Confucius, a great educator in ancient times, advocated "teaching students in accordance with their aptitude". The essence of "teaching students in accordance with their aptitude" is consistent with the "hierarchical teaching" we are going to talk about now. The differences among junior middle school students in mathematics foundation, learning ability, learning attitude, physical development and psychological characteristics are objective. There are many students in one class. If the teaching method of "the same model" is adopted in teaching, and the teaching is carried out at the level of middle school students, in the long run, the top students will inevitably "have insufficient food" and the underachievers will inevitably "have no food", and the top students will lose their interest in learning and the underachievers will lose their confidence in learning, which will seriously hinder the development of each student. It also seriously affects the overall quality of education and teaching, which obviously runs counter to the concept of the new curriculum standard: "Mathematics should be geared to all students, so that everyone can learn valuable mathematics, so that everyone can get the necessary mathematics, so that different people can get different development in mathematics." Therefore, teachers must update their ideas, and the teaching should be geared to all students, proceed from reality, teach students in accordance with their aptitude, step by step, fully stimulate students' enthusiasm for learning, give play to students' personal creativity and stimulate innovative thinking, so that students at different levels can learn things at the original level, gradually improve and finally achieve the expected teaching effect.

First, the principle of hierarchical teaching implementation

1. Horizontal similarity principle. Students with similar learning conditions should be classified as "the same layer" when stratified.

2. Difference fuzzy principle. Stratification is dynamic. Progress can be "upgraded" and retrogression should be "upgraded", and the stratification results should not be published.

3. Feel the principle of success. When making teaching objectives, methods, exercises and homework at all levels, students should jump first before they can pick apples and feel the joy of success in stratification.

4. The principle of zero integration and zero separation. The combination and division of teaching content, students' "freedom" and "support" and hierarchical counseling after class should follow this principle.

5. Regulation principle. Because students at all levels have different requirements, they should focus on learning and discussion in class. Teachers should be good at stimulating interest, guiding, stressing and inducing, regulating students' learning at all levels, and giving classified guidance.

6. Positive incentive principle. The evaluation of students at all levels is mainly vertical. Through observation, feedback, timely praise and encouragement, teachers will promptly transfer students who have made great progress to a higher level, and those who are relatively backward will agree to transfer to another level.

Second, the implementation of hierarchical teaching

1. Graded students. In teaching, according to the differences of students' mathematical foundation, learning ability, learning attitude and academic performance and the requirements of improving learning efficiency, students are divided into three levels: A, B and C according to the ratio of 3:5:2. Grade A is a top student, that is, he can master the content of the text, complete exercises independently, complete the review reference questions and supplementary questions assigned by the teacher, and actively help and answer Grade B and Grade C. Grade B is a student with average grades, that is, he can master the content of the text, complete exercises independently, complete exercises under the inspiration of the teacher, and take the initiative to consult with Grade A students. Grade c is for students with learning difficulties, that is, students who can work in teachers and grade a.

Help master the content of the text, complete the exercises and some simple exercises.

2. Hierarchical teaching objectives. Preparing lessons at different levels is the key to do a good job in hierarchical teaching. Teachers should teach students in accordance with their aptitude, and at the same time, design the whole process of hierarchical teaching according to the actual situation of students at different levels. Determine specific and feasible teaching objectives, and distinguish which belong to the same goal and which belong to hierarchical goals. There are also specific requirements for students at different levels, such as designing some flexible and difficult topics for A-level students, requiring students to deeply understand the basic knowledge, flexibly use knowledge, cultivate students' creativity and innovative spirit, and develop students' personality; It should be a little difficult for students of Grade B to design, which requires them to master basic knowledge skillfully, use basic methods flexibly and develop their understanding and thinking ability. More guidance should be given to C-level students. The design problem can be simpler and the gradient slower. They can master the main knowledge, learn basic methods and cultivate basic abilities.

3. The teaching process is hierarchical. Teaching stratification is the most difficult part in classroom teaching and the most creative part for teachers. In order to encourage all students to participate in classroom activities and make the classroom full of vitality, teachers should let students at level A answer difficult questions, give students at level C preferential treatment for simple questions, and give students at level B the opportunity to answer appropriate questions, so that students at all levels can equally participate in classroom activities and make the classroom active. When students have difficulty in answering questions, the teacher will give appropriate guidance. For students of Grade B and Grade C, we should deeply understand their problems and difficulties, help them solve difficult problems, stimulate their active learning spirit and maintain their strong thirst for knowledge. For A-level students, we should pay attention to inspire students to think and explore, understand basic knowledge and methods, sum up general laws and conclusions, and then guide students to change questions and help them explore variants. For A-level students, "release" is the main thing, and "help" is included in "release".

4. Class practice stratification. Hierarchical practice is the core link of hierarchical teaching, and its significance lies in strengthening students' academic achievements at all levels, timely feedback and correction, detecting the achievement of learning goals, transforming the knowledge they understand into skills through hierarchical practice, feeding back teaching information, and compensating, evaluating and developing students at all levels.

Training, to achieve the purpose of layer by layer implementation. Therefore, when preparing lessons, teachers should carefully design and arrange classroom exercises according to the actual situation of students and the content of textbooks, or reorganize the exercises in textbooks or re-select exercises at different levels. When choosing three different levels of exercises, we must follow the principle of consistent basic requirements and encouraging individual development.

South work stratification. Homework can feed back the knowledge of students at different levels in time, reflect the teaching effect of a class, and achieve the purpose of consolidating knowledge initially. Therefore, homework should be designed at different levels. For students at different levels, homework with different questions and difficulties should be designed for students at different levels to choose from, and the questions should be gradually changed from easy to difficult. Group c does basic homework; Group b is based on basics, with a small number of slightly improved questions; Group A does basic homework and has some flexible and comprehensive topics. Make the amount and difficulty of homework so that every student can "jump up and pick apples". So as to arouse the learning enthusiasm of students at all levels.

6. Test layering. Testing is to test a student's understanding and mastery of knowledge. We can't measure every student with the same requirements and standards. In the compilation of test questions, according to the teaching objectives, we can divide the test questions into basic questions and hierarchical questions, in which the basic questions account for 80 points and the hierarchical questions each have 20 points, which can complete the test questions at the same level or higher. If you complete the higher level test, the score in this part will double.

In short, although there are some shortcomings in the implementation of hierarchical teaching, it cannot be denied that hierarchical teaching can face all students, make different students develop differently, truly realize the concept of new curriculum reform, and achieve the teaching purpose of teaching students in accordance with their aptitude. How to make this teaching method play a better role needs our continuous research and exploration in the future teaching practice.