First, the principles and methods of hierarchical teaching
The application of layered teaching method needs to grasp specific details and norms, including: the principle of similarity; Difference fuzzy principle; The principle of feeling success; Regulating control principle; Positive incentive principle. Among them, similarity principle and difference fuzziness principle are important principles for classifying students, and only students with small differences, similar or equivalent abilities need to implement hierarchical teaching methods; The principles of feeling success, regulation and positive encouragement are important principles of students' basic psychology and feelings. The purpose of hierarchical teaching is to improve students' comprehensive ability and mathematical vision. If some students have contradictions or other negative emotions because of hierarchical teaching, this method should be stopped immediately.
The implementation method of hierarchical teaching should be formulated on the basis of the above principles, and the basic steps can be summarized as follows: to understand each student's learning ability, learning attitude and learning level, and to master the overall learning situation of students; Obtain the consent of students and parents; Students are stratified according to the ratio of 1: 2: 1; When arranging seats, try to conform to the principle of matching top students and underachievers. In this process, teachers should always adhere to the standards of fairness, justice and openness.
Second, the organization and operation process of hierarchical teaching
1. Students are stratified.
Student stratification is the most basic hierarchical organization. After fully understanding the mathematics foundation of the whole class, the teacher divides the students into three levels according to their abilities, foundations, attitudes and grades, and takes the form of top students with underachievers when arranging seats.
2. Stratification of teaching objectives
Mathematics teachers divide the teaching content into three levels after carefully studying the teaching objectives. The basic level is mainly aimed at mastering and applying basic knowledge; Intermediate aims at the application of difficult knowledge; Advanced level aims at the comprehensive application of mathematical knowledge and the solution of difficult problems. In addition, teachers should strictly follow the principle of three levels before each class, so that every student can easily complete the teaching standards of this class. For example, when teachers teach the nature theorem of isosceles triangle "the two bottom angles of isosceles triangle are equal", they can be divided into the following three levels: ① understanding and memorizing the theorem (basic knowledge, suitable for students with weak foundation); ② By studying this theorem, it is concluded that two equal opposite sides are also equal (suitable for students with strong mathematical ability); ③ This theorem can be used for numerical calculation (suitable for students with good mathematical ability).
Preparing lessons by layers is the key to the stratification of teaching objectives. Only when teachers master the mathematical ability of students at different levels in teaching can the method of teaching students in accordance with their aptitude produce higher results.
3. Stratification of teaching process
The teaching process is hierarchical, that is, questions are asked to students at different levels according to different levels of questions. The hierarchical teaching process is the most difficult part. A math teacher often has to teach 2-3 math classes at school. If there are about 40 students in a class, the total number of students in 2-3 classes can reach hundreds. It makes it difficult for teachers to remember the basic situation of each student clearly, or ask a classmate the same level of questions many times. Therefore, it is suggested that mathematics teachers who implement the teaching process stratification can make full preparation for asking questions before teaching, and can also record the outstanding problems of individual students while correcting homework, so that students' mistakes can be effectively corrected in class.
4. Stratification of classroom practice
The ultimate goal of classroom exercises is to deepen students' impression of listening to lectures, consolidate teachers' teaching contents and apply pure mathematics knowledge to specific mathematical problems. The completion of classroom exercises is the direct feedback of students' knowledge mastery, and it is also a portrayal of testing whether teachers have achieved the teaching objectives of the course. So math teachers can arrange exercises at different levels for students at different levels, so that the whole class can meet the basic requirements.
5. Work stratification
Doing homework is a scientific process for students to review what they have learned. On the basis of goal stratification, teaching stratification and practice stratification, students' homework assignments should also be layered. Like the stratification of classroom exercises, homework stratification should also adhere to the principle of combining difficulty with difficulty, so as to achieve a bumper harvest effect of mobilizing students' enthusiasm and improving their grades.
6. Test layering
Design test questions that meet the requirements of students at different levels and grasp the understanding range of students at different levels. According to the basic level, the basic test questions can be 80% and the difficulty test questions can be 20%; Intermediate level basic questions 60%, difficult questions 20%, difficult questions 20%; Advanced basic questions 40%, difficult questions 30%, and difficult questions 30% are arranged in proportion.
7. Assessment stratification
The comprehensive subject evaluation of a student is not only the basic point to promote students' better interest in learning, but also the coordination and guidance of students' learning ability, performance and attitude at a certain stage. Students of different levels should adopt different guiding methods when evaluating. For example, for low-level students, we should grasp the means of encouraging more and blaming less, praising more and criticizing less; Praise should be given priority to middle school students, but at the same time, it can give directions to their outstanding problems; Students with a higher level also need praise, but like students with a medium level, they also need to point out outstanding problems and mistakes. The division of grades is not static, and teachers can make appropriate adjustments according to specific conditions.
The application of hierarchical teaching in junior high school mathematics teaching can not only make students feel the concern and attention of teachers, but also make students actively participate in the exploration and learning of mathematics knowledge. Students constantly experience the joy of success in the learning process, and their physical and mental development is also comprehensively improved under the implementation of teaching methods. The method of teaching students in accordance with their aptitude completely makes up for the previous "equal treatment" education method and greatly improves the comprehensive quality of students. Of course, there are still many problems in the practical operation of hierarchical teaching, such as how teachers prepare lessons in different levels, how to divide the levels of teaching objectives, how to change the traditional habits of unified examinations and so on. These are thorny issues that we need to continue to explore and reform in the future.