transform some C-level students into B-level students.

2.4 student-centered, hierarchical teaching process.

There are obvious differences in the acceptance ability of different types of students, which requires teachers to teach at different levels in the teaching process. A-level students mainly study independently, ask questions through thinking, and teachers tap the divergent thinking of A-level students through guidance; B-level students learn by self-study and proper guidance from teachers; C-level students are mainly explained by teachers. By explaining a question type and then asking students to do similar exercises, students can quickly master the question type. For C-level students, teachers need to spend more time and energy to help them study actively, or A-level students help them study, so that C-level students can consolidate their knowledge through more time and guidance. Finally, through the layered teaching method in the teaching process, students at all levels can gain something.

2.5 hierarchical evaluation of students

Hierarchical evaluation has the functions of summary, improvement and feedback, which is the guarantee of implementing hierarchical teaching. Take different evaluation criteria for students of different levels and give full play to the incentive role of evaluation. For C-level students, the evaluation should be based on encouragement, helping them build up self-confidence and treat their academic performance correctly; For students of Grade A and Grade B, we must first affirm their achievements, but we must master the standards to help them realize their own shortcomings and avoid students' complacency.

3 Conclusion

Although there are many problems in hierarchical teaching, it makes up for the shortage of class teaching system, stimulates students' interest in learning and mobilizes their enthusiasm. As long as teachers seriously study and learn the essence of hierarchical teaching and find corresponding solutions to the problems existing in hierarchical teaching, they can give full play to the advantages of class teaching system and hierarchical teaching, so as to better serve junior high school education in the new period.