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
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3. Subject of the thesis
Cooperative process of teaching mathematics in primary schools.
4. Hypothesis

Chapter 1: Literature review and practice
Chapter 2: Implementing cooperative teaching in Mathematics in Primary schools
Chapter 3: Pedagogical experiment
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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

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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.
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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
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students to bring efficiency to the formation and development of cognitive and personality of 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.
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CHAPTER 2: THE IMPLEMENTATION OF COOPERATIVE TEACHING IN MATHEMATICS IN
PRIMARY SCHOOLS
2.1. Directions of applying cooperative teaching in primary schools
- Need to apply perspective on cooperative learning activities.
- School cooperation must be integrated with the game
- Take measures to overcome the limitations of cooperative teaching
- Ensure coordination between cooperative learning and other teaching methods.

group to cooperate with the following requirements "Adding brackets and then the result of the expression."
7
×
( 6 + 16 : 2 + 2 ) = 112 ( 7
×
6 + 16 ) : 2 + 2 = 31
7
×
( 6 + 16 ) : 2 + 2 = 79 7
×
6 + 16 : ( 2 + 2 ) = 46
7
×
( 6 + 16 : 2 ) + 2 = 100 ( 7
×
6 + 16 ) : ( 2 + 2 ) =
2
29
7
×
( 6 + 16 ) : ( 2 + 2 ) =
2
77
7
×
[( 6 + 16 ) : 2 + 2 ] = 91
7
×
[ 6 + 16 : ( 2 + 2 )] = 70
For example: Sophists, "40: 8 = 41"

Depending on the content, objectives, requirements to achieve the lesson, students object that teachers have the
pedagogical design in any direction to suit.
2.4.The process of organizing cooperative teaching in teaching mathematics in primary
The thesis research cooperative teaching model includes elements of teachers, students and learning content. Here
we are pleased to offer a cooperative organization of lessons in accordance with the conditions of the schools in
Vietnam. Cooperation in teaching the structure of the lessons can be summarized as follows:
2.5.Use some typical situations in teaching Mathematics in Primary
2.5.1. Teaching math concepts
Mathematics in Elementary school does not require students to define the concept. Main road to the concept by
way of induction that is: Derived from the individual objects such as real objects, models, drawings, teachers lead
students to analyze, compare, abstraction, generalization to find the characteristic signs of a concept expressed in this
particular case, which went to an intuitive understanding of concept depending on the requirements of the program.
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Preparation
Process
Implementation
process
Review and
evaluation
process
For example. Formation of the concept of fractions (Math – 4 grade) by two different paths that: Forming
concepts fraction from measurements of quantities and the concept of fractions from the division of two natural
numbers.
In the first way, teachers can conduct information such as lesson plans are designed based on a collaborative
learning process
2.5.2. Learning rules, methods
In the process of teaching was also having some of the rules but do not carry enough of the characteristics
specific algorithm, but has some of the characteristics and proved to be effective in action and solving instructions.
That is the rule upon the award shall be understood as a finite sequence of instructions follow a defined sequence to
transform the information into a class problem into information that describes the solution of the problem class it. In

3-5 minutes Fig 2.3: TableclothsTechniques
- When all students have finished, proceed to share and discuss the answers. Write the general opinion of the group in
the box between the tablecloths.
Obviously, when applying this technique, the first problem of the teacher will be removed effectively.
Pieces Technical (Jigsaw model improvement)
How to proceed: as shown
Round 1
Round 2
Fig 2.4: Jigsaw model
Round 1
Activities in groups 3 persons
Each group is assigned a task (for example: Group 1: task A; Group 2: B tasks, group 3: tasks C)
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t
e

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p
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r
s
o
n
a
l


\
2
21 3 1
\
2
2
\
2
3
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2
1
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2
2
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2
3
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2
Make sure each team member to answer all questions in their assigned tasks. Each member presented the results
of the group and answer the new group will become experts in the second round. (In the first round groups do not
report the results of groups that move in round 2)
Round 2
Form three new groups, new tasks will be assigned to the group has formed to solve. [18, 5]
Example: Divide a rectangle into 4 rectangles or triangles of equal area? (Math 5)
Round 1:
- Task A: Divide a rectangle into 4 rectangles of equal area?
- Task B: Divide a rectangle into four triangles of equal area?
- Task C: Divide a rectangle into 4 equal area? (Which consists of two triangular and two rectangular)

difference is the placement of a comma in the divisor or the dividend. For example: Perform the division:
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a) 23.56: 6.2 b) 235.6: 6.2
c) 2.356: 6.2 d) 235.6: 0.62
e) 0.2356: 0.62
Divide students into groups; delivery handout and instructions on how to work for each group:
Conduct group discussion, problem analysis and unified solution to solve the problem by moving the decimal on
the analysis of a natural number and a decimal.
After the discussion, the group based on the transfer of a decimal of a natural number and a decimal to draw
conclusions on how to move the comma position of the divisor, the dividend in make a calculation process.
Step 3: Conclusion
- The group reported results.
- Teacher assessment, review the results of each group on the transfer decimal achievement of natural numbers
and the decimal; implementation of operations. general conclusions about the teacher performs division rules decimal.
2.6.3.2. Cooperative learning and project-based learning
For example. collaborative teaching project-based learning combined:
When teaching about statistics collection and charting (grade 5), teachers can incorporate project-based learning
and cooperative learning groups as follows:
Project implementation (small) sample set of data (grade 5), plotted.
Introduction of the project
Organized for students of the class to learn about the subject of the class. Small-scale project, associated with the
monitoring of changes in learning, the class score. The objective of the article is: students understand how to set up
tables, graph represents data at the request of the teacher, draw some conclusions.
Combining project-based learning and cooperative learning
Phase 1: Divide the group, choose a theme, define operational objectives for the group.
Teacher split the class into small groups (4-6 students), each group appoint a leader and a secretary. In this
project can select a group of students with similar interests to learn about a certain subject. teachers suggestions and
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help the group choose a topic and define project objectives, such as: Group 1 select the forum that "test scores in math
class"

(can be used for enclosed booklet). Then, the total area of the four sides, the total area of the six sides of the box (the
fastest way).
- Can be combined graft techniques to discuss how to calculate the total area of 4 sides, 6 sides of the box area.
Step 3: Conclusion
The group self-test to detect the fastest calculation of the total area. teachers complete formula of 4 on the side,
total 6 sides of the box, introduced the name: the surrounding area, the total area of the box.
2.7.Student’s assessment in the process of applying the cooperation of teachers teaching
Collaboration of students scoring via surveys combined monitoring books of teacher learning. This assessment by
the Ministry of Education and Training in collaboration with the Centre for Education based on experience (CEGO) of
the Catholic University of Leuven, Belgium. Specifically: Tools observations: Observation • Record the observed ones
in the capability and behavior of students.
Considered to meet the target capacity assessment of teaching students in PISA through cooperation
Thus, seen from the perspective of the PISA assessment, evaluation, grading cooperative learning process of
students in mathematics in primary schools need to consider the formation and development in students the following
capabilities:
The ability to connect knowledge of mathematics to practical problems.
The ability to access, search for information from various sources in accordance with the circumstances and the
individual or collective goals for problem solving in math.
Ability to act in a self-reliance, creativity, protect and assert personal opinion, demonstrated personal
responsibility to the limit in the process of group interaction.
The ability to define operational targets, develop and implement personal plans targeted goals; way to decide and
can change in accordance with circumstances.
Ability to establish good relations with friends in the group and outside the group.
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CHAPTER 3: EXPERIMENTAL PEDAGOGY
3.1. Experimental purposes and requirements
Additional experiments in order to adjust and to complete the theoretical studies in order to find the right direction,
suitable for use cooperative learning in teaching mathematics in primary school in order to contribute to improve the
effectiveness of teaching .
3.2. Experimental area

objectivity and fairness.
Grades compared with the experimental results for the following documents: some good points up 5 posts; Posts
of pretty up 3 items; Posts lower down 6 Posts; weaknesses reduce 2 posts (concrete results is presented in Section
3.5.2 of this chapter). This shows that the first step to apply cooperative learning in teaching mathematics in grade 4
was the most effective.
3.4.1.5. These issues need to learn from experience in the first round
From the results achieved in the first round, we found that the experimental lesson on this can only be a part of
pedagogical intentions when planning lessons and only a small contribution to the improve the efficiency of the unit.
Because the quality of teaching depends on many other components of the teaching process as teaching content,
teaching facilities, particular object depends on the student and environmental factors. The empirical existence of
round 1 we have to learn from experience and consistent with the teacher how to fix it in the second round.
3.4.2. Held within two experimental
3.4.2.1. Target
Experimental organization within 2 to explore the effect of adjusting the plan based learning, teaching
cooperation.
Experiments in the second round in order to answer the question: The coordinated use of the forms, methods,
methods and techniques of teaching mathematics in grades 4 in collaborative teaching has been consistent and effective
adjustment results? All that needs to be further verified in practice by experimentation.
3.4.2.2. Conducting experiments
In the second round, our teachers based on experimental designs within one design lesson plans. Each
experimental teachers presented their plan design, the concerns and problems. Then we do the same with the
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experimental teachers of the three cases discussed to reach a consensus lesson plans for the second round. teachers
conducted teaching experiments four empirical articles in the past 2 presented in Section 3.3 of this chapter.
3.4.2.3. The experimental results
After using the experimental time, we examined the quality of the experimental class and the control class. We
are preparing the test, guide dots, how to test, marking a serious, objective for the next one.
After collecting all the dots, we see the effect of the experimental classes increased dramatically. Compared with
the results in the first round, good rose 4 items, the average of all scores fell 2 Posts, Posts weaknesses down by 2 (the
specific results presented in Section 3.5.2 of this chapter).

(sociable interaction with social groups, mathematical ability) by organizing experimental teaching cooperation.
3.5.1.2. Quantitative
We evaluate the effectiveness of teaching hours based on the level of the students did in the test. Assessment of
student work on a 10 point scale. Lowest scoring scale for a content of 0.25 points and rounded to the Resources
section. Classified by four points: Excellent (9, 10); Pretty (7, 8); Average (points 5 and 6); Weak (under 5). The
specific content of each of the points shown in the guide spots.
3.5.2. The experimental results over the past
3.5.2.1. Quantitative
In Summary, through two past experiments, the qualitative assessment, we found that if teachers caused
excitement for students and appear in their demand for real cooperation, cooperation does not take place a shield to
resist, the students are trained in a potential mathematical capacity development and sociable group interaction capacity
in view of the PISA assessment. This shows that the application of cooperative teaching methods in Mathematics in
Primary have started to contribute to the adaptation to the requirements reviews some of the key capabilities of students
in PISA.
3.5.2.2. Quantification
Chart 3.3: Comparison of experimental results for round 2 with the initial results.
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3.5.3. General assessment of experimental results
Through two rounds of experiments, we evaluated a number of basic points:
Firstly, compared with the initial quality survey before the experiment, the quality of teaching some lessons do
math in grades 4 has increased significantly. Percentage of students scoring pretty, good in higher experimental system
and an average rate and weak lower than the control system, the experimental results higher in the second round in the
first round results. This is a very important quantitative results, as a basis for proving the feasibility of the application
of cooperative learning in teaching mathematics in grade 4 in particular and mathematics in primary schools in general.
Second, the experimental results show that: teachers and students began to "get acquainted" with cooperative
teaching methods proposed by us. This shows that if the application of rational methods of teaching Mathematics in
Primary teaching method education cooperation during teaching process at school will contribute to improving the
effectiveness of teaching.
Third, cooperation in teaching Mathematics in Primary project will contribute proactively VNEN mass can be
implemented in the 2015-2016 school year in order to contribute to the building of the "new school model in Vietnam "