Group cooperative learning is of great significance to today's classroom teaching reform. Through study and research, the author finds that group cooperative learning has not achieved ideal results in primary school mathematics teaching practice, or there are still some problems that need further study and improvement in theory and practice. If there are only formal group activities, there is no substantive cooperation; Only listen to or watch a good student's operation or speech, without interaction between students; Students are unfriendly, do not listen, do not share, etc. Some foreign scholars also have some similar problems when studying cooperative learning. For example, several scholars in the Netherlands (see Resources Note) pointed out in their article "Cooperative Learning in Dutch Primary Schools" that their cooperative learning has not achieved the desired results. The important reason is that teachers lack enough cooperative learning training and do not know how to give students more time to manage their cooperative learning. This requires in-depth theoretical analysis and solid practical research in order to make group cooperative learning play its due role.

(A) Group activities attach importance to form, lack of substantive cooperation.

Cooperative learning is not simply to divide students into several groups, not to stay in the superficial form, but also to pay attention to many deep-seated problems in the specific teaching process. The author listened to a group cooperative learning class of "finding the law". During the exercise, the teacher asked the students to do an open exercise in groups: distribute many cards with blank patterns to each group, so that students can use their imagination and draw regular and beautiful patterns. After each student draws a pattern, there is little communication between groups, which basically stays at the level of autonomous learning. Without real discussion and cooperation, the advantages of group cooperation have not been brought into play. The learning results can't fully represent the level of the group. The reason is that junior students have poor self-management ability and have not yet formed the consciousness and ability of cooperative learning. In the process of learning, the teacher did not remind and guide the students in each group to discuss and communicate with each other in time.

(B) students' participation is unbalanced

Through observation, the author found that group cooperative learning does increase the opportunities for students to participate, but good students have more opportunities to participate, which often helps. When students with learning difficulties become listeners, they often get information directly from good students outside the opportunity of independent thinking, resulting in poor students getting less benefits from group cooperation students than classroom teaching. Any teacher who has listened to the open class will find that good students have many opportunities to speak in group activities, and there are many phenomena of reporting on their behalf. There are many reasons for this phenomenon, for example, teachers are under great pressure to attend open classes, afraid of affecting teaching effect or delaying time, and dare not let students with difficulties talk too much; Teachers only pay attention to the ideas of each group and don't care about the learning situation of individual members, thinking that good students can represent their groups; Teachers' guidance and supervision of the group is not enough, and the division of labor among the group members is not clear. In addition, in most of the cooperative learning classes I have heard, there is a phenomenon that it is easier to let things drift in group activities, which is more serious than the class teaching system. The students in the classroom are all facing the podium, so it is easy for the teacher to find out whether the students are listening carefully. In group study, students sit around the table, and it is not easy for teachers to find that students are absent-minded, which is caused by objective reasons. The main reason for this phenomenon is that teachers only pay attention to the learning results of groups, but not to the learning process and individual learning. Part of the reason is that the group leader did not manage the group activities well, and the students who deserted lacked personal responsibility.

(C) the relationship between students is not harmonious

In the process of group cooperative learning, students should form a good mutual assistance and interaction relationship. However, in group activities, there are often unfriendly, non-listening and non-sharing problems, which will affect the smooth development of cooperative learning. A teacher had a group cooperative learning class on "Statistics". The teacher distributed flowers of various colors to the students, and asked the students to work in pairs, put out pictograms and count the number of each flower. Some students took all the cards and refused to let another student show them. Another student argued that "the teacher asked us to show together" and then operated together. At present, most students are only children, and some are selfish and independent, which has caused the above problems.

(D) Did not complete the teaching objectives well.

Teachers' understanding and design of the arrangement intention of key contents in textbooks is a very important factor affecting cooperative learning. In order to achieve the teaching goal, teachers should carefully study the teaching materials, make clear what the key content is, what teaching purpose to achieve, and how to design the teaching content to complete the task. The author has listened to a class "Understanding Numbers within 100". According to the arrangement intention of the teaching materials, we should count 100, 10 and 10 bundles one by one. Students should communicate more in the process of cooperation, saying that 10 is ten and 10 is one hundred, and understand why 10 should be tied into a bundle. Let students perceive the size of 100 in the process of cooperation and communication, understand the order of numbers in 100, and count the numbers in 100; The basis of understanding counting is the decimal counting method, knowing that 10 is ten and 10 is one hundred. However, when the teacher was teaching, after the students counted 100 sticks in groups of six, there was no communication among the members, and then the representatives of each group were asked to report how many sticks they counted and how they counted them. Students spend a lot of time reporting themselves as 1, 2, 2, 5, 5 ... Then the teacher found that time was not enough, so he hurriedly ended cooperative learning and entered the next teaching session. In fact, this is because the teacher did not fully understand the arrangement intention and key points of the textbook, did not design well how to make students understand what they have learned through cooperative learning, and did not explain clearly to the students what the requirements and purposes of cooperation are. Students don't know the decimal counting method. 10 is ten, and 10 is one hundred.

(5) Pay attention to and reward the whole rather than the individual.

When we study group cooperative learning, we think that group cooperative learning is based on the performance of the group, which is undoubtedly correct. However, this may lead to a misunderstanding among teachers who implement group cooperative learning: teachers often put too much evaluation and reward on the whole group in teaching, thus ignoring individual development. The author found that this problem is common in observation. Of course, researchers know that group cooperative learning is just a form, which serves the all-round development of students' personality. The question is: How do teachers deal with the relationship between group cooperation and individual development?

(6) Too many classes are not conducive to group activities.

Most of the cooperative learning classes I have heard are in groups of 6 people, with 6-8 groups in each class. Due to the limitation of conditions (the group occupies more space than the non-group), in some cases, a small number of students did not come to class. As we all know, there are a large number of classes in schools in China. According to the author's investigation in school for many years, there are generally about 50 students, many of whom even reach 70 or 80, which brings certain difficulties to group cooperative learning. Generally speaking, the class size is less than 50 people, which makes it easier to manage in groups. There are too many people to manage in groups. In addition, most schools fix classrooms according to classes, which brings a lot of inconvenience to group cooperative learning, because many classes do not need group cooperative learning, and it is unrealistic to rearrange the desks and chairs of a class during a few minutes of recess.

Third, strategies to solve the above problems

For most primary school mathematics teachers, group cooperative learning is a new thing, and it is normal for some problems to appear in the teaching practice of group cooperative learning. The crux of the problem is that we should study how to overcome these obstacles through theoretical study and teaching research, so that group cooperative learning can play its due role.

(A) teachers should update their educational concepts.

Curriculum standards put forward some basic ideas: the basic starting point of mathematics curriculum is to promote students' all-round, sustained and harmonious development; Everyone can get the necessary mathematics, and different people get different development in mathematics; Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics; Students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning; Evaluation not only pays attention to the results of learning, but also pays attention to the learning process, helping students build confidence. From the above discussion, it can be found that the curriculum standard advocates: not only to let every student acquire the most basic mathematical knowledge, but also to recognize and respect the individual differences of students; Great changes have taken place in the way students learn mathematics, from teachers' lectures to students' own learning; Students' dominant position in learning has really been established, and teachers' roles and functions have changed greatly. Great changes have taken place in the methods, means and contents of evaluation. The author recently found in the experimental area of textbook reform that some teachers' ideas have not changed. Where new teaching methods and learning methods should be used in group cooperative learning, traditional methods and means are still used for teaching. After a class, teachers lead students, which does not reflect the new ideas of students' subjectivity, inquiry learning and algorithm diversification. Group cooperative learning is just a form. The reform of mathematics education is a whole, and the form of teaching organization is a part of it. Only when teachers seriously study the ideas put forward by curriculum standards and change their own educational concepts can they do well in group cooperative learning.

(2) Handle the relationship between autonomous learning and cooperative learning.

As mentioned above, cooperation is becoming more and more important in the increasingly fierce market competition; But cooperation can only be carried out on the basis of personal ability. For example, a computer expert cannot be willing to cooperate with several ordinary high school graduates to develop software, but must cooperate with people who engage in computers to develop software. The author means that the cooperation between students and adults is different. Adults have completed the task of going to school to lay the foundation. The main purpose of their cooperation is to solve various problems in their work with their existing knowledge, no matter how they develop. The main task of students is to learn the existing knowledge and experience of human beings. One of the main purposes of student cooperation is to promote everyone's development, cultivate innovative spirit, practical ability and problem-solving ability, and develop emotional attitudes and values in the process of solving problems. Then we can talk about the cultivation of cooperative consciousness and ability. Only when students have such personality can they lay a foundation for working independently or cooperating with others. These personalities have many independent components, so we should deal with the relationship between autonomous learning and cooperative learning. Before cooperative learning, let students think independently. After each student has a preliminary idea, they can explore and communicate together and solve problems together. This provides opportunities for students who don't like thinking or have certain difficulties in learning, which is helpful to improve their study. The relationship between group cooperative learning and traditional teaching forms is not a substitute relationship, but a complementary relationship; Teachers should have a scientific attitude in the research and experiment of group cooperative learning, and don't go from one extreme to the other without mentioning the traditional teaching form. Too much unprincipled cooperative learning may also limit the space for students to think independently, which is also unfavorable to the development of students' personal ability.

Teachers should not only examine the achievements of each group, but also pay attention to the development of each member of the group. They can use some irregular quizzes to check each student's study. Each member has his own advantages. Giving full play to everyone's wisdom and making everyone enjoy it is far more beneficial than a so-called good student's "concentrated discussion". The group leader should be responsible for managing each member well, and make independent and selfish students show positive personality characteristics such as cooperation and mutual assistance through cooperative learning.

(C) handle the relationship between form and goal.

From the form of group cooperative learning alone, its significance has been discussed before; But we should not only pay attention to the form, but also deal with the relationship between the form and the goal. Any form of teaching organization serves the teaching goal, and the all-round development of students should be realized through various forms of teaching organization. The starting point and destination of all teachers' teaching behaviors are for the all-round development of students' personality. Group cooperative learning can not only make students master knowledge and skills, but also cultivate students' inquiry ability, healthy psychology, good emotional attitude and values. Good students can't report and communicate on behalf of the group alone, or each group leader becomes a small teacher. It is necessary to cultivate group members to establish an equal, democratic and mutually beneficial relationship, establish a sense of responsibility for group learning tasks and individual learning, and ensure that group cooperative learning does not let itself drift and stays on the surface.

(D) the cultivation of teachers' cooperative learning teaching skills

Teachers should not only have a correct understanding of group cooperative learning in theory, but also strengthen the cultivation of cooperative skills. Teachers' cooperative learning skills at least include the following aspects.

1. Group cooperative learning. Teachers should carefully study and design the grouping of the whole class, preferably according to heterogeneous grouping, that is to say, the organizational ability, learning ability, academic performance, thinking activity and gender of members in each group should be balanced. To determine the division of labor of each member, a rotation system can be adopted, such as group leader, recorder, librarian, rapporteur, etc. The team leader is responsible for the organization and management, the recorder is responsible for recording the cooperation process, the documenter is responsible for collecting the learning materials, and the rapporteur is responsible for writing the learning report and reporting the learning results on behalf of the group.

2. Instructional design of cooperative learning. When preparing lessons, teachers should study the teaching materials in depth and make clear what new ideas should be reflected. The content of cooperative learning should be difficult, worth exploring and discussing, and the questions should be open. How much time does each link of a class take, what content needs cooperative learning, how much time is cooperative learning, and so on. For example, in the process of data collection and collation, the process of data collection and collation generally requires cooperation, and simple questions can make students think independently.

3. Classroom implementation of cooperative learning. For primary school students, especially junior students, their knowledge, ability and awareness of cooperative learning are limited, so it is difficult to carry out effective cooperative learning. However, we can't give up the application of group cooperative learning in lower grade teaching, which requires teachers to train students step by step. In primary school mathematics teaching, cooperative learning is rarely fully used, and most of the teaching should combine the class teaching system with group cooperative learning and use it flexibly. Every class should be taught according to the teaching design before class, and group cooperative learning should be carried out when necessary. In the process of group activities, teachers should strengthen the supervision and guidance of each group, pay special attention to the performance of students with learning difficulties in the activities and give them more opportunities to speak.

4. After-class summary of cooperative learning. It is very necessary for teachers to follow up after class, get feedback information, reflect on achievements and shortcomings, and make a comprehensive evaluation of learning, which is conducive to improving teaching. Teachers can collect information through classroom observation, correcting homework and talking with students. And reflect on the lessons of success and deficiency, and then give specific guidance for the performance of each group, such as learning ability, emotional attitude and students' cooperation ability. Then each group will reflect, which will gradually form a virtuous circle of group cooperative learning.

(E) the cultivation of students' cooperative learning ability

Learning to cooperate with others is the basic quality of every citizen in modern society. Due to the influence of the traditional class teaching system, students can't fully adapt to group cooperative learning, lack the skills to communicate with others and maintain interpersonal relationships, and have a weak sense of personal responsibility; Most students just express their ideas and lack the awareness and skills to discuss and communicate in groups. Students' cooperative skills can be divided into learning skills and social skills, including at least the following points.

1. Learn to collect information. Generally speaking, the topic of cooperative learning is more difficult, and sometimes it is necessary to collect some information. Now is the information society, and it is very important to cultivate students' awareness and ability to collect useful parts from a large amount of information, which is very helpful for study and work.

2. express your opinions. Language expression is the basis of interpersonal communication and interaction, and it is also an important symbol of personal communication ability. Cooperative learning requires each member to clearly express his own ideas and understand each other's views, on this basis, we can explore problems in cooperation.

3. discuss the problem. Discussion is the key to cooperative problem solving. After each member has expressed his ideas, some people may have solved the problem, or no one may have completely solved the problem. We need to discuss, overcome difficulties and form a solution.

4. Understand the importance of cooperation. Because of personality differences, some students who study well are unwilling to cooperate in learning and think they have the ability to solve problems; There are also some students who are unwilling to associate with others. Teachers should make students understand a truth: a person's ability is limited, and both study and work need cooperation to achieve more things.

5. Establish a relationship of mutual trust, unity and mutual assistance. Only by establishing a relationship of mutual trust, solidarity and mutual assistance can members treat each other honestly, share weal and woe, regardless of personal interests, and work hard for the same goal, which is also conducive to cultivating good ideological quality.

6. Personal responsibility. Every member of the group should participate, be responsible for the group's learning tasks and their own learning, so as to motivate themselves to participate in group cooperative learning.

7. Treat disputes amicably. Class is a small society, and there will be some disputes or even contradictions among group members because of study or other things. Members should make it clear that the purpose of the debate is to acquire knowledge and solve problems better, and the goal is the same. When arguing, we should focus on the interests of the group, not people-oriented, and always maintain unity.

8. Thinking about cooperative learning. Teachers should always guide students how to communicate, get along and explore problems in cooperation, so that students can gradually experience many problems that they can't solve, which can be solved through cooperative learning. Cooperative learning can improve everyone's ability, make everyone get along well, and thus have a sense of identity with cooperative learning.

(6) Reduce the number of classes and provide cooperative learning classrooms.

In the course of investigation, the author learned that many schools have reduced the class size when enrolling students in grade one in order to implement the spirit of classroom teaching reform in curriculum standards and facilitate group cooperative learning, but because they are good schools, they still reach more than 60 students in each class. Therefore, when the school enrolls students, it would rather recruit one more class and control the class size within 50 people, which is conducive to group cooperative learning. In addition, schools should break away from convention and allocate classrooms according to the needs of classes rather than classes. Each grade has a fixed classroom for group cooperative learning. Schools should create conditions for group cooperative learning from hardware facilities.