First, pay attention to individual differences and implement scientific discipline stratification.
People's personality, autonomy and creativity are very different, so teachers must pay attention to the individual differences of students, deeply understand the intellectual and non-intellectual factors of each student in the class, scientifically and reasonably classify students, adhere to "life-oriented" teaching, and take care of each student in the classroom. On the basis of comprehensive evaluation, the whole class is divided into three grades: A, B and C. Group A is poor students, Group B is average students and Group C is excellent students. However, the level of students is not static. Teachers should observe students from a dynamic point of view and a developmental perspective, and always pay attention to the development and changes of students. For students who have made progress, it is necessary to adjust the stratification in time to satisfy their self-motivation, which is conducive to their better development.
Second, scientifically set teaching objectives.
Teaching goal is the starting point and destination of teaching and plays a guiding role in the implementation of teaching. Therefore, teachers should set different levels of teaching objectives according to the teaching materials and students' reality. First of all, teachers should carefully study the syllabus and teaching materials, and make clear the key points, difficulties and objectives of this lesson under the overall grasp of the syllabus and teaching materials; Then combined with the actual situation of students, layers of production. A-level students only need to master the basic knowledge in textbooks and learn basic methods; On the basis of mastering basic knowledge, B-level students can use knowledge flexibly and solve practical problems. On the basis of Grade B, students of Grade C are required to cultivate innovative consciousness, form certain mathematical ideas and have good mathematical quality. Let each student have his own "nearest development zone", and through hard work, "jump and pick peaches", motivate himself with success, give full play to the internal drive of knowledge and realize his own small goals. For example, the teaching goal of "the sum of the internal angles of a triangle" can be divided into three levels: layer A, students can say that the sum of the internal angles of a triangle is 180 degrees and can make simple calculations; B-level students are required to understand and master that the sum of the internal angles of the triangle is 180 degrees, and can skillfully apply it; C-level students are required to understand and master the reasoning process in which the sum of the internal angles of the triangle is 180 degrees, so as to cultivate students' ability to find problems from special to general, cultivate students' ability of reverse thinking and use them flexibly. When students of different levels reach the set goals, the underachievers have the confidence to learn, the potential of the average students is tapped, and the ability of the top students is continuously released, and finally the goal of improving the teaching quality in an all-round way is achieved.
Third, optimize teaching links and implement hierarchical teaching.
Respecting students' individual differences, teaching students in accordance with their aptitude and teaching at different levels are the guarantee to promote students' all-round, sustained and harmonious development. The purpose of hierarchical teaching is to make every student develop in different degrees, which requires teachers to do hierarchical teaching in every link of actual teaching, adopt diversified teaching methods and teaching guidance strategies as much as possible, and put forward different learning requirements for students with different degrees and personalities.
1, the teaching content is stratified.
The stratification of teaching content is based on the curriculum standards and grasps the "degree" of teaching materials, which is the teaching content corresponding to the teaching objectives at all levels. The teaching content of each class is under the same circumstances, aiming at A-level students, the teacher provides them with some improved teaching content that is suitable for this class, so as to further explore the depth and breadth of teaching; When the students in Class B have mastered the basic knowledge, teachers can guide the students to use what they have learned to find and solve problems, so as to achieve the purpose of mastering knowledge. For C-level students, on the basis of passing the exam, checking for missing and filling vacancies, focusing on imparting basic knowledge and training basic skills. For example, when teaching the area of a rectangle, students at one level only need to explain to them the origin of the formula for calculating the area of a rectangle and calculate it according to the formula. B-level students can learn the idea of transformation, understand the role of transformation in learning mathematics and master this method. C-level students can be supplemented by examples, and through the analysis and answers of examples, they can cultivate A-level students' understanding of creativity.
2. Stratification of teaching methods
The realization of teaching objectives always depends on certain teaching methods. The popular saying now is that "there is a law to teach, but not to teach, and to teach correctly." In other words, teaching methods should be flexible, and different teaching methods should be suitable for students at different levels. In classroom teaching, "letting go" is the main way for gifted students, and there is "help" in "letting go", which focuses on guiding self-study; Priority should be given to "helping" middle school students and underachievers, and there is "letting go" in "helping", focusing on guiding students to learn. For example, when teaching the characteristics of multiples of 3, let C students explore the law independently, and B students hint appropriately. A students tell him directly that the characteristics of multiples of 3 are that the sum of all digits is multiples of 3. Doing so can not only stimulate the curiosity of class C students, but also maintain the confidence of class A students in learning mathematics and try their best to meet the learning needs of students at different levels.
Hierarchical exercise
Hierarchical practice is one of the important links in hierarchical teaching. Teachers should design exercises at three levels: the first level is basic exercises, mainly the direct application of knowledge, which requires everyone to do, which is conducive to mastering basic knowledge and acquiring necessary basic skills; The second level is variant questions or simple comprehensive questions, which are limited to the level that middle school students can reach; The third level refers to the exploration questions with thinking and openness, so that top students can think and other students can choose and do their best. When practicing in layers, I will clearly tell students what topics everyone must understand and what gifted students should understand, so that students can know what effect they should achieve. The "layered test card" of Mingde project has played a key role in practice. In the process of practice, I ask the students in Class A to complete only the basic exercises, the students in Class B to complete not only the basic exercises, but also the comprehensive exercises, and the students in Class C to complete them. This kind of exercise does not frame all the students together, which increases the thinking, broadens the thinking and mobilizes the learning enthusiasm of all the students, and each student has improved to varying degrees on the original basis. In short, the design of exercises should be carried out in different "proximal development zones" for students of different levels. Underachievers should basically meet the requirements of the syllabus, and top students should strive to improve themselves, meet the learning needs of students at different levels, and let them learn and have fun.
4, layered operation
Math homework is a daily job. Homework is a little more difficult, and it is difficult for students with learning difficulties to complete it, which leads to frequent delays in homework and easy loss of learning confidence; However, the topic is too difficult. For top students, it takes little time and energy, and the value of homework is not great. Therefore. You can use the method of hierarchical assignment. The principle of "two works and three layers" should be followed in specific design exercises. "Doing two things" means that the exercise is divided into two parts: mandatory and optional. "Three levels" means that teachers should have three levels when dealing with exercises; The first level is the basic practice of directly applying the knowledge learned, which is an essential part for all students; The second level is variant questions or simple comprehensive questions, which are limited to the ability that students in group B can achieve; The third level is comprehensive questions. Can be used as a multiple-choice question. This gives students in Group C the opportunity to choose practice, and students in Group A also have room to give full play to it. Teachers should not only carefully design basic questions, but also design a certain number of exploratory and open exercises. On the basis of completing the basic questions, all students can freely choose to do exploratory and open exercises, and also give extra points to encourage them. In this way, the requirements for them are moderately reduced, the psychological pressure of underachievers is alleviated, and their enthusiasm for doing homework is greatly mobilized.
5. Effective individual counseling.
Individual counseling is an important auxiliary link of hierarchical teaching, and its purpose is to check and fill the gaps, and at the same time, to help students with temporary difficulties. Therefore, I start with correcting the learning attitude of students with learning difficulties, clarifying their learning objectives and cultivating their hobbies, patiently guiding them to finish their homework within their ability, realizing the joy of success after hard work, gradually restoring their self-confidence, gradually overcoming the image of "loser" in the subconscious with "I can do it", stimulating their learning enthusiasm, cultivating good will quality, gradually overcoming the difficulties encountered in the learning process, and gradually forming a sense of learning, so that students can learn to learn. For the guidance of secondary school students, I pay attention to inspiring their thinking activities, using what they have learned flexibly and gradually improving their self-study ability; For top students, I pay attention to cultivating their independent thinking ability and the ability to integrate and apply knowledge, cultivating their good habits, cultivating their hands-on operation ability and enriching their thinking, imagination and creativity. In the form of counseling, I insist on "four combinations": first, the combination of collective and individual, collective counseling for common problems, and individual guidance for individual problems. The second is the combination of explanation and self-study. On the basis of clarifying the key points of knowledge, teachers encourage students to study around difficult problems, find relevant knowledge, and inspire students to learn by themselves, think independently and solve problems by themselves. Third, the combination of in-class and out-of-class can solve the problems existing in students' study in class. For example, the problems that can't be solved in class can be arranged to make up after class, or the second class can be extended and supplemented appropriately to broaden their knowledge horizons. Fourth, the combination of school and off-campus, teachers and parents reach a consensus, cooperate with each other and jointly implement teaching requirements.
Fourth, pay attention to different students and implement multiple evaluations.
"The Standard" points out: "The main purpose of evaluation is to fully understand students' mathematics learning process, motivate students' learning and improve teachers' teaching; An evaluation system with multiple evaluation objectives and methods should be established. The evaluation of mathematics learning should pay attention to the results of students' learning, but also to the process of students' learning. "The development of primary school students' learning behavior depends largely on the teacher's evaluation. If we use the same scale to evaluate students with different learning abilities, it will not only stifle the learning enthusiasm of students with learning difficulties, but also affect the learning enthusiasm of top students. Therefore, teachers should accurately according to the actual situation of students, respect the differences of students, make targeted evaluation, better promote outstanding students to strive for perfection, protect the self-esteem of students with temporary learning difficulties, improve their learning interests and hobbies, and create a strong classroom democratic atmosphere. Hierarchical evaluation is particularly important. We should adopt different evaluation standards for students at different levels, praise and evaluate students with temporary learning difficulties, find their bright spots, affirm their little progress in time, and mobilize their learning enthusiasm. The use of incentive evaluation for middle school students not only reveals the shortcomings, but also points out the direction of efforts, prompting them to be positive, adopting competitive evaluation for top students, insisting on high standards and strict requirements, and prompting them to be more rigorous, modest and constantly surpass themselves. In teaching, I generally adopt the following hierarchical evaluation methods:
1, classroom observation language evaluation. When students answer questions, explore exchanges and practice, they should give appropriate oral evaluation to their performance, so as to achieve the purpose of encouraging, strengthening, or guiding and correcting.
2. Regular evaluation of bonus system. Evaluate and add points to the performance of students in the group every day, including: classroom performance, homework and so on. Five-pointed stars are awarded in grades according to the accumulated scores in a week, and each grade selects the students with the best performance and the greatest progress this week to become math stars to show encouragement.
3. Evaluation of stage growth records. The learning process of mathematics is also the process of students' growth. Evaluating students' learning is a teaching strategy, a teaching model and a teaching concept. Teachers try to tap the learning potential of students at different levels in teaching, cultivate their learning ability and pay attention to their all-round development; While teaching for all students, we should pay attention to students' personality differences and their current and subsequent development.
Through the evaluation, students with improved grades will be promoted to one level, and students with backward grades will be downgraded to one level. So as to form a sense of competition in the class, so that students at different levels have the possibility of success. But in the process of evaluation, we should attach importance to evaluation.
1, Difference: Hierarchical evaluation uses different standards to measure students at all levels, and more is to examine whether students at all levels have reached the preset goals and development at this level. This differentiated hierarchical evaluation pays more attention to each student scientifically and reasonably, laying a foundation for establishing a harmonious teacher-student relationship of equality, trust, understanding and mutual respect and creating a democratic classroom teaching environment.
2. Timeliness: Hierarchical evaluation is ubiquitous in teaching, and it should be evaluated in time in exploration, discussion and practice. Teachers should enthusiastically affirm every student's little progress, arouse students' enthusiasm, enhance students' self-confidence, and encourage students to achieve their goals, especially those who have made progress.
3. Motivation: Teachers' evaluation should pay attention to the process of students' development, emphasize the comparison between students' past and present, and let students truly experience their own progress through evaluation. Therefore, evaluation should be stimulating, so that students can truly experience their own progress. Competitive evaluation is often used for students with B and C levels. Combining with positive evaluation, rather than blindly affirming and praising, it is the premise for students to enjoy the joy of success, but there is a "degree". Evaluation not only encourages students to succeed, but also cultivates students' courage and perseverance to continue to challenge and guide students to learn correctly. For A-level students, we should give priority to encouraging evaluation, fully mobilize the enthusiasm of learning, encourage them to study hard and not bow to difficulties.
In short, "admit differences, use differences and develop differences" and "let every child develop better". This should be the responsibility of each of our teachers. Hierarchical teaching is an experimental teaching mode based on students' personality differences and actual level, with their "nearest development zone" as the development goal and following the educational law and learning development characteristics. Compared with traditional classroom teaching, the implementation of hierarchical teaching in mathematics teaching is more conducive to the improvement of students' comprehensive quality, the publicity of students' individual ability, the display of excellent students' comprehensive ability and the extension of low-level students' potential ability, so as to implement quality education in mathematics teaching.