INTRODUCTION 1. Rationale Orientation of teaching methodology innovation has been institutionalized in the Education Law: "The method of education to promote self-discipline, positive, proactive, creative thinking of learners; self-learning capacity building, practical ability, passion for learning and will "(Education Law, 2005, chapter 1, article 5). The four pillars of the XXI century education by UNESCO affirmed that: "Learning to know- Learning to do - Learn to affirm yourself - Learn to live." Thus the educational objectives of the educational world clearly show that education not only provides knowledge but also forms learners the skills and attitudes so that they can live and work in the ever-changing society after completing general education programs. Cooperative teaching is one of the active teaching methods in non-traditional teaching trends, It contributes to orientation of teaching methodology in our country. Especially in the current period, when Vietnam officially joined the Program of International Student Assessment (PISA) and Vietnam is implementing new model school projects Vietnam - Global Partnership for Education - Vietnam Escuela Nuevo (VNEN), so teaching develops its strength in meeting the standards for student groups to scale integration capability of the PISA assessment as well as of VNEN requirements. In primary schools in general and mathematics in primary schools in particular, no works have mentioned the application of cooperative learning in a concrete and systematic way. For these reasons, we chose "Applying cooperative teaching in mathematics in primary schools" for the research topic. 2. The objectives and tasks of the thesis Objectives : Study the theory of cooperative teaching to apply in teaching mathematics in primary schools to help improve the effectiveness of teaching. Tasks: Based on the research purpose, the thesis has the following tasks: - To study the theoretical basis of cooperative teaching - Find out the current situations of teaching Mathematics in Primary cooperative teaching. - Propose process to apply cooperative teaching and a number of methods to support the teaching Mathematics in Primary schools - Organize cooperative teaching experiment and assess the results of the experiment 1 3. Subject of the thesis Cooperative process of teaching mathematics in primary schools. 4. Hypothesis From the research of teaching methodology based on cooperative teaching, if the authors propose the process and a number of supporting measures to apply the methods of cooperative teaching in teaching Mathematics in Primary schools, these can help teachers improve their teaching effectiveness. 5. Methodology - The study of theory: Research, analyze, synthesize documents about methods of teaching mathematics in Vietnam and abroad related to the thesis topic. - Investigation - Survey: Investigate the situation of applying collaboration in teaching Mathematics in Primary schools in order to clarify the factual basis of the subject. - Observations: To observe some classes to complement theory and adjust processes and measures to support the cooperation in teaching Mathematics in Primary level. - Pedagogical experiment: Carry out an experiment about cooperative teaching in Mathematics in Primary in order to confirm the feasibility and effectiveness of the dissertation topic. 6. Scope of the research This research is about teaching Mathematics in primary schools in Vietnam. 7. The issues are given in the thesis -Cooperative teaching achieves the dual objectives. They are to achieve the objective of equipping with knowledge, to practice some skills of learning Mathematic and cooperative skills in learning. - Viewpoints of applying cooperative teaching in Mathematics in Primary level are appropriate and can be implemented according to the design process and the supporting measures proposed in the thesis. 8. The new contribution of the thesis - In theory: An overview of a theoretical basis for cooperative teaching; clarify the basis of age psychology and pedagogical psychology of elementary school students from that put forth the proper orientation of applying cooperative teaching in math at primary level 2 -In Practice: Propose organizational processes of cooperative teaching and a number of supporting methods to carry out cooperative teaching in math at primary schools; Organize some cooperative teaching classes in some typical situations based on orientation of teaching methodology innovation in teaching elementary math 9. Structure of the Thesis In addition to the introduction, conclusion, references and appendices, the main contents of the thesis consist of three chapters. Chapter 1: Literature review and practice Chapter 2: Implementing cooperative teaching in Mathematics in Primary schools Chapter 3: Pedagogical experiment 3 CHAPTER 1: LITERATURE REVIEW AND PRACTICE 1.1. History of the study 1.1.1. History of World-wide researches Cooperative learning is the common learning perspective in developing countries with education and its effective education can not be denied. Educational researchers have mentioned this problem in many works. In 1878, two British educators are Ben and Lancanxto conducted teaching as tutors . This mode is called "mentoring system". Contributions to the educational development of Georg Michael Kerschensteiner, the general activities of the group not only arouse a sense of responsibility, a sense of the students but also eliminate selfish motives. The form of organization for students studying liberal group by Roger Cousinet is of great significance. It helps provide students with the ability to get along with the community, have a habit of working without the teacher's control, overcome the status of lazy thinking. John Dewey, the American pragmatic educator, is considered to be the first to initiate the trend of cooperative teaching. John Dewey said that the role of education is to teach people how to live collaboration. Slavin said teaching group significantly improved the students' way of thinking. Elliot Aronson with first class models Jigsaw (1978) marked a milestone in the completion of the forms of cooperation in cooperative teaching. Geoffrey Petty concludes that through cooperative learning groups, they can achieve what they can not do it alone. Wilbert J. Keachie mentions peer learning and collaborative learning. Authors demonstrates that cooperative learning groups is an effective approach of learning. Robyn M.Gillies, Adrian F.Ashman and Jan Telwel highlight the different ways in which teachers can form groups of interaction between the students and encourage students to discuss in groups. The main role of the teacher in the implementation of pedagogical practices and promotion of thinking. 1.1.2. Research situation in Vietnam In terms of theory, recently there have been many research works as well as many articles of interest to collaborative teaching. Cooperative teaching has been mentioned by Nguyen Huu Chau, Nguyen Van Cuong, Tran Ba Hoanh, Nguyen Ba Kim, Lam Quang Thiep, Thai Duy Tuyen The teaching at the primary school level in general and the teaching of Primary School Mathematics in particular are still the problem that no author has studied in detail. Therefore, organizational issues, using cooperative learning in 4 mathematics in primary schools should be concerned in studying a particular way and successfully applied in the context of Vietnam. 1.2. An overview of cooperative teaching 1.2.1. The concept of cooperative teaching Cooperation: According to Vietnamese Dictionary, cooperation is to work together to help each other in a task, which has a common purpose. Group: According to the dictionary, group means that many groups are involved in a joint action. According to Tran Ba Hoanh, "group" is a small collective form to perform a certain task in a certain time. [39] Thus, our concept of the group is a collection of individuals, at least two or more, which are linked together in a joint operation to implement a common goal, among them the existence of the value general and certain rules to be followed. Cooperative teaching group: When analyzing and comparing features of cooperative learning groups and other social groups, we see some differences. The difference is defined by the contents of that group learning activities which are conducted. We think that the cooperative teaching is a constituent unit of collective classes, including a collection of individual students which are linked together in a joint operation to perform the task of general learning, and it is in the process of linking information and integration of relationships, norms and rules of the group. Cooperative teaching is a form of organization: When referring to cooperative learning as an organizational form of teaching, that is viewing it as a way of organizations conduct teaching activities to suit purpose and content of the lesson. This approach was acknowledged by the theoretical teaching such as: Dang Vu Hoat, Nguyen Ngoc Quang Cooperative teaching is a teaching method: Refering to teach cooperative group is a teaching method that is referred to it as a means, a way to achieve the purpose of teaching school. This view is also acknowledged by some theorists such as Thai Duy Tuyen Tran Ba Hoanh, Teaching cooperation is the interference between teaching methods and forms of teaching In the teaching process, the types of work just acts as a method, just act as an organizational form of teaching. Thus, the study of cooperative learning can be approached from many different angles. However, there are some common traits that all approaches are mentioned: The trainees are learning in groups; working together to solve common tasks. 5 From the concept of the method, teaching methods, teaching the concept of cooperation, from the results of the study of characteristics of cooperative learning group, we affirm that teaching cooperation is a teaching method in which each student is learning in one or more groups of the cooperation between members, between groups and with the interaction of the teachers in order to achieve a common goal. 1.2.2. The feature, characteristics, principles, and meaning of cooperative teaching methods We believe that applying cooperative teaching is the process of implementation of these measures which has a scientific basis to organize and control the relationship between the elements: teacher, student groups and knowledge, and develop in a certain order to make the mission of teaching. Characteristics: In the opinion of modern teaching theory, teaching process is the cooperative organization of some of the following basic characteristics: learning tasks, content, methods, forms of official teaching and assessment. Rules: In cooperative teaching, group co-operation is effective, it is necessary to apply rules that John C. Maxwell gave such as importance rule, Panorama rule, Suitable rule, the rule of chain link, the impact rule, and the rule of communication. Meaning: In the trend of innovative content and teaching methods, teaching cooperation have important implications in the implementation of integrated trends connection between people and people in certain conditions. 1.2.3. Scientific basis of teaching cooperation 1.2.3.1. Philosophical basis Learning is a continuous process arise and resolve conflicts inside and outside. That creates internal resources and external resources to promote the development of the learners themselves. Basis for conflict resolution is the harmony between individual interests and collective consciousness and responsibility of the individual before the collective. [68] 1.2.3.2. Pedagogy basis In view of activities: Collaborative learning will enable the students to have more learning opportunities and activities in exchange. Since then they have got better motivation, excitement . The nature of learning is the process of organizing different activities for students to be active and acquire the knowledge, skills, and techniques. 1.2.3.3. Basis of psychology There have been many research works on cooperative learning in groups. Learning mechanism that is explained by a number of psychological theory. 6 1.2.3.4. Social basis Education, in nature, is the personal socialization process. The relationship between socialization and personalization is a dialectical relationship. The group is the intersection between the effects from individual to society and the impact of feedback from individuals back into society. 1.2.4. Cooperative teaching approach to teaching activities Approach based learning activities can be interpreted such as how to learn about teaching activities based on a certain method. 1.2.5. Collaborative teaching models A collaborative lesson can be designed in many different models. But the ultimate goal is to help students complete the learning task in the direction of cooperation. The theory of teaching has launched four models to meet the criteria of access to the school in the direction of cooperation. 1.2.5.1. Group learning - STAD STAD was developed by Robert Slavin at Johns Hopkins University. This is probably the simplest model shows the approach towards cooperation. 1.2.5.2.Jigsaw groups Jigsaw groups and experimental development were done by Elliot Aronson and his colleagues at the University of Texas. 1.2.5.3. Investigation group (Group Investigation - GI) This model belongs Herber Thelen’s outline. Then Sharan and his colleagues at Tel Aviv University has expanded and improved it . This model is considered to be small model of collaborative teaching. In contrast to STAD and Jigsaw, in this model, students are involved in the planning of academic topics as well as how to conduct the investigation. 1.2.5.4. The model structure Another model of collaborative learning has been developed over the past decade mainly by Spencer Kagan and his colleagues. Here are two structures that Kagan has grown. 1.2.6.The scale and types of cooperative learning groups According to the model, above each group consists of 4 to 6 students and the members of the group have their inconsistency in the level of social skills, personality, gender This difference will promote effective teamwork. 7 Classification of cooperative learning groups there are many different perspectives, as we use teaching methods in cooperative learning, teachers should be based on objectives, and teachers can split cooperative learning groups according to certain criteria to match. 1.2.7. Relationship between Cooperative teaching and other teaching methods 1.2.7.1. The relationship between cooperative teaching is to detect and solve problems teaching method Detection method is to solve the problem, the student partially or completely self-identify issues that need to comprehend, looking for a way to solve that problem. These problems can include several types of theories and practice, to be addressed in class or at home, individuals or a group of students to solve. With this teaching method, students are to create conditions for promoting creativity, improve cognitive interest, thereby fostering the qualities and behaviors of researchers. These characteristics are also evident in teaching cooperation for the process to solve the problem by cooperation of students performed under the support of the teachers. 1.2.7.2. Relationship between the Cooperative teaching with project-based teaching Obviously, working together to complete the project is one of the main requirements for project-based learning. The basic requirements of cooperation in the implementation of the project: Cooperation directly impact on the success of each other; interdependence in a positive way is the role and responsibility of the individual and of group; contribute relevant life skills training are guaranteed in the process of implementation of collaborative group work. 1.2.7.3. The relationship between cooperative teaching and constructive teaching There are two types of construct in basic teaching Which are basic construction and social construction. Constructivist teaching not only emphasizes the potential of thinking, active learners themselves in the process of knowledge creation, but also emphasize the possibility of dialogue, interaction, student debate in the creation and recognition of knowledge. The active dialogue, interaction, debate in knowledge creation is also the teaching activities carried out in cooperation to build new knowledge. [95, 111-112] 1.3. Some issues about the process of teaching Mathematics in Primary school 1.3.1. Psychological characteristics of primary school students We believe that: Learning is the main activity of primary school children, this activity forms and develops in the heart of funny activities, exchanges between students. Elementary school students' activities should be integrated with funny activities and through cooperation and exchange. Therefore, when applying cooperative learning in mathematics in primary school, we should have pedagogical design for appropriate learning content development of psychology 8 students to bring efficiency to the formation and development of cognitive and personality of elementary school students. 1.3.2. Games for Learning Mathematics in Elementary In Elementary school age, although active players have retreated to the back, to give the leading role to learn, but the game still has an important place in the lives of children. 1.3.3. Goals, plans and the basic spirit of the program content in Elementary Mathematics - Goal: Give initial basic knowledge of arithmetic, the natural numbers, fractions, decimals; common quantities; several factors simple geometry and statistics. Form practical skills, measure, solve the problem with many practical applications in daily life. Give Initial capacity development thinking, the ability to infer reasonable and proper expression (oral and written). - The basic spirit of the program content in Elementary Mathematics: Program structure content in Primary Mathematics thoroughly ideas of modern mathematics and suitable to each development phase of primary students. The content of the program coordinated closely with other organic, thorough unity of Mathematics, to ensure the continuity between Primary and Secondary. 1.4.Status of application of cooperative learning in teaching Mathematics in Primary Find out the status of teaching mathematics teaching and the organization of work for primary school students, we have surveyed over 268 teachers of a number of primary schools in the provinces: Phu Tho; Vinh Phuc and Yen Bai. 1.4.1. Actual use of organizational forms and methods of teaching mathematics in primary schools. Form of teaching that teachers have used mainly as the whole class and as individuals. Group form is only used very little, mainly to practice and reinforce old knowledge. Traditional teaching methods that teachers use mainly such as: presentations, questions and answers, students are active in the learning process. students are passive to acquire knowledge by teachers to communicate 1.4.2.Assess the awareness and attitudes of teachers for teaching cooperation, the extent to which they use in practice When using cooperative teaching methods, teachers help students reflect on and consolidate knowledge, skills and techniques of old, other purposes are not interested in full. This is a limitation to be overcome. Thus, the use of 9 cooperative learning groups is not a teacher, it needs to be adjusted, improved teaching accordingly to achieve effective team collaboration. 1.4.3. The advantages and disadvantages of teachers to organize cooperation for elementary school students. Benefits Teachers evaluated the effectiveness of teaching and have an attitude of cooperation to support the use of cooperative learning in teaching in primary schools. Characteristics and cognitive needs of students at Primary are suitable for teaching cooperation. Collaboration in teaching helps students respond very enthusiastically and be more interested in learning. Difficulties - On Awareness: Many teachers understand in a simple way, they said that they will divide the class into groups (optional) and then groups together to solve the task of the teacher is cooperative teaching requirements - In terms of qualifications, skills of teachers to apply cooperative teaching method: teachers don’t often use cooperative teaching method effectively . Specifically, teachers lack some of the necessary skills. - Students also lack some skills in cooperative learning needs such as: ability to work in groups; communication skills, interaction; skills to create a collaborative environment; skills to build trust; to resolve conflicts - On the choice of teaching content: Not all learning content can become the theme to organize effective teaching cooperation. But the fact that regular teachers have selected content in my opinion that is not based on any criteria. Thus, many phases of cooperation is the author, not the student's need for cooperation. - About studying environmental conditions: With practical class sizes are quite large, structured and conventional classroom space from 40m 2 to 54m 2 , fixed equipment and furniture all hinder the relocation of mobility at the request of the cooperative teaching. 10 . teaching. Cooperative teaching has been mentioned by Nguyen Huu Chau, Nguyen Van Cuong, Tran Ba Hoanh, Nguyen Ba Kim, Lam Quang Thiep, Thai Duy Tuyen The teaching at the primary school level in. dictionary, group means that many groups are involved in a joint action. According to Tran Ba Hoanh, "group" is a small collective form to perform a certain task in a certain time. [39] Thus,. teaching school. This view is also acknowledged by some theorists such as Thai Duy Tuyen Tran Ba Hoanh, Teaching cooperation is the interference between teaching methods and forms of teaching In