Thiết kế và sử dụng tài liệu theo môđun trong dạy học môn PPDH toán cho sinh viên CĐSP nước CHDCND lào tt tiếng anh

MINISTRY OF EDUCATION AND TRAINING
HANOI NATIONAL UNIVERSITY OF EDUCATION

DONE SOUPHIDA

DESIGN AND USE MODULAR MATERIALS IN TEACHING
MATHEMATICS
TEACHING METHODS FOR STUDENTSOF TEACHER TRAINING
COLLEGES
IN LAO PEOPLE'S DEMOCRATIC REPUBLIC
Specialty: Theory and Method of Teaching Mathematics
Code: 9.14.01.11

SUMMARY OF DOCTORAL DISSERTATION
IN EDUCATIONAL SCIENCES


HANOI, 2020
COMPLETED AT
HANOI NATIONAL UNIVERSITY OF EDUCATION

Supervisor: 1. Assoc. Prof. Dr. Tran Trung
2. Dr. Hoang Ngoc Anh

Reviewer 1: Assoc. Prof. Dr. Dao Thai Lai
Reviewer 2: Assoc. Prof. Dr. Tran Viet Cuong
Reviewer 3: Assoc. Prof. Dr. Nguyen Trieu Son

The dissertation is protected in front of the School-level Dissertation Committee at:
Hanoi National University of Education at ......hour .....date .......month....year 2020

The thesis can be found at:
National Library of Vietnam, Hanoi or


Library of Hanoi National University of Education
LIST OF PUBLISHED WORKS
1.

Pham Anh Giang, Done Souphida (2016), “Developing a syllabus on the
Method of Teaching Mathematics in pedagogical schools in accordance with
the approach of implementation capacity for pedagogical students”, Journal of
Educational Sciences, The Vietnam National Institute of Educational Sciences,

2.

Issue of 01/2016 (pp. 43-44).
Tran Trung, Done Souphida (2019), "Designing modular materials for
mathematics teaching method in pedagogical colleges in Lao People's
Democratic Republic to develop the capacity of students", Journal of

3.

Education, Issue of 04/2019 (pp. 322-327).
Tran Trung, Done Souphida (2019), "Designing teaching modular materials for
Secondary school mathematics in pedagogical colleges in Lao People's

4.

Democratic Republic", Journal of Education, Issue of 05/2019 (pp.150-154).
Tran Trung, Done Souphida (2019), "Designing teaching modular materials for

mathematics teaching methods for students studying Mathematics Pedagogy at
pedagogical colleges in Lao People's Democratic Republic", Journal of
Educational Sciences, The Vietnam National Institute of Educational Sciences,

5.

Issue of 7/2019 (Letter of publication acceptance dated 07/6/2019).
Tran Trung, Done Souphida (2020), "Using materials by module in teaching
maths - teaching methodology module for maths students at Lao teacher
training colleges", Vietnam Journal of Education, Volume 4, Issue 1 (p.25-29).


1

OVERVIEW
1. Rationale
The philosophy of education in the 21st century shows the main idea is to take
"lifelong learning" as a foundation, based on the general goals of learning: learning to
know, learn to work, learn to live and learning to be human
From the above orientation, Lao People's Democratic Republic has proposed
training plan for human resources from 2006 to 2015 in four directions: (i) Strengthen
the content of teaching in the general education program in the Lao People's
Democratic Republic, general education lasts 12 years; (ii) Encourage and expand the
opportunities of people with school attendance age, improve quality and educational
connection; (iii) Organize strategy and action plan of educational sciences; (iv) Pay
attention to expand technical schools and vocational training. Lao's education and
training system is increasingly improving the quality of human resource training
To improve the quality of teaching, the problem should be fostering for teacher
training students the necessary competencies right from the time they were still studying
in universities.

Currently, one of the approaches that are drawing interest is modular teaching. In
education, the modular approach goes with the ideology of teaching technology, it is a
modern way of structuring or organizing the teaching content so that the training program
becomes more flexible.
For the above-mentioned reasons, we choose the following research topic for the
dissertation: "Designing and using modular materials in teaching Mathematics
Teaching Methods for students in the pedagogical colleges in Lao People's
Democratic Republic".
2. Aims of the study
Designing a module-based document on Teaching Methods in secondary school
Mathematics and to produce a methodology for using those modules in the teacher
training process at the Teachers Training College in Lao PDR, to improve the quality
of training and contribute to fostering self-study capacity for students of
Mathematics Teacher training College.
3. Research Scopes
Mathematics teaching method in Teacher Training College, Lao PDR mainly an
outline of teaching methods in high schools, not deep skills on teaching methods of
specific content. While, the specific subjects of secondary school math lack the part
of teaching method of this knowledge, which mainly teaches pure knowledge of
secondary school mathematics and high school mathematics. Therefore, Therefore,
the topic design documents according to the Mathematics method of teaching module
in Mathematics at secondary school.


2

4. Research subjects and objects
4.1. Research Objects: Modular documents on teaching methods of specific contents
in Secondary school mathematics for students of Teacher Training Colleges in Lao
People's Democratic Republic.

4.2. Research subjects: The process of teaching Mathematics at secondary school for
Maths teacher training students of at Teacher Training Colleges in Lao People's
Democratic Republic.
6.
Scientific hypothesis
If you can design modular documents on Mathematics teaching methods and use
them in Math teacher training at Teacher Training College, Lao PDR, it will
contribute to improving the quality of teaching Mathematics methods in teacher
training in Lao PDR, at the same time contributing to the development of self-study
capacity for students.
7.

Research mission

6.1 Research on the theoretical basis of the design and use of materials in modules in
teaching mathematics teaching method for Teacher Training College students in Lao
PDR.
6.2. Surveying the status of design and using materials in modules in teaching
secondary school mathematics for Teacher Training College students in Lao PDR.
6.3. Design, compile modular documents in teaching secondary school mathematics
for Teacher Training College students in Lao PDR.
6.4. Organized teaching secondary school mathematics and using module-based on
teaching methods in training for Teacher Training College students in Lao PDR.
6.5. Pedagogical experiment to test the feasibility and effectiveness of the proposals
in the thesis.
7. Research mathodology
7.1. Theoretical research methods: Research theoretical documents related to the
design and use of modular documents in teaching general teaching method. Study the
content of curriculum using module materials in teaching teaching method in Lao
PDR in particular.

7.2 Methods of investigation and observation: Using questionnaires, discussing with
experts to investigate the actual situation of teaching and learning with designing and
using modular materials in teaching secondary school mathematics at Teacher
Training College, Lao PDR.
7.3. Method of Pedagogical experiment: Organize experiment of the content of and
using modular materials in teaching secondary school teaching mathematics at Ban
Keun Teacher Training College, SavannaKhet Teacher Training College, Lao PDR to
assess the feasibility and effectiveness of the topic.
7.4. Methods of mathematical statistics: The dissertation uses qualitative analysis


3

methods, quantitative analysis to draw conclusions related to the contents considered.
Evaluate results by using mathematical statistical methods in educational science.
7.5. Case study method: Monitoring, analyzing and evaluating self-study results of
some students participating in pedagogical experiments to see the impact of
pedagogical effects on weak students. Average, capable and good.
8. Contributions of the dissertation
8.1. Systematize and clarify some theoretical bases on the design and use of
modular materials in teaching of Teaching Training Colleges students, Lao PDR.
8.2. The dissertation adds more modular materials on Mathematical Teaching
Methods in "Secondary school mathematics" subject to help students self-study.
8.3. Designed and proposed the method of using modular materials to improve
the effectiveness of teaching on teaching methods in Secondary school mathematics
at Teacher Traning Colleges, Lao PDR.
8.4. Facilitate for Secondary school mathematics teachers (and other subjects)
with reference materials to design and use modular materials in teaching at colleges.
9. The points are defending the thesis
9.1. The designing and using of materials according to the module on

Mathematical teaching method in mathematics training teacher at Teacher Training
College, Lao PDR is necessary.
9.2. Materials according to the Mathematical Teaching module have been
designed and how to apply them in Math teachers training in Teacher Training
Colleges, Lao PDR is a feasible and effective self-study material, contributing to
improve the efficiency of teacher training and develop self-learning capacity for
students.
10. The structure of the thesis
In addition to the Introduction and Conclusion, the content of the thesis
includes three chapters:
Chapter 1. Theoretical and practical basis
Chapter 2. Design and use of modular materials in teaching Mathematics
teaching methods for Teacher Training College students, Lao PDR.
Chapter. Pedagogical experiment.
The thesis includes references and attached Appendix.


4

Chapter 1
THEORETICAL AND PRACTICAL BASIS
1.1. Overview of study history of the topic
1.1.1. Studies in foreign countries
The first module appeared in the United States, in the early 20th century, it was
appeared in the instant refresher training program in the automobile factories so that
workers could learn by themselves or learn by themselves under the guidance. of the
engineers (typically the car maker General motor and Ford car).
In France, courses with modular structures were held during the post-World War
II era in coal mines. But the difference is that American workers are trained to meet
the demand of the production line.

In Sweden, the training program for logging workers is structured in accordance
with the order and basic content through training modules. The training system in
Sweden has been put into use since the year 50 of the 20th century.
Modular training is not only limited to America and Europe but also developed
in Australia, typically a model of model training widely developed in Australia.
The modular teaching organization is widely deployed all over the world,
especially the International Labor Organization (ILO).
The credit system comes from Harvard University, which was conducted by
President Eliot in 1872. The rigid classical training program is replaced by a wide
selection of programs.
Some Southeast Asian countries such as Thailand, Vietnam, and Singapore have
deployed universal modular teaching that can be used for all subjects. International
Conference on "Deploying and applying modules in training"
Southeast Asia countries such as Thailand, Singapore, ... have also acquired and
applied modularized techniques of teaching content, and organized modular training.
The 21st century is the era of science, technology, information and
communication, the rapid transformation of the market economy; this leads to the
inevitable that the knowledge economy has been opened.
In conclusion, the program with a modular structure and modular training
methods have been developed and widely applied in many countries around the
world. Building the modular program structure in each country, in each field.
1.1.2. Studies in Vietnam
The modular training program has been around since the 70s of the twentieth
century in American programs in South Vietnam. In the North of Vietnam, the
modular training program was introduced a little later with new techniques and
technologies mainly came from Eastern European countries.


5

Vietnam has been developing a modular training program since 1988 through the
topic "Self-study candidate" of the Institute of Higher Education and Research in
terms of capabilities and conditions for effective application of modular teaching.
Author Nguyen Minh Duong in the work "Module of practicing skills - approach
and compilation" has given the theoretical basis of the teaching module.
Following Nguyen Minh Duong, author Do Huan has built up the structure of the
technology training program according to the modular structure, the products of the
thesis "Modular approach in building the structure of vocational training programs"
systematized. get the rationale for the apprenticeship program according to the
module approach.
The author Dang Thi Oanh continues to develop her research direction, and has
successfully defended the Ph.D. thesis in Pedagogical Science - Psychology: “Using
simulation situations to train technology design skills New document research papers
for students of the Faculty of Chemistry, Pedagogical University "
Also following this research direction, the author Pham Van Lam has done a
doctoral thesis with the topic: “Improving the quality of practice in general physics at
the Technical University by self-study with modular guidance. "[29].
On the basis of studying the theoretical basis of the module, teaching module,
structure of the teaching module, the module-oriented self-study method, advantages
and disadvantages of modular guided self-study methods.
In 2010, Duong Huy Can, in his doctoral dissertation on education with the
topic: "Enhancing self-studying skills for students studying chemistry at pedagogical
universities with modular guided self-study method".
In 2010, in Doctoral Dissertation on Education of Nguyen Thi Nga with the
topic: "Building and using modular guided self-study materials of general chemical
knowledge - specialized chemical high school program learn to improve students'
knowledge ”[32].
In 2017, Tran Duc Khoan conducted his doctoral dissertation with the topic
"Building and using modular guided self-study materials in general physics to foster
the self-studying capacity for university students studying engineering".

In conclusion, the study of teaching modules has been conducted by many
Vietnamese scientists under different perspectives but they have a common direction
when studying the module is to clarify the nature.
1.1.3. Studies in Lao People's Democratic Republic
To develop the country, the first thing to define is human resource development,
in which education is the key factor determining the human resource of Lao PDR.
Training and developing human resources in Laos is especially important in the
industrialization and modernization of the country.
The "Human resource development strategy up to 2020" by the Central


6

Committee of the Lao People's Revolutionary Party (2002) [43] mentioned the topic
quite comprehensively.
Right from 2006, the Resolution of the 8th Party Congress of Lao People's
Revolutionary Party [48] affirmed that "The most important resource to implement
industrialization and modernization is human resources".
In order to improve teaching capacity for teachers, there are many project topics
on renewing teaching methods in universities, colleges and high schools such as the
book on "Materials for fostering Mathematics teachers at Secondary and High
School"
Study on innovation of teaching method in general and teaching method of
Mathematics in particular in Lao PDR, there are a number of scientists interested in
research such as the Doctor of Education Science thesis.
In general, the above scientific works have focused on studying the most basic
and general problems of Mathematics teaching methods under Lao's Ministry of
Education in order to develop human resources in general.
There has been no research on the construction of modular guided self-study
materials in teaching for pedagogical students in Laos; No works have been fully and

systematically presented the promotion of self-studying skills of students in using
modular materials at pedagogical colleges in Lao PDR
1.1.4. Some comments
In general, the authors studied modular materials for Mathematical teaching
methods on many aspects such as:
- Modular materials for Mathematical teaching methods is a requirement of
teaching innovation and it affirms the importance and necessity of modular materials
for teaching methods.
- The dialectical relationship between external factors and internal factors of
document design during modular teaching.
- The actual situation of designing modular materials for teaching methods of
some teachers and students is still limited. Self-study activities are not frequent.
- Some authors have pointed out the manifestation of the capacity of teaching
mathematics of students studying mathematics pedagogy in colleges.
- There is no set of tools for assessing the self-study skill level of students of
pedagogical colleges in Lao PDR.
- Measures to develop self-study skills of pedagogical students in teaching
curriculum have not been proposed.
- There are no documents and means to support pedagogical students in Lao
PDR to self-study the Maths teaching methods.
Therefore, we focus on studying the above issues through students studying
Mathematics Pedagogy of Lao PDR.


7

1.2. Training program for students studying Mathematics Pedagogy in
pedagogical colleges of Lao PDR
1.2.1. Output standard of the training program of Mathematics Pedagogy of Lao PDR
The output standard of training program of maths pedagogy in colleges of Lao

PDR is approved by the Ministry of Education and Training with five basic
requirements:
- Political, moral and lifestyle qualities: Patriotism, love of socialism, compliance
with the Party's guidelines and policies, the State's policies and laws. Has educational
ethics, love for works, attachment to education.
- Has the ability to understand the subject and the educational environment: There
is a method of regularly collecting and processing the information on the needs and
characteristics of their subjects.
- Math learning capacity: Students studying Mathematics Pedagogy in colleges
need to ensure subject knowledge, master knowledge, and ensure accurate subject
content, system,
- Educational capacity of the subject: Performing the task of educating ideologies,
feelings and attitudes through education and integrating the contents in accordance
with the built plan.
- Deployment skills: Skills of expression and interpretation make others understand
their meaning, emotion, and attitude accurately and effectively.
In order for students to meet the professional standards, the future teachers
themselves need to practice professional skills during the time of studying at the
pedagogical colleges.
Therefore, the output standards of students will reflect the strengths - weaknesses
in the current training program and find out the issues that need to be supplemented.
1.2.2. Training program for Math teachers in Teacher Training Colleges of Lao
PDR
Education reform in Lao PDR is currently oriented towards capacity
development for learners..
We also agreed to approach the competencies in the general education program of
Vietnam to apply in teaching at the pedagogical colleges of Lao PDR.
From the academic year 2013-2014, the pedagogical colleges are assigned by the
Lao's Ministry of Education and Sports to train teachers in the form of 12 + 4 (4-year
system) with the math modules in the training program as follows:

8
Credits

Secondary school
Mathematics:
2(0-4-0)
High school
mathematics 1 :
3(0-4-3)
High school
mathematics 2:
3(0-4-3)
History of
mathematics:
2(2-0-0)
Analytic geometry:
4(2-2-3)
Basic algebra:
3(1-2-3)
Basic geometry:
4(2-2-3)
Advanced algebra:
4(2-2-3)
Calculation 1
4(2-2-3)
Calculation 2:
4(2-2-3)
Probability and

statistics 1:
4(2-2-3)
Probability and
statistics 2:
4(2-2-3)
Differential
equations: 4(2-2-3)
Calculus:
4(2-2-3)
Advanced algebra:
3(1-2.3)
Math teaching
method: 4(2-4-0)

st

1 year
Semester
1
2

2nd year
Semester
1
2

3rd year
Semester
1
2

4th year
Semester
1
2

2(0.4.0
)
3(0.4.3)

3(0.4.3)

2(2-0-0)
4(2-2-3)
3(1.2.3
)
4(2-2-3)
4(2.2.3
)
4(2.2.3
)
4(2.2.3
)
4(2.2.3
)
4(2.2.3
)
4(2.2.3
)
4(2.2.3)

3(1.2.3
)
2(2.0.0
)

2(0.4.0)

The training program consist of 3 sections:
- Advanced math subjects such as Algebra, Calculus, Statistics, Geometry, etc.
- "Math teaching method" includes general knowledge about theory and teaching
methods of mathematics in high school; “History of mathematics”, etc.
- Secondary and high school Mathematics courses include elementary math
knowledge and math knowledge in high school textbooks,


9

In which, Secondary school mathematics has 4 credits (65 periods), including 1
theoretical credit and 3 practical credits.
- The ability to think and use mathematical language correctly.
- Math solving ability, ability to apply knowledge, skills, mathematical methods to
solve a specific problem with a high target.
- Ability to detect and solve problems, this is a very important capacity for students
of Faculty of Mathematics in the process of studying in the College.
- Math problem solving capability including ability to present problems; Identify
ways and plans to solve problems.
- Scientific research capacity in mathematical education: Ability to detect, set and
solve problems arising in practical education – teaching.
- Ability to apply mathematical knowledge into practice. Students of Faculty of
Mathematics need to be able to observe and analyze practical situations.

- Ability to evaluate and self-assess. In traditional-style teaching, the role of
teachers is enhanced so the students' autonomy is greatly restricted.
Thus, the above capacities are intertwined, supporting each other, creating the
general capacity of students. Those capabilities are also the capacity of scientific
researchers.
1.3. Modular materials in Mathematics teaching at the pedagogical colleges
1.3.1. Modular teaching materials
Along with the rapid development of science and technology has changed the
operating mechanism of many professions, including a direct impact on education.
The term modular is used in many technical disciplines such as architecture,
electronics, weapon engineering, and space travel.
Transforming training modules in the field of science and technology into the
field of education and training is a big turning point and so the content,
Modular material used in teaching is designed to include teaching modules,
each of which can be classified into smaller modules called secondary modules.
According to Nguyen Ngoc Quang's understanding is expressed as follows:
"Teaching module is a relatively independent program unit, specially structured to
serve learners. It contains both teaching objectives, teaching content, teaching
methods and a system of tools to evaluate comprehension results, closely linked
together into a complete body " [37].
It should be noted that the teaching module is not a textbook or monograph but
is a document designed according to the contents of knowledge to learn and follow a
certain logic.
A teaching module is specific to a unit of knowledge to learn, a primary
module is usually small and medium called a large module, a secondary module is


10

often considered a small module, or it can also be a sub-module containing learning

materials.
A teaching module consists of three major constituent parts as follows: Input;
Module body; Output. These three parts are a unified whole [7].
Input

Module’s
body

Output

Diagram 1.1. Structure of the teaching module
(1) The input of teaching module includes: The name or title of the module;
Introducing the role, importance and benefits of the module;
(2) The module body contains a full range of teaching content, along with
necessary instructions on ways to learn to help students gain content and form selfstudy methods. The module body is a key part of the module.
(3) The Output includes: A general summary; A final exam; Instruction system to
continue learning. If all goals of the module are met,
1.3.2. The process of designing modular materials in teaching Mathematics
teaching methods
In this thesis, we study the design of documents according to the Mathematics
module of Secondary School (1st semester) in Mathematics Teaching Program at
Teacher Training College, Lao PDR.
Design module documents on Mathematics teaching method for students in
Teacher Training Colleges, Lao PDR to improve the quality of teacher training.
- Ensure the science of document design according to implemented modules.
- Ensuring the pedagogical quality of modular document design content. In
order to elucidate students' cognitive levels.
- Ensure the feasibility of modular document design.
- Ensure practicality. It is the content and presentation of modular document
designs.

1.3.3. The process of designing documents according to modules in teaching
Mathematics teaching method
The process of designing documents according to modules in teaching or teaching
module for short is the process of modifying documents.
The materials after modularization have the same structural form as the structure
of the teaching module (including Input System, Module Body and Module System)
and carry the full integrity of the teaching module.
- Integrity of capacity development for students: Students will develop some
competencies after doing research and self-study with teaching module materials to


11

help students acquire knowledge.
- Integrity in structure: Modulated self-study materials not only contain
educational goals and contents, but also integrate in it both content and
implementation process to achieve the goals.
1.3.3.1 Prepare the script
1.3.3.2. Prepare learning materials for Secondary Mathematics
For example, with the Mathematics subject at lower secondary school in the
Math Teacher training program at the Lao PDR Vocational College, you can design
modules on Mathematics teaching method according to each specific content in the
training curriculum.
Submodule is a relatively independent part of a teaching module to perform the
task of a knowledge content.
At the same time, teachers can compile into theoretical modules, exercise
modules, and supplementary modules to support students' learning.
1.3.4. The process of using modular materials in teaching at Lao PDR vocational
schools
Modular materials have the effect of improving the quality of teaching and

learning, thereby contributing to improving the effectiveness of math teachers'
training at Lao PDR vocational schools.
+ Using modular material as a reference in teaching for teachers and students.
+ When using the material, it is necessary to adjust the parts and the content of the
sections to ensure it is suitable for learners.
+ Teachers who use modular materials in class need to change traditional teaching
methods.
1.3.5. Modular Document Evaluation Method and Criteria
As with other teaching materials, modular material is developed and used as a
teaching material for students.
1.3.5.1. Develop evaluation criteria for modular self-study materials
The author uses the questionnaire evaluation criteria to consult experts
according to the suitability or inappropriateness level in teaching at colleges with the
5-level Liket scale.
1.3.5.2. Modular self-study document review method
To evaluate modular self-study materials, the research topic uses the method of
consulting experts on the proposed content.
1.4. The situation of teaching about Mathematics teaching method in Teacher
Training College, Lao PDR.
Before 1996, the yearly training program in the Teacher Training Colleges in
Lao People’s Democratic Republic was issued and the textbook of the Lao People’s
Democratic Republic was compiled and used.


12

In order to investigate the status of teaching mathematics teaching method in the
teacher training colleges, Lao PDR, we designed and distributed survey
questionnaires for 35 teachers teaching Maths Teaching Methods in 2 Colleges in Lao
People’s Democratic Republic, including: Ban Keun Teacher Training College and

Savannakhet Teacher Training College.
For the investigation on teachers using teaching methods for math students, the result is
as follows:

Usage level
Teaching methods
Presentation
Oral method
Discovering and solving problems

Regularly

Sometimes

Not use

63%
70%
53%

35%
30%
44%

2%
0%
3%

The survey results show that teachers have used many methods, in which the
oral method is used the most which accounts for 70%, Less use accounts for 30% and

Not apply accounts for 0%,
Presentation method is similar to the oral method, teachers regularly using this
method accounts for 63%, less using accounts for 35% and not using accounted for
2%.
To learn about the current status of teaching Mathematics teaching method in
Secondary school mathematics for students in teaching training colleges, Lao
People’s Democratic Republic.
Question 1. In the module of Mathemetics Teaching Method, what content did you
learn below?
A) Theory and general tecahing method
B) Specific content teaching methods in Mathematics
C) Method of solving mathematics exercise.
Question 2. In addition to the Mathemetics Teaching Method, did you learn about
teaching methods in specific subjects in Math?
A) No
B) Yes but only a little
C) Learned a lot
Results: 100% of students answered the interview,
Question 3. For the Secondary school Mathematics module, did you study the
knowledge of methods of teaching equations and geometry?
A) No
B) Yes but only a little
C) Learned a lot
Results: 100% of students answered the survey, interviews said that they learned
the method of solving problems by topics.


13

The content of Secondary Mathematics in Mathematics teaching methods

program is done after students have studied and researched the module “Mathematics
teaching method”.
Studying Secondary School Mathematics is organizing for students to apply the
general knowledge they have learned to implement the mathematics lesson at the
Pedagogical Schools.
We also studied and in-depth interview about the difficulties of secondary school
teachers when applying the knowledge of Mathemetics teaching method, learned in
Pedagogical Colleges of Lao People’s Democratic Republic.
Teachers do not take pains to explore and improve teaching methods. During
teaching hours, many teachers are more serious about giving presentations than
encouraging students to study. Students are less involved in the development of
lesson content, usually only mechanically recorded, etc.
1.5. Conclusion of Chapter 1
The thesis has synthesized and analyzed the achieved results of research works of
domestic and foreign authors in the approach of modules in teaching. On the basis of
research on the training program of Mathematics in Pedagogical Colleges and the
Output Standard of the Mathematical Pedagogical Curriculum, we study and teach in
the direction of capacity development for students Pedagogical College of in Lao
People’s Democratic Republic.
Although the general level of teachers and students in Lao People’s Democratic
Republic is still relatively low, it is still possible to exploit and apply teaching
perspectives and theories and some Maths teaching methods according to modules at
pedagogical colleges.
CHAPTER 2
DESIGN AND USE OF MODULAR MATERIALS IN TEACHING
MATHEMATICS TEACHING METHOD FOR STUDENTS IN
PEDAGOGICAL COLLEGES OF
LAO PEOPLE’S DEMOCRATIC REPUBLIC.
2.1.An overview of Secondary School Mathematics in the Mathematical teaching
method program in Lao People’s Democratic Republic

In the Secondary school Mathematics training and research program in
pedagogical colleges in Lao People’s Democratic Republic, the module has
objectives that students must achieve after studying to complete the lesson module,
- In terms of knowledge: Students must master the concepts, properties,
formulas, reasoning and seconday school mathematics.
- In terms of skills: Students must have the skills to acquire knowledge and
observe and apply knowledge to the practice of teaching Math


14

- Regarding attitude: Students have a serious attitude in learning, well prepare the
theory, exercises and collect, accumulate self-study
The structure of the materials of Mathematics secondary school curriculum
includes 13 chapters and the Lao College of Education is taught in students
including:
Chapter 1: Redundancy, equality, square root
Chapter 2: Geometry in plane
Chapter 3: Vector
Chapter 4: Linear function, inequations
Chapter 5: Trigonometry
Chapter 6: Inscribed angle in circle
Chapter 7: Area and volume
Chapter 8: Indices and radical equations
Chapter 9: Geometry transformations
Chapter 10: Quadratic function
Chapter 11: Linear equations
Chapter 12: System of equations and inequations
Chapter 13: Probability and Descriptive Statistics
The time of Secondary school Mathematics has 2 (1-4-0); 2 credits = 65

lessons
1 theory = 13 lessons; 4 practices = 52 lessons; 0 self-study
So far in Laos, secondary school mathematics has not been generally differentiated
in the output standards according to the training stages in the pedagogical college.
- Knowledge criteria: Understanding the teaching and learning principles of basic
Mathematics teaching methods in the program such as Algebra, Geometry,
Trigonometry, etc. in the Secondary school Mathematics textbooks.
- Criteria of teaching skills: Ability to use various subjects of Mathematcis
subjects in the program such as Algebra, Geometry, Trigonometry, Calculus etc.
Secondary school Mathematics textbooks.
- Criteria for assessing and commenting on the learning process: Having skills to
use many basic assessment strategies of Secondary school Mathematics in the
program such as Algebra, Geometry, Trigonometry, Calculus, Integral, etc. in the
secondary school textbooks.
2.2. Designing modular materials for Secondary school Mathematics method in
teacher training college Lao PDR
2.2.1. The structure module documents secondary school maths teaching mathod
in Teacher Training College Lao PDR
According to the framework program of the Ministry of Education and
Training of Laos designed for math colleges students, Colleges put the Mathematics
part of secondary school in the Math teaching method and there is a difference when


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designing detailed outlines for This module
To overcome the difficulties in teaching and learning Secondary Mathematics
of teachers and students, we design materials according to modules based on the
above principles.
In the subject of Mathematics at the lower secondary school, the research

includes the following basic contents according to the training program of the Lao
PDR Vocational School [50], [51], [52].
Modular document design to help students self-study with guidance to suggest
and guide students to study each problem.
The structure of modules on teaching method of mathematics in Secondary
Mathematics is designed according to each chapter in the subject's curriculum and is
supplemented to teaching and self-study, including:
Chapter 1. Redundancy, equality, square root
Content 1.1. Solving exponential equations, equalities and the square root
equations
Module 1.2.Teaching methods for exponential, equality, the square root of 2
Chapter 2. Geometry in plane
Content 2.1. Solving plane geometry questions
Module 2.2. Teaching methods for plane geometry
Chapter 3. Vector
Content 3.1. Solving vector equations
Module 3.2. Teaching methods for vector
Chapter 4. Linear function, equation, inequation
Content 4.1. Solving linear function, equality, inequality
Module 4.2. Teaching methods for linear function
Module 4.3. Teaching methods for equation
Module 4.4. Teaching methods for inequation
Chapter 5. Trigonometry
Content 5.1. Solving trigonometric equations
Module 5.2. Teaching methods for trigonometry
Chapter 6. Inscribed angle in circle
Content 6.1. Solving inscibed angle in circle exercises
Module 6.2. Teaching methods for inscribed angle
Chapter 7. Area and volume
Content 7.1. Solving area and volume exercises

Module 7.2. Teaching methods for area and volume problems
Chapter 8. Indices and radical equations
Content 8.1. Solving indices and radical equations
Module 8.2. Teaching methods for indices and radical equations
Chapter 9. Geometry transformations


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Content 9.1. Solving geomrtry transformation questions
Module 9.2. Teaching methods for geometry transformations
Chapter 10. Quadratic function
Content 10.1. Solving quadratic function
Module 10.2. Teaching methods for quadratic function
Chapter 11. Linear equations
Content 11.1. Solving linear equations
Module 11.2. Teaching methods for linear equations
Chapter 12. System of equations and inequations
Content 12.1. Solving system of equations and system of inequations
Module 12.2. Teaching methods for system of equation
Module 12.3. Teaching methods for system of inequation
Chapter 13. Probability and descriptive statistics
Content 13.1. Solving probability and descriptive statistics ecxercises
Module 13.2. Teaching methods for probability
Module 13.3. Teaching methods for descriptive statistics
- The first construction direction: Constructing documents according to the text
form module of the Mathematical program at Lao College of Education with each
module consisting of smaller modules.
- Second construction direction: Building materials according to digitalized
modules. Arithmetic modules include modules and smaller modules.

2.2.2. Structure of modular materials for Secondary school Mathematics in
teacher training colleges Lao PDR
The following is an illustration of the 2 modules: 1 module on teaching method
of algebraic content, 1 module on teaching method of geometrical content used in
teaching Mathematics at secondary schools in Lao PDR:
2.2.2.1. Modular illustration of teaching method of algebraic content
MODULE 4.3
TEACHING METHOD FOR EQUATION
1. module introduction
In Lao’s common textbook, along with the number system extension is solving
the equation in each corresponding set of numbers. The concept of equations is
formed from hidden to explicit.
Equation is a central, fundamental content in algebraic programs at secondary
schools. In the main curriculum as well as in advanced program,
According to Bui Van Nghi (2012), there are some notes about the presentation:
When changing equations, it is recommended to write in the form of propositional
functions, for example: (x - 1) (x - 2) = 0 � x - 1 = 0 or x - 2 = 0. The word "or" is
used with the meaning “equivalent to”.
2. Target of using modules


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* Knowledge
- Definition of linear equation, quadratic equation  with an unknown member and
solution formula
- Equation form equals to linear equation, quadratic one with an unknown
member and corresponding condition
- Vieta's formulas and its applications
- Knowledge of absolute value

- Knowledge of domain of a function
- The identities that need to remember
- Calculation rules with algebraic expressions.
- Solving problems by setting up equations
* Skills
- Skills to make students aware of the dynamics of set of roots in the process of
transformation
- Skills of analyzing both semantic aspects and syntax aspects of equations
- Skills to guide students to represent solutions on the number axis, on the
coordinate plane, on the circle of units
- Practical application of equations in practice: In math textbooks in Laos,
there are not yet many practical problems.
- Skills to systematize forms and methods of solving equations (included in the
program) for students
* Attitude: Students have a sense of serious attitude in learning, selfassessment, good preparation of self-study contents
3. Basic conditions to learn Module subject
* Knowledge in Mathematics: Student learned Mathematics at Secondary
School
* Reference
[1]. Education Department (Laos), Textbook 8, 9 grade, Educational publisher.
[2]. Education Department (Laos), Department of training teachers.
Mathematics syllabus Secondary School, Education of publisher.
[3]. Education Department (Laos), Textbook 8, 9 grade, Educational publisher
[4]. Bui Van Nghi (2014). Teaching methods for detailed contents of
Mathematics. Publishing of Vietnam University of Education
4. The unit should research knowledge
Sub-module 1. Teaching Superlative equations a hidden
Sub-module 2. Teaching Quadratic equations a hidden
Sub-module 3. Notes in teaching equations
THE FIRST TEST

B. MODULE
I. Sub-module 1: Teaching Superlative equations containing a hidden
1. THEORY


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1.1. The equation containing one hidden
1.2. Two equivalent equation
1.3. Equation transformations
1.4. The first equation is a hidden and a solution
2. Exercises
II. Sub-module 1.2: Teaching quadratic equations containing a hidden
1 . THEORY
2. EXERCISES
III. Sub-module 1.3. Notes in teaching equations
Teaching ways to solve equations is to solve Mathematics, therefore it should
be noted some following activities:
- Noting for students to understand the concept, from there, identify and classify
with some types of basic equations
- Noting practice for students have skills to solve the types of equations
discovered and found.
- The most important noting for students to remember some of basic issue of
equations such as, Experimental and experimental experience
- Another note in teaching equations is semantics and syntax. The semantics are
abstract
+) Syntax side, note for students how to use correctly symbols (such as symbols of
equivalence “

”symbols of inferred “

”symbols

- When teaching mathematics by making equations, the teacher should pay
attention to the students to represent the elements of task
- When summarizing at reviewing the content of equations, teachers need to ask or
organize systematic common forms of equations and solutions for students.
C. INSTRUCTIONS FOR REVIEWING
D. FINAL TEST
2.2.2.2. Illustration of module of teaching method of geometric content


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MODULE 2.2
TEACHING METHODS OF THE GEOMETRY ON THE PLANE
1. Introduction to module
In teaching and learning geometry in secondary schools, there are different types
of activities, such as drawing activities,
2. The purpose of the module
* Knowledge
- Activities to prove geometry of the student’s Secondary School
- Teaching and training activities geometric proof for secondary school students
* Skills
- Training geometry proofing activities
- Exploiting, building the system or a number of a form exercises to train skills
to prove geometry for students
- Self-study skills, application of information technology in learning and
research
* Attitude: Positive and actively during both self-study and cooperation

3. Conditions required for learning modules
* Mathematical knowledge: Students learned Mathematics at Secondary school
*Reference
[1]. Education Department (Laos), Textbook 7 grade, Educational publisher.
[2]. Education Department (Laos), Department of training teachers. Textbook
of Mathematics at Secondary School, Educational publisher.
[3]. Education Department (Laos), Textbook 8, 9 grade, Educational publisher.
[4]. Dao Tam (2009). Teaching methods for the geometry at high school
Publishing of University of Education.
[5]. Pham Gia Duc, Pham Duc Quang (2011). Innovative textbook of the
Mathematical teaching methods in secondary schools to establish and develop
creative capacity for students. Publishing of Vietnam University of Education.
4. The unit should research knowledge
Module 1. Some forms of mathematics prove geometry at Secondary school
Module 2. Activities to prove geometry at Secondary school
A. INITIAL TEST
B. CONTENT
Module 1. Some forms of Mathematics prove geometry at secondary school
I. Target
* Knowledge
- Students understand the concept of geometric knowledge, geometric form of
activities and some geometric activities at Secondary Schools
* Skills
- Having capacity analysis some activities that is active geometry, identify,
classify active form geometry


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II. Guide students to self study

Request 1. Students research on material geometric to define some basic
geometric forms of Secondary School students
Request 2. Students exploit textbook materials, Teacher’s Geometry books at
Secondary School
III. Contents
Prove that the two triangles are equal
(2) Proving that two straight lines are equal
(3) Proving that the two angles are equal.
(4) Proving two parallel lines.
(5) Proving three points in line
(6) Proving two perpendicular lines
(7) Proving related to triangle
(8) Identification signs related to quadrilateral
2.3. Using module materials on secondary school Mathematics at teacher
training colleges Lao PDR
2.3.1. For the students
Using module materials on secondary school Mathematics at teacher training
colleges, Lao PDR can be in many forms: self-study completely, self-study under the
guidance of teachers.
When studying with the Mathematics module of Secondary School
Mathematics at the Lao PDR Vocational College, the teacher must carefully guide the
students on the learning method to achieve the highest efficiency.
The principle of learning with modular materials must ensure 3 contents: (i)
Individualized learning; (ii) Improve students' learning motivation
2.3.2. For the lecturer
In addition to the advantages, there are still many limitations in the modular
Mathematics materials for Secondary School, such as the time teachers have to spend
a lot of effort in collecting documents as well as choosing the knowledge part in the
process of building modules.
Besides, the materials according to the Mathematics module of Secondary School

have been built based on the characteristics of Mathematics students
With this teaching method, the teacher can only teach some lessons in the
classroom training program, the rest of the lessons, the teacher assigns students to go
home for self-study and self-study in the form of assigning tasks to students.
The most important and decisive step in the teaching process is effective learning.
In order to learn effectively accordance with module materials, based on the practical
process of students 'self-study as well as teachers' classroom teaching process.
2.4. Conclusion of Chapter 2
On the basis of theory and practicability presented in chapter 1, we have analyzed the
position and content of Mathematics at secondary school. Develop and give forms of


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using modules according to modules to contribute to practical skills for students of
Lao’s pedagogical colleges.
CHAPTER 3
EDUCATIONAL EXPERIMENTS
3.1. Experiential target
Educational experiment is conducted to test the feasibility and effectiveness of the
materials according to the module developed in the dissertation and the materials in
the teaching process in order to teach teaching methods of detailed content in
Mathematics at Secondary for Laos Teacher training College students is more
effective in self-study,
Educational experiment is conducted via 2 steps with responsible detail
following: Educational experiment the first in order to test the effectiveness of the
materials by modules for Laos Teacher training College students
3.2. Object, location and implementation time
Educational experiment research contents of the dissertation were conducted
during a year from the 2017-2018; 2018 - 2019 the academic school years with the

following tasks and locations
The first in 2017 - 2018: Experiment of exploring the teacher’s for comments and
evaluations and students who are learners and study results on compiled documents
The object is the junior students who have studied and are studying the part of
the Mathematics at Secondary in Ban Keun Teacher Training College. Classes
organize experiences and competitions according to the actual year or the previous
year of the school.
Experiment and Control Class
No.

School years

1

2017 - 2018

2

2017 - 2018

School
Ban
Keun
Teacher
Training College
Savannakhet
Teacher
Training College

Class of

experiment

DC Class

K5A1

K5A2

K3B1

K3B2

3.3. Contents of experiment
To deploy experiments in two directions:
- Using the materials accordance with modules under text form or digital form to
help students learn by themselves.
- Use material accordance with modules to support teachers' teaching in the
classroom. Round 1 organization teaches with 2 modules including: equation and


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Geometric in plane teaching methods;
How to proceed as follows
- For the experiment group: Students self-study Mathematics at Secondary
through module materials and complete the tasks of learning in the form of using
materials according to the module mentioned in Chapter 2.
- For the Control group: We organize for students study by themselves in the
usual way such as, studying according to the notes, the teacher’s words, according to
the curriculum and the materials reference.

Case studies content in the use of module materials: Tracking the self-study of
the Mathematics at Secondary of typical students group.
3.4. Experimental methods of education
- Methods of investigation: Giving survey forms for selected the Mathematics
Teachers and Students of Teachers training College to collect information around the
exploitation and using of the module materials on Mathematics teaching methods in
Mathematics for Secondary students.
Observation method: how students use materials by the module on teaching
methods of detailed content of the Mathematics Secondary outside class hours.
Monitoring the process of self-studying Mathematics of secondary with
materials according to modules of a group of students with different levels of
awareness, belonging to the experimental group during the educational experiment to
assess the progress of students on self-study
- Based on the activities of students through the pedagogical lessons, analyzing
the learning process of students in general, the self-study process in particular.
We evaluate the learning results by a scoring scale (a 10-grading scale) divided into 4
levels as follows:
+ Very good : 9,0 – 10
+ Good: 7,0 – 8,0
+ Average : 5,0 – 6,0
+ Weak: under 5,0
Through the survey results, we research, synthesize, analyze data and assess
the feasibility and effectiveness of the using of the module material contribute to
fostering teaching methods the specific contents Mathematics at Secondary for
Students
3.5. Result of experiment
3.5.1. Result educational experiment round 1 (semester 1, 2017 – 2018)
- Content 1: Organizing for students self-study accordance with module
materials to check the feasibility of documents.
+ Experiment of group: Organizing for students self-study with 2 module

(Teaching methods equation; Geometric teaching methods on the plane) in two
directions
+ Control group: Organizing for students to study in the usual way.