Faced with the traditional education of "a thousand people have one side", people have raised various questions and gradually realized that people are the core and essence of education. Education is not only "preaching, teaching and dispelling doubts", but also the starting point and destination of education. The voice of people-oriented education is getting stronger and stronger. This kind of questioning has prompted the educational model and system to change constantly.

Starting from the basic concept of "face up to differences, admit differences and let every student develop",

Starting from 1997, we tried to carry out hierarchical teaching of mathematics in real estate price evaluation specialty. Through several years' exploration and practice, a hierarchical teaching mode of "treating differently, step by step, and realizing the development of individual advantages as the teaching goal" has been formed, and efforts have been made to find a way to steadily improve the teaching quality.

First, the background analysis of the implementation of hierarchical teaching

(A) Theoretical background

1. Background of hierarchical teaching

Hierarchical teaching is an ancient teaching topic. /kloc-in the middle of the 0/7th century, the Czech educator Comenius expounded the "class teaching system" in On Great Teaching. Since then, the class teaching system has replaced the individualized teaching with a long history. The slogan of "teaching all knowledge to all people" expands the scope of education knowledge and puts forward the ideal of popularization of education. Education began to move from nobility to commoners. Obviously, it is the product of capitalist mode of production-a teacher can teach dozens of students at the same time, randomly arrange classes according to age and teach at the same time. Teachers treat every student equally, and students study the same subject equally, and then accept unified evaluation with the same exam, so as to identify students with good and poor grades.

Every coin has its two sides. Classroom teaching will inevitably pay attention to one thing and lose another, and caring about sex can't care about personality. People are the most different creatures, and there will not be two or more identical people in the world.

At the end of19th century, some people began to advocate the organizational form of "grouping teaching according to academic ability and achievement" to correct the disadvantages of the class teaching system. However, in the 1940s, this form of teaching organization was criticized: undemocratic, easy to discriminate against "mentally retarded children" and spoiled "high-energy children". 1957, the Soviet satellite was launched into the sky, and European and American countries realized the danger of backward technology, resulting in a sense of urgency to speed up the training of cutting-edge talents. Therefore, they re-recognized and re-evaluated the "group teaching" in the last century.

China's old saying is right: great events in the world must be combined for a long time and divided for a long time.

2. Teaching students in accordance with their aptitude

Confucius, a great educator, "three thousand disciples and seventy-two sages". Why not "Three Thousand Sages"? Personality differences make this so. Confucius said: "Above the middle, it can also be discussed; Under China people, you can't speak orally. " ("The Analects of Confucius"). In Song Dynasty, Zhu summarized Confucius' educational thought and experience in this respect as "Confucius teaches people and teaches students in accordance with their aptitude" (Volume 19 of the second suicide note), that is, Confucius gave different education according to the specific conditions of students. For a long time, this teaching principle has been inherited and carried forward and has become a fine tradition of education in China. It is considered that teaching students in accordance with their aptitude is a major teaching principle and a recognized basic requirement that must be followed in the teaching process. Modern pedagogy explains the meaning of teaching students in accordance with their aptitude: under the same training goal, according to the specific situation of the educated's ability, specialty, personality and original foundation, different requirements are put forward and different education is given.

3. The theory of zone of proximal development

Vygotsky, an educational psychologist in the former Soviet Union, put forward a new viewpoint on the relationship between teaching and intellectual development-zone of proximal development. The main idea of "zone of proximal development" refers to the distance between the existing foundation and level of students and the level that students have not yet reached but can reach through the guidance of teachers. When teachers can fully understand the students' recent development zone, and then use the contradiction between the students' current development level and the level of the recent development zone to organize teaching, it can promote the students' rapid and sustainable development and accelerate the development speed.

Student background

With the intensification of social competition, people's pursuit of academic qualifications is increasing day by day, and the high school fever and college fever are heating up, which makes the quality of students in vocational schools decline. Years of enrollment statistics show that students' basic cultural knowledge is uneven on many levels. For example, in 2004, the distribution of mathematics scores of senior one in our school was: 100 or above, 16.3%, 40-99, 42.6%, below 39, and 4 1. 1%. Statistics show that students' mathematical foundation spans a large span, and their interests and needs for mathematics learning are diversified.

(C) the significance of implementing hierarchical teaching research

In the face of students with poor cultural foundation, strong personality and different levels of learning needs, if teachers still implement teaching according to unified standards, it will be difficult to grasp the objectives and requirements of classroom teaching and effectively carry out classroom teaching; If we don't grasp the relationship between students' interests, needs and teaching objectives, we can't mobilize all students' learning enthusiasm well, and some students will easily feel tired of learning, making the classroom difficult to manage. In addition, the unified teaching is not conducive to the further development of students with good foundation, and it is undoubtedly a great blow to students' interest in learning mathematics and physics, which leads to the loss of these students in the mathematics classroom. The implementation of hierarchical teaching mode is an effective way to improve students' interest in learning, improve teaching effect, make all students learn well and promote their success. At the same time, the implementation of hierarchical teaching can encourage teachers to constantly explore teaching methods that adapt to the actual situation of students, thus improving their teaching and research level and teaching ability.

Second, the implementation of the guiding principles of hierarchical teaching

The exploration in the past few years shows that hierarchical teaching has played a certain role in improving students' learning enthusiasm, but it may also bring some disadvantages that affect students' development. For example, the middle class, which has a large number of people, is relatively easy to succeed when the teaching objectives are reduced, and it will produce a sense of satisfaction and slack. Even if I have the ability, I don't want to study at a higher level. However, some students at a lower level can easily lose their self-confidence in learning, because they still can't finish their studies after lowering their teaching objectives. In order to take care of all students as much as possible and make each student develop on his own basis, the hierarchical teaching in our school follows the following guiding principles:

(A) the principle of difference

To study hierarchical teaching, we must first study the differences between students. According to psychological research, we divide students' differences into variable differences and constant differences. Variable difference refers to the differences between students in knowledge reserve, learning strategies, attitudes and skills. These differences are learned and can be changed. Invariant differences refer to the differences between students in personality characteristics, subject specialties, hobbies and so on. Compared with variable differences, it can't be changed in a short time. These differences are the differences of students' advantages. We should make use of these characteristics of students to promote the development of students' individual advantages and make them have expertise in learning. Based on these understandings, we have formulated the principle of "facing up to differences, acknowledging differences, using differences, eliminating differences and developing differences", which provides the direction for the implementation of hierarchical teaching.

(B) the principle of rationality

A correct understanding of "stratification" is the prerequisite for the effectiveness of stratified teaching. The implementation of "shift system" hierarchical teaching depends on how students, teachers and parents treat it. In this regard, in order to establish a correct concept of stratification as the primary content of implementing stratified teaching, they must be made to realize that stratification is for the needs of students' development, rather than grading students. Only in this way can we change the situation that we only pay attention to a few outstanding students or "March in haste" in the past, and teachers can only provide different levels of teaching to promote the general development of students with differences. Getting rid of those unrealistic and useless teaching and teaching students in accordance with their aptitude as much as possible is the real equality in teaching.

Students are developing. When students' basic level and ability level have reached the highest point of their own "nearest development zone", they should be promoted to a new and higher level of "nearest development zone" development; On the contrary, if the negative development is lower than the lowest point of your "nearest development zone", you should go to the "nearest development zone" that is most suitable for your redevelopment. Schools need to provide students with reasonable mobility opportunities, that is, stratification must be dynamic. The basis of stratification is as follows: diversification, not only achievement; Consider students' interest and determination in the subject; Respect students' wishes and choices.

(C) the principle of subjectivity

In the process of education and teaching, we should form a democratic atmosphere conducive to innovation, form a harmonious relationship between teachers and students that is democratic, cooperative and equal, and completely change the disadvantages of the traditional classroom teaching model. Try to provide students with opportunities, time and space for independent thinking and choice. Teachers should be good at inspiring students to ask questions, creating a problem environment, tolerating students' naive or even absurd ideas, making students want to ask, dare to ask and ask questions kindly step by step, making students the masters of learning and making learning a good thing for students. Only by fully implementing the subjectivity of students' learning in all aspects of hierarchical teaching can the effect of hierarchical teaching be qualitatively improved.

(D) Incentive principle

The theory of successful education tells us that every student has the need and potential for success. Hierarchical teaching pays attention to the development of each student's potential, creates various conditions and opportunities for students at different levels to try, explore, discover and develop, and greatly improves students' learning enthusiasm and self-confidence. Including successful incentives, evaluation incentives, etc. The motivation of success is to gain motivation from the existing success, so as to enhance the motivation, enthusiasm and confidence of innovation and actively strive for new success; Evaluation and encouragement means that the starting point and destination of evaluating students is to discover their success and progress. Evaluation should be based on students' individual performance, that is, emphasizing each student's progress on his own original basis, persisting in praise and encouragement, and tolerating students' shortcomings.

Third, the implementation of hierarchical teaching

(A) student stratification

1. Investigation preparation

In 2004, our school selected eight classes of three similar liberal arts majors (property management, international business and real estate management) to try out the "shift system" of mathematics hierarchical teaching.

In order to fully understand the students' situation, collect reliable information and make a reasonable teaching plan, the Mathematics Group conducted a comprehensive survey of 459 students in the pilot class. Students' feedback information is as follows:

Identify with the general

disagree

1. Mathematics is an important subject 39. 1% 25.6% 35.3%

2. Willing to learn mathematics 25.3% 34.5%

40.2%

3. 75.3% 10.4% 14.3% accepted stratified teaching.

From the statistical data, we can see that: on the one hand, students have questioned this traditional basic course. They are already losers in junior high school (even primary school) mathematics learning, and most of them have given up the pursuit of mathematics; On the other hand, although they can't fully accept the study of mathematics, they support the hierarchical teaching of mathematics.

Touch the bottom and layer.

The purpose of organizing the entrance examination of mathematics is to understand the actual mathematics level of students, and the content should not exceed the junior high school syllabus. Considering that students have not reviewed junior high school knowledge after the senior high school entrance examination, they should try to avoid rote learning when making propositions. Fractional distribution:

Score100 ~ 8079 ~ 6059 ~ 4039 ~ 2019 ~ 0

Percentage 8.3% 14.6% 35.2% 23.9%

18.0%

It should have been divided into three grades: A, B and C according to the ratio of 1: 2: 1, but the result was somewhat unexpected. After full discussion, according to the students' possible learning level, it is decided to divide them into four grades-A, b 1, b2, C and eight classes * * * two bundles. The analysis of students' differences in intelligence factors, non-intelligence factors, original knowledge and ability shows that students with good academic performance, strong interest in learning, initiative in learning, quick acceptance or diligence belong to layer A; Those with average acceptance, moderate academic performance or unstable learning mood belong to b 1 layer; Students with poor ability, learning difficulties but still willing to learn belong to b2 layer; Students who have great learning difficulties, are negative and tired of learning, or are naughty and don't learn belong to layer C.

3. Teacher selection

The selection of teachers is based on the principle of suitability and the characteristics of teachers' teaching. Teachers in Class A, Class B/KLOC-0, Class b2 and Class C are selected. It is worth noting that teachers have accumulated rich teaching experience in the original administrative courses, which will inevitably form a teaching mindset. If we organize teaching according to previous teaching experience after stratified teaching, it will not conform to the basic principles that stratified teaching should follow and will inevitably affect the quality of stratified teaching. Therefore, teachers are required to study new teaching objectives and corresponding teaching methods in time to ensure the teaching quality at all levels.

Target stratification

Goal stratification refers to determining the teaching goals suitable for students at all levels, including cognitive goals and intelligent goals stipulated in the syllabus. Considering students' cognitive ability, emotional level and behavior operation comprehensively, the most basic teaching requirements in the syllabus are determined as basic goals, which are suitable for low-level students; All the teaching requirements in the syllabus are determined as hierarchical goals, which are suitable for upper middle school students. The former is a same-sex goal, universal and belongs to basic knowledge and skills; The latter is a selective goal, challenging, and belongs to the application category, with more ability and intelligence. The goal stratification is grasped by teachers and closely linked with students; It can not only meet the basic requirements, but also encourage personal development. The teaching objectives at all levels are as follows:

B 65438 A class +0 class b2 class C class

We should further broaden our horizons, broaden our thinking, reveal the essence, improve our ability and creatively complete the learning task of mathematics textbooks. Lay the foundation for students' lifelong learning;

Be able to master the basic knowledge and skills of mathematics textbooks, have certain independent thinking ability, have certain ability to analyze and solve problems, and strive for a higher level of development;

Take employment and life knowledge as the educational goal, basically master the most basic knowledge of mathematics textbooks, have the most preliminary calculation skills, and basically complete the learning task of classroom teaching;

Starting from their mathematical ability, we don't emphasize that we must learn from the knowledge of middle school, but mainly make up the basic knowledge of mathematics in junior high school so as to have a common sense understanding of mathematics in life and employment.

(C) Teaching stratification

1. Classroom stratification

Class A, Class B/KLOC-0 and Class b2 are the core of hierarchical teaching. The classroom teaching strategies adopted for students at different levels are as follows:

Grade a, grade b 1 grade b2

( 1)

The same content, the same speed reduces the explanation of basic questions, appropriately increases the gradient of ability questions, and reveals the internal relations and laws of knowledge; Focus on basic questions with the same content and speed, increase the difficulty with small gradient, and emphasize the application of basic knowledge and methods;

Select the content to explain the basic questions at the same time and understand the application of basic knowledge and methods.

(2) The classroom focuses on analysis, with clear thinking, supplemented by blackboard writing, which increases the capacity and has strong pertinence;

Pay equal attention to classroom analysis and blackboard writing, encourage students to participate and teach them to examine and solve problems; Classroom analysis is meticulous, writing on the blackboard is detailed, fully mobilizing students' attention, teaching students to understand the meaning of the question and imitating the problem solving.

(3)

Cultivate students' mathematical thinking ability by using "divergence" and "inquiry" teaching methods; Cultivate students' mathematical logic ability by using "inspiration" and "question" teaching methods; Use "emotion" and "appreciation"

Teaching methods to cultivate students' mathematical order.

(4) Classroom training, which cultivates students' learning will and the spirit of daring to compete and struggle, and emphasizes the sense of crisis;

The combination of classroom teaching and practice can cultivate students' ability to analyze and solve problems, encourage more and criticize less, and cultivate students' sense of accomplishment;

Intensive lectures and more practice in class can cultivate students' awareness of concentration in learning, promote their common progress and cultivate their perseverance in learning.

(5)

Cultivate students' deductive ability, pay attention to the summary of knowledge and methods, and cultivate students' mathematical thinking and mathematical thinking; Induction is often used to guide students to sum up knowledge and methods, so that they can understand mathematical thinking and cultivate certain mathematical thinking;

Use imitation method more, do a good job in the study of basic knowledge, so that students' thinking can be initially exercised and their interest in learning can be maintained.

(6)

Pay attention to cultivating students' rigorous and extensive mathematical thinking, and gradually train abstract thinking; Using the method of combining numbers and shapes, it focuses on cultivating students' intuition and visualization of mathematical thinking;

Pay attention to cultivating students' imitation thinking and sustainability, and gradually improve their imagination.

The teaching of Class C focuses on junior high school knowledge, and the classroom adopts a step-by-step practice method. Ask students to "sit down-raise their pens-"

Imitation-thinking ",bit by bit accumulation, not asking for more, just asking for understanding, not giving up learning." "

2. Exercise and homework are layered.

According to the teaching content and students' actual learning ability, teachers select and compile basic consolidation exercises, expansion exercises and comprehensive exercises at different levels. At the same time, teachers' tutoring and correcting homework reflect different ways.

Grade a, b 1 grade

Class b2 class C.

Group A practices to consolidate knowledge, Group B practices to consolidate foundation, and Group B practices to strengthen understanding.

Consolidate the basic group A questions, add basic exercises and some group B questions to learn junior high school knowledge, and lay a solid foundation.

After-school homework should be practiced by comprehensive application of knowledge, with research exercises on one question per week and intensive training moderately increased.

Practice based on consolidating knowledge and focusing on basic knowledge of junior high school.

3. Consultation stratification

The guidance for students at different levels from learning content to learning methods varies from person to person. Class C students should be timely, meticulous and patient; Class B should strengthen inspection and supervision and pay attention to feedback; Check the students in Class A regularly, strengthen extra-curricular counseling and design experiments.

B 65438 A class +0 class b2 class C class

For the students who are relatively weak in learning, the classroom tutor organizes spare students to participate in the tutor's comments on ideas and problem-solving formats, and tries one-on-one tutoring.

Teachers increase practice time, comment on ideas and problem-solving formats, and give guidance one by one to master the time when students can concentrate.

Correcting after class

The teacher corrects all or all, the students approve each other, the teacher corrects all the mistakes, the teacher corrects all the homework or corrects it face to face, and evaluates all the homework in detail.

Teachers are all correcting, and make detailed comments.

(d) evaluation stratification

Evaluation adheres to the principles of difference, timeliness and motivation, and has the functions of summarizing, feeding back, correcting and improving. Hierarchical teaching is an effective means to realize developmental evaluation, and hierarchical evaluation needs to reflect the role of promoting curriculum development, student development, teacher development and school development. Since the purpose of hierarchical teaching is not to classify students, the evaluation system for students should not be keen on ranking and comparing. The specific method is that the teacher makes a growth file for each student, records the students' interests and progress, often analyzes the personal progress track with the students, and pays attention to the evaluation of the process. There are three types of assessments:

(a) process evaluation

Record students' usual classroom behaviors (such as attendance, students' concentration, and lecture quality). From classroom questioning, homework correction, daily quizzes, weekly questioning, etc. You can see the progress of students reaching the standard and give a regular process evaluation in time.

(3) case evaluation

Because students in hierarchical teaching are in the position of relatively equal, and their level of understanding is relatively consistent, it is easy for teachers to grasp the subtle changes within students. Teachers can make a comprehensive survey of all aspects of students through observation, conversation and communication with class teachers, so as to correct the disadvantages of neglecting case evaluation in traditional teaching. Referring to the evaluation of students' learning adaptability put forward by Chiyosuke Chenno, a Japanese education evaluation expert, the case evaluation of each student's non-cognitive factors includes:

1. Learning attitude: including learning desire and learning plan;

2. Learning methods: including reading methods and note-taking methods, memory methods and thinking methods;

3.

Learning environment: family material and psychological environment, school environment, friend relationship;

4. Physical and mental health: independent attitude, perseverance, anxiety, psychological sensitivity and good health.

The term evaluation is completed by teachers, students and study groups, which embodies the principles of equality, understanding and interaction. Proportion of various evaluations in students' whole semester evaluation:

Process evaluation, evaluation and case evaluation of evaluation

30% 50% 20%

(5) other work.

In order to enable teachers to grasp the teaching feedback information in time, adjust the teaching content and progress, and improve teaching methods, we conducted qualitative and quantitative surveys on students at different stages and with different purposes, as follows:

1.

The purpose of pre-stratification survey is to understand the students' situation, grasp their wishes and prepare for stratification and placement;

2.

The purpose of the adaptation period survey is to understand students' adaptability to their own level, so as to make small-scale adjustments;

3.

The purpose of the mid-term survey is to understand students' adaptability, requirements and suggestions to teachers' teaching methods and teaching progress in hierarchical teaching. Knowing that students think there is a lack of competition between classes, teachers at all levels immediately adopt different reward mechanisms to encourage students to participate in intra-level competition and inter-level competition;

4. The purpose of the adjustment period survey is to understand the influence of diversion on students' learning mood, learning attitude and learning goals, so as to provide psychological counseling for students;

5.

The purpose of the later investigation is to have an overall understanding of stratified teaching and lay a foundation for the comprehensive spread of stratified teaching in the future.

Fourth, the harvest of layered teaching.

After adopting "hierarchical teaching", teachers feel that teaching is easier, students learn happily and the teaching effect is obviously improved.

The students have made great progress in their studies.

1.

Willing to learn

At present, the biggest problem encountered by schools in course teaching is that some students are tired of learning, especially in basic cultural courses such as mathematics. We analyze that there are many reasons why these students are tired of learning, one of which is that they lose confidence or even give up because of poor foundation and unacceptable course content. Hierarchical teaching pays full attention to students' personality differences, sets appropriate teaching objectives and selects appropriate teaching content, which ensures that classroom teaching content is accepted by students to the maximum extent, and students feel the joy of success from it, thus enhancing their confidence in learning and starting to try to participate in learning.

Step 2 take part in the competition

Because of the establishment of inter-layer flow mechanism, hierarchical teaching has a competitive atmosphere. This kind of atmosphere is a kind of motivation for those students who want to make progress, which will encourage them to enhance their initiative and enthusiasm in learning; It is also an improvement for those students in the middle and lower reaches. They are consciously or unconsciously exposed to this competitive atmosphere, and their learning effect has also been improved. According to the survey data, 75.7% of the students think that the teacher's teaching content is more targeted after hierarchical teaching, and 45.3% of the students think that their learning effect is much better than before.

(B) Teachers' teaching ability has been greatly improved.

Five, the experience of layered teaching

(A) do a good job of psychological adjustment of students in order to facilitate the development of teaching.

The hierarchical teaching of "walking class system" is different from the hierarchical teaching and implicit teaching of fixed majors, and both teachers and students have a process of psychological adjustment. Perhaps teachers are more adaptable than students in terms of psychological adaptability and understanding level. Therefore, teachers should try to keep the same height as students to understand the influence of this teaching mode on traditional teaching. For example: how to divide classes? What is the basis? How to win the upper position? What if we go down to the next floor? Today's students are brave on the surface, but psychologically fragile. When teachers encounter these problems, they should observe the changes of students' behaviors and facial expressions in time and try their best to solve their psychological obstacles. Usually in class, do more mobilization and psychological counseling.

Such as: how to deal with the problems in shunt?

Divide the students at the critical points of A, b 1, b2 and C into different classes, and then decide whether these students will continue to study at this level or rise or fall. For upward-flowing students, some students are unwilling to enter a higher level of study, which reflects that they have a greater degree of recognition of this level of study, but it also reflects that these students lack self-confidence. Their idea is that it is better to be at the top of Grade B than at the bottom of Grade A, so that they can experience more success and joy. For these students, we agree to stay at the original level to meet their psychological needs on the premise of fully soliciting their own wishes. In fact, this part of the students do not flow, which has not affected the overall principle of hierarchical teaching. For the downward-flowing students, this level of learning is obviously out of touch, so it is necessary and inevitable for them to choose a new level of learning. Teachers must pay full attention to the understanding of students' psychological state of downward diversion. Through observation and conversation, these students are generally depressed and have the phenomenon of giving up on themselves. Their self-confidence reconstruction needs the concern of class teachers and classroom teachers. In fact, after half a semester, the polarization of these students is very serious. For example, Li Tongxue, who applied from Grade A to Grade b 1, found that his study at Grade b 1 could better reflect his own value and his self-confidence was greatly increased. Originally, he never passed Grade A mathematics, but when he reached Grade b 1, he took the initiative to answer every class exercise. On the contrary, a student who studies at b2 level and has a good brain but doesn't study hard enough will give up on himself when he reaches b2 level. Not only did he not study, but he also influenced other students. It can be seen that the mentality of these students is extremely complicated. In the process of education, they should not be designated as the objects eliminated from A, b 1 and b2 grades, but should be given more encouragement and care, so that they can integrate into new groups as soon as possible and regain their confidence.

(B) based on diversity, in order to stabilize the teaching order

Simply dividing teaching into four levels, A, b 1, b2 and C, is far from meeting the actual needs of students, and it is difficult for students' personality to be truly developed. The learning potential of middle school students at the same level varies greatly. It is bound to cause some students' "dissatisfaction" and affect their study. In some cases, some students in Class A want to lower their requirements, want to go to Class b 1, and deliberately go to class to sleep for "retreat"; Some students in Class B strive for Class A to prove their strength, while others want to quit. The students in Class C are carefree and don't make progress ... These problems are largely due to finding out the case and making the final decision. In view of the universality of a situation, we can increase the recommendation of the class teacher and individual voluntary adjustment methods to meet the requirements of students and stabilize the teaching order.

(C) determine the appropriate teaching objectives to meet the actual ability of students.

Teachers at all levels should determine appropriate course objectives, choose appropriate teaching contents and adopt diverse and appropriate teaching methods according to the learning ability of classes and the personality characteristics of different students. Because different students have different cognitive level, understanding ability and understanding degree of mathematics. In terms of how to establish the teaching content of Class C, teachers and students have done a lot of investigation and adjustment, that is, to make up the knowledge of primary school and junior high school. Increase practice classes? Problems such as attending technical secondary school have caused a lot of controversy, and they are still being explored and tried out.

Sixth, the development direction of hierarchical teaching and the places that need to be improved.

(A) improve the quality of teachers

Students generally hope that the mathematics classroom is rich in content and active in atmosphere. Teachers should not only try their best to fully mobilize the enthusiasm of students, but also emphasize the process of re-learning, go deep into students to find and solve problems, and at the same time learn from each other, communicate with each other and evaluate each other, so that teachers' continuing education is more purposeful, planned and targeted.

(B) improve the evaluation system

The evaluation of students should be comprehensive, reflect the principles of democracy and encouragement in teaching, and meet the teaching objectives at all levels. The purpose of grading evaluation is to assess how much students have learned, not how much students can't do. How to obtain reasonable and fair credits by implementing hierarchical teaching needs further discussion.

(C) standardize the corresponding management system

The stratified teaching mode of the shift system puts forward new requirements for teaching management, and the school management system also needs to be standardized and improved accordingly. For example, the differences between shift teaching and traditional administrative classes in teaching management, the cooperation between class teachers in administrative classes and the collaborative management of educational affairs, students and administrative departments need to be further clarified and improved through school systems or regulations.

(4) Promoting stratified teaching in an all-round way.

The experience of hierarchical teaching reform in mathematics has laid a good practical foundation for the comprehensive implementation of hierarchical teaching in grade 05 of this school. Individual differences of students always exist between disciplines. Basic disciplines can learn from and promote hierarchical teaching, and professional disciplines can try out implicit stratification according to students' interests and wishes.

The development direction of the above-mentioned stratified teaching will be further discussed as a new topic, and more effective, scientific and complete experiences and strategies will be formed, which will be popularized and applied.

In fact, the hierarchical teaching mode creates a better environment for students' subjectivity. Students can actively plan and design their own learning according to their own needs, interests and potentials, and can truly teach students in accordance with their aptitude at a deeper level, which requires our educators to devote themselves to in-depth research and discussion.