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How to implement hierarchical teaching in mathematics teaching and teach students in accordance with their aptitude
Quality education faces all students and promotes the all-round development of students' quality in all aspects. No matter from the theoretical level or from the perspective of teaching practice, I deeply feel that students are independent personalities and there are individual differences among students. This difference not only includes basic skills, learning methods, study habits, interests, hobbies, will, morality, etc., but also includes adaptability to teachers' teaching means and methods. It is precisely because of these differences, mainly manifested in the differences in students' academic performance, that the so-called outstanding students, ordinary students and students with learning difficulties have emerged. By analyzing the traditional teaching methods, teachers often use the same methods and rulers to measure and demand students in a class with dozens of students, while teachers' teaching requirements are often aimed at middle-level students, which makes excellent students feel dissatisfied with their lack of new ideas, and students with learning difficulties cannot digest them, resulting in a mountain of problems. Therefore, only by following the principle of teaching students in accordance with their aptitude and aiming at the different situations of students can we truly face all students and let them develop. In recent years, I have tried to teach Chinese at different levels and achieved good results.

First, the theoretical basis of hierarchical teaching.

The so-called hierarchical teaching is to carry out teaching activities at different levels under the guidance of advanced teaching ideas according to students' different learning levels and abilities, and give corresponding learning methods guidance according to the needs of students at different stages of development, so as to achieve the teaching goal of all students' all-round development. The practice of chemistry teaching has proved that many teaching methods have obvious effects on a certain aspect or level, and the effectiveness of these teaching methods only partially involves solving teaching problems. Therefore, teaching methods need to be integrated and optimized, rather than the situation that "one method can take over the world". . Teaching by learning means taking learning as the foundation, taking scientific and efficient learning methods as the fundamental basis for determining teaching methods, facing every student and every aspect of students, so that students can learn lively, actively and harmoniously.

2. Advantages and feasibility of hierarchical teaching.

(1) Advantages of hierarchical teaching.

Hierarchical teaching means that teachers fully consider the differences between students and strengthen the learning guidance for different types of students, so that each student can get the best development. Hierarchical teaching is committed to promoting the maximum development of the whole class in terms of teaching objectives; In the form of teaching organization, classes, groups and individual teaching forms are used alternately; As far as the teaching effect is concerned, students at all levels are expected to have a successful experience. Hierarchical teaching fully embodies the teaching characteristics of omni-directional, hierarchical sub-optimization, teaching students in accordance with their aptitude and subject participation, which is very effective in stimulating students' interest, prompting students to acquire knowledge actively and improving their academic performance on a large scale. Hierarchical teaching can mobilize students' learning enthusiasm at multiple levels, enhance their competitive ability, dilute the form, pay attention to reality, and have the functions of keeping a sharp edge, promoting the middle school and making up for the poor students.

(2) Hierarchical teaching and feasibility.

Middle school students have objective differences in physical development and psychological characteristics, especially in psychological intelligence, interests, hobbies and other factors. According to different people, different teaching objectives, different teaching requirements, different teaching contents and different teaching methods are formulated to maximize the enthusiasm of each student and fully promote the intellectual development of students. This teaching method can better break through the difficulties of the class teaching system, take care of the limitations of students' individual differences, and implement teaching in accordance with their aptitude.

Third, according to the actual situation, it varies from person to person and is reasonably stratified.

The first problem in implementing hierarchical teaching is to carry out hierarchical teaching correctly and reasonably. According to the students' reality, I divide the students into three grades: A, B and C. Group A students are also called excellent students. They are quick-thinking and receptive, and they can't meet the demand for knowledge with conventional teaching methods, teaching processes and teaching contents. Group B students are middle school students, who can better grasp the requirements of curriculum standards and better use what they have learned to solve practical problems in life. Group C students are students with learning difficulties. Influenced by various objective factors, they feel more difficult and stressed about learning activities. Considering the protection of students' self-esteem and the mobilization of their enthusiasm, on the one hand, I actively strive for the support of parents, so that parents can understand, understand and support the activities carried out by the school through home visits, parents' schools and other opportunities. On the other hand, I let students analyze their own learning and ideological status, choose corresponding groups according to their own reality, and I will put forward reference opinions according to the individual characteristics of students.

Fourth, the use of teaching to implement hierarchical guidance.

Classroom is the main position to implement quality education, and the main way to implement hierarchical guidance is to conduct hierarchical guidance in classroom teaching. In the teaching process, how to make good use of this teaching method to achieve the best overall effect? Through several years of teaching practice, I think it should be carried out in six basic teaching links, such as "preparing lessons, attending lectures, asking questions, practicing design, correcting homework and evaluating", which has systematic teaching ideas and all-round teaching vision. (A) "preparing lessons", we should seriously consider the layered target teaching method.

Preparing lessons is the first step in the application of hierarchical target teaching method. In this link, teachers should focus on two things:

1. Students should be dynamically stratified according to their differences. Due to various reasons, students' differences in learning mathematics generally show three levels: good, medium and poor. This objective level difference is not only known to teachers, but also to most students. This kind of tacit knowledge between teachers and students is often difficult to say and unclear because teachers are afraid of hurting the self-esteem and self-confidence of some middle and lower class students. In order to implement the stratified target teaching method, teachers can't avoid this problem, but they should consider students' psychological endurance, announce students' stratification in public, and pay great attention to the methods. For example, you can talk to students alone, guide them to face the differences calmly, and clarify their own positioning level (of course, it is best to let students know about this stratification, and teachers should pay attention to confidentiality); At the same time, let students know that this stratification is relative, dynamic and temporary, and they can enter a higher level as long as they work hard; It is also necessary for students to truly understand that the purpose of teachers' stratification is not self-destruction or bring disgrace to oneself, but to help them choose the "starting line", let go of their ideological burdens and cooperate with teachers to implement the hierarchical target teaching method.

2. According to the stratification of students, textbooks should also be stratified. On the basis of thoroughly understanding the syllabus and teaching materials, teachers should prepare lessons by semester and unit, and prepare lessons scientifically and reasonably. The teaching requirements of each class should be divided into three levels: high, medium and low, that is, set a higher-level learning goal for students who study well, a middle-level learning goal for students who study moderately, and a lower-level learning goal for students who study poorly. While designing suitable teaching objectives for students at all levels, teachers should also carefully consider how to ask questions and perform in class.

(B) "class", we should consciously use the layered target teaching method.

Classroom is the key link in the application of hierarchical target teaching method, and teachers should mainly do two things:

1. Make clear the teaching objectives at different levels in time and encourage students to strive to meet the standards. Although every student knows his current level in a relatively confidential situation, he often doesn't know how to find his own learning position when it comes to each class. Therefore, teachers should generally show students the teaching objectives at all levels at the beginning of each class (in order to maintain students' self-esteem and self-confidence, students should not be directly divided into three levels: good, medium and poor, but should be called three levels: A, B and C). Because every student's learning goals are clear,

2. Grasp the teaching requirements at different levels, and strive for everyone to learn something. The main psychological characteristics of junior students are: first, they love to express themselves; The second is to listen to praise. In classroom teaching, teachers should always check students' learning level in the form of classroom questioning and blackboard writing exercises, and adopt the method of asking questions from different people and at different levels. For example, let some students with poor learning level answer more questions about memory and do more difficult questions; Let some middle-level students answer more questions that need serious consideration and do more ladder-type questions with moderate difficulty; Let some students with better learning level answer more questions about intelligence application and do more difficult comprehensive questions; Teachers should give timely encouragement to students who get the right answers, especially those with poor grades, so that every student has a chance to express himself and get praise as much as possible, so that students with poor grades can feel the joy of successfully learning mathematics, students with good grades can feel the pressure, students with good grades can be neither arrogant nor impetuous, and students with poor grades can not be discouraged. (3) Ask questions in layers.

In order to encourage all students to participate in classroom activities and make the classroom full of vitality, according to the goals and specific conditions of students at all levels, some questions with different difficulties and gradients are designed to meet the different needs of students at different levels. For example, all students are required to master basic questions that reflect the basic requirements of teaching materials, especially low-level students should answer well; For typical exercises that reflect the general requirements of teaching materials, students with middle and high level, especially middle level, are required to think carefully and answer carefully; For flexible exercises that reflect the higher requirements of textbooks, students with good academic performance are mainly required to think and answer; Of course, students at other levels are also encouraged to do their best. In short, A-level students should answer difficult questions, C-level students should give priority to simple questions, and B-level students should have the opportunity to answer moderate questions. When students have difficulty in answering questions, teachers give appropriate guidance and guidance.

(4) Practice design layering.

2. Exercise design should be aimed at different levels. Designing Chinese exercises does not care about "quantity" but "quality". The exercises compiled by the textbook are forbidden to let students "cook in one pot" at any time. Instead, we should design some exercises with different difficulties and gradients according to the target requirements and specific conditions of students at all levels to meet the different needs of students at different levels. It can be divided into three layers: the topic of the first layer of exercises is to turn the most basic content of the textbook into exploratory questions. The key point is to make it acceptable to C-level students, taking into account the leakage and filling-in of A-level and B-level students and exploratory induction, and at the same time infiltrating all students with the most basic learning methods (in the review class, the first-level exercises are used to comprehensively cover the basic knowledge and basic methods, so that A-level and B-level students can lay a solid foundation, and C-level students can fill-in the gaps). This exercise is generally designed as an objective question, and most students can finish it in a short time, and there are guesses. Secondary learning is a problem to guide students to try, which belongs to the basic exercise of "understanding" and "mastering". When designing, the basic knowledge that should be involved should be transformed into subjective questions according to the content of each class. These exercises are required to embody universality, reflect basic methods, steps, laws and scope of application, and expose the knowledge "blind spots" that students may have in peacetime when necessary. The amount of questions is based on the ability of B-level students to complete. The goal of the third level exercise is to use and variant training. Generally, it is necessary to decide whether to set and set exercises according to the actual situation of students and the content of teaching materials, so as to achieve the degree of flexible use, focus on solving the context of teaching materials and the key to solving problems (for example, why do you think of this method and skill, etc.). ), conduct ability training and explore the regularity of problems; After a month, a semester or even more time to gradually improve, and then gradually increase this topic from easy to difficult, so that students can gradually reach the level of A and B.

(5) classification.

3. Correcting homework should be tailored to suit your needs. When correcting homework, teachers should not only be satisfied with "√" or "×", or give a score, but also give comments. For example, some poor students, some exercises are wrong, but the homework is written neatly, and the accuracy of homework is greatly improved than before. Teachers should write some praise and encouragement comments in their exercise books, and at the same time point out the existing problems objectively and concretely, which I believe will be corrected soon. Let them feel the teacher's care and love for themselves. Second, you can't just be busy with the whole batch of homework. The key is to do a good job in correcting records and carefully find problems. Teachers' homework correction records mainly include good examples, wrong examples, special ideas, specific names and so on. Finding problems mainly means that teachers should find some universal, typical and tendentious problems at all levels or among students through the materials and materials collected from homework correction records, so as to prepare for "the right medicine" and do a good job evaluation.

(six) assessment and evaluation of layered incentives

Teaching in the traditional sense is not only manifested in the singleness of teaching means, contents and methods, but also in the assessment and evaluation of students. The same standard, the same test paper to evaluate different students. I made a useful attempt in the Chinese subject examination in my class, and gave students a layered examination. In the evaluation process, I divide the evaluation into unit clearance detection and stage detection. According to the teaching objectives of students at all levels. Each question includes four categories: speed-down questions, basic questions, improvement questions and expansion questions: speed-down questions are aimed at students with learning difficulties and only at C-level students; The basic questions are for all students, and all students have to do them; Improve the problem for middle school students, C-level students choose to do it, and A-level and B-level students must do it; The expansion problem is aimed at gifted students, which is selected by B-level students and must be done by A-level students. After the examination, put forward the goal of "consolidating" or "expanding" for the students who meet the standards; For students who fail to meet the standards, through remedial classes and individual counseling, mutual aid groups are established for "corrective help". Allow them to take part in the second interview, so that students can get self-satisfaction as much as possible in the evaluation.

Five, composition and extracurricular reading set hierarchical goals.

For most students, writing a composition is often an annoyance. In the process of writing, I carefully analyze the writing level of each student, and set the requirements of each composition as three levels: A, B and C, so that students can choose freely. For example, for narrative, the language goal can be designed as follows: a narrative should be expressed in words, and there should be some comments and lyricism on the basis of the narrative. B. Make sentences with words and be reasonable and clear. C word into a sentence, no typos. As long as students achieve the selected goals, it is a successful composition, which will be praised and affirmed, and will also encourage those who achieve better goals to improve their goals. In this way, the students found excitement in the composition and strengthened their confidence. I will appropriately adjust the target difficulty at all levels, so that students' composition is always in the process of going up the stairs, and their composition level has been significantly improved. Extracurricular reading and reading notes are effective ways and means to improve students' academic performance, especially their composition performance. However, the poor conditions in rural middle schools and the lack of school books have seriously restricted students' reading and writing. Is this the reason why the composition content of rural students is empty and the level of composition is far from that of county middle schools? In this regard, I use the limited books in the school library, based on the required reading list stipulated by the Ministry of Education, appropriately expand the scope, select some books as extracurricular reading materials for students, and divide the materials into three levels according to the complexity and difficulty of the content: A, B and C. I analyze the students' situation in detail, guide them to choose suitable reading materials, and set three goals for reading notes, such as: A extract, write experiences and feelings after reading. Extract and write your thoughts after reading. C excerpt. Students choose their own goals according to their actual level, because with the foundation of textbook stratification and composition stratification, the implementation of reading stratification will be smoother. In recent years, the average reading volume of the students I have taken is over 2 million words, and the reading notes are over 50,000 words. 90% students can write a good reading experience or feeling after reading on the basis of extracting words, words, sentences and paragraphs, which effectively promotes the improvement of students' writing level.

Six, "extra-curricular activities", also using hierarchical target teaching method.

Students' extracurricular activities are not aimed at the subject of Chinese. As a Chinese teacher, we should be good at guiding students to contact Chinese in extracurricular activities, so that extracurricular activities can serve both Chinese classroom teaching and Chinese classroom teaching. Mainly should pay attention to two points:

(A clear focus of extracurricular activities of students at different levels. For students with good Chinese performance, we should encourage and promote them to form Chinese specialties through extracurricular activities as much as possible; For poor students, especially poor students, their interest and hobbies in Chinese are cultivated mainly through extracurricular activities.

(2) Do a good job in extracurricular activities at different levels. Extracurricular activities are both related to classroom teaching and relatively independent. Extracurricular activities can not be made into a simple continuation and repetition of classroom teaching, so that they can be used to make up lessons and do homework. Extracurricular activities must emphasize that students are the main body and flexibly guide students of different levels to participate in different types of Chinese interest groups. In the high-demand Chinese interest groups, teachers should not only base themselves on textbooks, but also jump out of textbooks to guide students to develop in breadth and depth of Chinese and urge them to form Chinese specialties as soon as possible; In the language interest group with lower requirements, teachers should give more face-to-face counseling to students of middle and lower levels in psychological quality, learning methods, learning habits and common mistakes. By helping them lay a good foundation of Chinese and cultivating their non-intellectual factors, they can mobilize and maintain their interest in learning Chinese. At the same time, teachers should also make proper use of extracurricular activities to guide students to apply what they have learned. For example, in the teaching practice, I put forward three requirements: 1 to collect information through observation, surfing the Internet, running the library and consulting newspapers and periodicals. , and get the specific figures. 2. Interview parents or relevant personnel to understand the past situation. 3. Select and sort out all kinds of data collected by observation and investigation, and make summary records. The above three questions. Students with learning difficulties, average students and excellent students are evaluated respectively. The students are full of interest and enthusiasm, which not only cultivates their practical ability, but also consolidates their knowledge. Let extracurricular activities truly reflect "vividness" and "mobility", which can effectively promote the improvement of the teaching quality of classroom stratification objectives.

Seven, hierarchical implementation of learning guidance.

Hierarchical counseling is an important auxiliary link of hierarchical teaching. Its purpose is to check and fill the gaps, and at the same time, it is necessary to do a good job in helping students with learning difficulties.

Therefore, I start with correcting the learning attitude of students with learning difficulties, clarifying their learning objectives and cultivating their interest in learning, 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 and comprehensive application of knowledge, cultivating their good habits, cultivating their practical ability and enriching their thinking, imagination and creativity. I pay attention to all kinds of students in a positive way, so that students can see great "Excellence" in their exercise books, or get short notes such as "calligrapher" and "little writer", taste their own learning results and feel the joy of success. The joy is beyond words. This encourages every student to study hard and makes them full of hope for learning.

Suhomlinski once said, "If children not only know, but also realize that teachers and collectives notice and appreciate their advantages, then they will make every effort to become better." In the process of implementing hierarchical teaching, I pay attention to let students at different levels get their proper places and develop to different degrees; Every student studies "happily" (pain first, then happiness), thus enhancing the confidence in learning and the courage to overcome difficulties. At the same time, unfixed stratification enhances students' autonomy, cultivates students' creativity and strong sense of competition; It promotes the interaction of teaching, helps to establish a democratic, equal and harmonious relationship between teachers and students, and helps to form a team spirit of mutual learning and joint efforts. At the same time, I also pay attention to guiding students to conduct self-evaluation, so that they can not only see progress, but also find their own shortcomings, strive to foster strengths and avoid weaknesses, so that students can correctly evaluate their own learning situation, enhance their confidence in learning Chinese well, and thus improve their learning efficiency. No pains, no gains, and my sweat was not in vain. After stratified teaching, the Chinese scores of students in our class are at the forefront of the same grade for three consecutive years. In 2005, the town ranked first in the eighth grade Chinese exam. Sun, my student, won the second prize in Suzhou in 2005 and the first prize in the town in 2006.

Eight, summarize some gains and losses in the layered teaching, I have the following experiences:

1, because students are grouped and have different requirements for different students, teaching students in accordance with their aptitude is really implemented.

2. Put forward different requirements for different students, so that each student can gain something in class and give consideration to poor students. Students can understand, listen and do in class, which is a virtuous circle in learning.

3. In the process of grouping, students appear in groups A, B and C, and there are no words such as poor students, which protects students' self-esteem. In addition, in class, some students in group A can understand some contents of group B, and some students in group B can understand some contents of group A, which enhances students' self-confidence.

4. In the process of tutoring, let the students of group A tutor the students of group B, and the students of group B tutor the students of group C, which not only cultivates the students' sense of participation, improves the students' initiative in learning, but also relieves the teachers' responsibility, so that teachers have more time and energy to do other teaching work.

5. Using hierarchical teaching, students can choose their own papers during the exam. Students will not hold their heads up because their exam scores are too low. Many students are willing to choose the last set of questions to show their progress in learning and enhance their initiative in learning.

6. Because the grouping situation will change at any time due to students' grades, students in Group A are unwilling to go to Group B and Group C, while students in Group C and Group B want to be promoted to Group A, thus introducing the competition mechanism into teaching, greatly enhancing students' learning initiative and improving learning effect more quickly.

In today's transition from exam-oriented education to quality education, it is a good method to teach students in accordance with their aptitude, so that all students can get maximum development in different degrees. The sea is wide and the fish jumps, and the sky is high and birds fly. Separate levels, broaden the broader development space, and improve better opportunities for the majority of students. Of course, I also know that there must be some problems in my specific operation process, but I still believe that "hierarchical teaching" is not contrary to quality education. As a headmaster once said metaphorically, "A school is like a big dining hall, and knowledge is like food. Every student' eats' here, but some don't have enough to eat and some don't have enough to eat. Hierarchical teaching is like dividing the food in this canteen into several layers, so that students can get their own places. " As long as the evaluation mechanism of teaching can also develop synchronously, I believe the front must be sunny!