Thiết kế tình huống dạy học các học phần phương pháp dạy học môn toán cho sinh viên đại học ngành sư phạm toán theo hướng tiếp cận năng lực thực hiện tt tiếng anh

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INTRODUCTION
1. Justification of the study
The Resolution of the 8th Central Conference of the 12th term on the
fundamental and comprehensive innovation of education and training emphasized
"... Strongly shifting the education process from mainly equipping knowledge to
comprehensively developing capacity and quality of learners, etc. Thus, universities
need to form and develop the necessary competencies for students in the training
process so that students can achieve professional competence in their teaching.
University graduates must integrate, adapt and meet the requirements of the society
and life.
Currently, implementation capacity training is becoming a popular trend in
the world. This method has been researched and implemented effectively in many
countries around the world such as the US, UK, Australia, etc. In Vietnam, some
schools have started to apply implementation capactity in training, however, the
application is difficult due to the lack of a theoretical system based on
implementation capacity.
In the field of Math teacher training in Vietnam within the implementation
capacity approach, there are also some related research and books such as those by
Tran Viet Cuong (2012), Nguyen Chien Thang (2012), Do Thi Trinh (2014), Tran
Trung, Tran Viet Cuong (2014), Bui Van Nghi et al (2016), Le Thi Tuyet Trinh
(2017), Le Minh Cuong (2017), etc. However, we have not found any Ph.D
dissertation focusing on implementation capacity development for students in the
Pedagogical school. This is also a gap that needs to be exploited, explored and
given opportunities for theoretical and practical contributions.
Survey on actual training of Math teachers at universities, especially in the
current situation of training under the credit system, it is clear that the situation of
training teaching skills for students is still not systematic, lack of in-depth contents ,
the time students spend on lesson planning, teaching practice is little, the process of
practicing practical skills, practice in high schools is still limited. Most teacher
training universities have not yet built up the process of training teaching skills for

maths for students, practical activities for students are not adequate.
From the above reasons, the author chose the topic: "Designing the
teaching situations of Math teaching method modules for Math teacher students
at universities within the implementation capacity approach" as the PhD
dissertation in education science.
2. Research aims: Designing some teaching situations to develop teaching capacity
for students of Mathematics major; organizing teaching according to the situations
designed in instructing math teaching methods at the university within the
implementation capacity approach to contribute to improving the quality of teacher
training at universities currently.
3. Subjects, objects and scope of the research
3.1. Subjects of the study: Some situations of math teaching method modules at
universities based on implementation capacity approach.
3.2. Object of research: The process of teaching the modules of math teaching
methods at universities based on the implementation capacity approach.
3.3. Scope of the research: The research was carried out at the following
universities: Hanoi Pedagogical University, Pedagogical College - Thai Nguyen


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University, Hanoi Pedagogical University N02, Tay Bac University, Vinh
University, Hong Duc University, Tay Nguyen University, Dong Thap University.
4. Scientific hypothesis: It is possible to practice and develop the implementation
capacity for math teacher students in teaching theory and math teaching method
modules through using situations because the implementation capacity can be
formed and developed through individual and groupwork activities of students
under the organization and support of teachers.
5. Research task
5.1. Studying the theoretical background of math teaching methods of Maths
at universities to train teachers in the implementation capacity approach

5.2. Surveying and assessing the situation of teaching the math teaching
method modules at universities which train teacher students in the direction of
implementation capacity.
5.3. Designing and organizing teaching activities based on the designed
situations in math teaching method modules at universities within the
implementation capacity approach.
5.4. Conducting pedagogical experiment to assess the feasibility and
necessity of designed teaching situations.
6. Research questions
- On what theoretical background does Math teaching method situation
designing based on implementation capacity approach rely on?
- What is the current status of teaching Maths teaching method modules at
universities to train teachers within the implementation capacity approach?
- What procedures are the situations of teaching Maths teaching method
modules at universities based on the implementation capacity approach designed
and implemented?
- Can the teaching of Maths teaching method modules at universities based
on the implementation capacity approach as the proposed procedure mentions
ensure the feasibility and necessity?
7. Research method
7.1.Theoretical research
7.2. Practical methods
7.3. Experimental method
8. The significance of the thesis
- Identifying the current situation of teaching Maths teaching method
modules at universities within the implementation capacity approach at the current
teacher training universities.
- Building a capacity framework, criteria to evaluate the performance of
university students in Math Pedagogy, including 9 skills and 5 levels.
- Developing the structure of 3-part teaching situations, with 5 characteristics

and proposing 6 principles to ensure the consistency of teaching situations.
- Designing and organizing the implementation of 4 situations in teaching
modules of Math teaching methods to develop implementation capacity for
university students in Math Pedagogy.
9. Design of the dissertation
In addition to the Introduction and Conclusion, the dissertation consists of 3
chapters:


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Chapter 1. Literature review
Chapter 2. Designing situations of Maths teaching method modules at
universities within the implementation capacity approach at universities
Chapter 3. Pedagogical experiment
References and appendices.
CHAPTER 1: LITERATURE REVIEW
1.1. Overview
1.1.1. Previous research in the world
The definition of competence should be viewed as a holistic concept – a
dynamic combination of knowledge, understanding and skills (or in Vietnam
competence is now regarded as a combination of knowledge, skills, attitudes and it
is reflected through activities). There are various definitions of the concept of
competence. González and Wagenaar (2005) defined competence as " something
that can be demonstrated to a certain level of achievement along a continuum" or
Rychen and Salganik (2003) considered competence as “the ability to meet complex
demands, by drawing on and mobilising psychosocial resources in context – i.e. a
complex action system encompassing knowledge (also tacit); cognitive and
practical skills; attitudes such as motivation, value orientations, emotions”.
According to Koster and Dengerink (2008), competency can be defined as the
combination of knowledge, skills, attitude, values and personal characteristics,

empowering the teacher to act professionally and appropriately in a situation,
deploying them in coherent way.
Many other international scholars have agreed and shared the
aforementioned definitions. They believe that competence - as the basic
requirements for teaching - articulated in knowledge, craft skills and dispositions.
Such definition focuses on the potentialities of continuous development and
achievement, associated with aims and objectives in a lifelong learning perspective,
and it specifies requirements for each of the three areas. The recent review by
Williamson et al. (2008), which sums up relevant existing studies, mentions the
following features in the knowledge area: subject matter knowledge; pedagogical
subject knowledge (for example, Math); pedagogical knowledge (in general);
curricular knowledge, educational sciences foundations (intercultural, historical,
philosophical, psychological, sociological knowledge); contextual, institutional,
organizational aspects of educational policies; issues of inclusion and diversity; new
technologies; developmental psychology; group processes and dynamics; learning
theories, motivational issues; evaluation and assessment processes and methods.
Deakin Crick (2008) proposed the definition of competence as a complex
combination of knowledge, skills, understanding, values, attitudes and desire which
lead to effective, embodied human action in the world, in a particular domain.
Weinert (2001) simply considered competence as the capacity and cognitive skill
that is inherent in individuals or can be learned to solve problems in life.
Gharajedaghi (2006) defined competence as a combination of psychologicalphysiological factors, knowledge and skills of each individual that bring high
efficiency in resolving specific situations. By the end of the 20th century, John
Erpenbeck stated that the basis of competence is knowledge that is used as the
ability defined by value, strengthened by the experience and implemented through


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the will". According to A. N. Leonchev, “competence is a personal characteristic
that regulates the successful implementation of a certain action.

1.1.2. Previous research in Vietnam
According to Nguyen Van Giao (2001): "Competence - defined as capacity is built up and developed to allow a person to succeed in a physical, intellectual, or
professional activity. The capacity is performed through the ability to perform an
activity or do a task ". Nguyen Vu Bich Hien et al. (2015) supported the idea that
"competence can be understood as the ability to fullfill the task or work
performance that is proven through the actual results of activity and it involves
knowledge, skills, attitudes and personal characteristics"; Pham Minh Hac thought
that "competence is a combination of the psychological characteristics of a
human/personality". Bernd Meier and Nguyen Van Cuong (2014) viewed
competence as the synthesis of knowledge, skills, as well as perspectives and
attitudes that an individual managed to act successfully in new situations. Defined
in the Psychology Dictionary by Vu Dung (2000), "competence is qualities of
personal psychology with a role as an internal condition, facilitating the
implementation of a certain activity". According to Nguyen Thi Kim Dung et al.
(2015): "Competence is the combination of knowledge, skills, attitudes and personal
experience enabling a person to take responsibilities, act effectively, carry out all
tasks, and solve problems in various professional, social, or personal situations".
Although the aforementioned definitions are different, there are some
common perspectives among them and they can also be separated into two types of
concept:
Firstly, in terms of psychology, competence is considered as a psychological
attribute or a personality trait. Secondly, the competence is included and displayed
through skills. Each type of competence is analysed and shown in the form of
specific skills, and different levels of performance will present different level of
competence development. In this way, the competence can be developed and trained
through skill training; Competence can be professionally developed and be reflected
not only in knowledge but also in skills and specific activity. Therefore, it is
necessary to evaluate the competence through practical activities; to be specific, it
can be measured and assessed through skill evaluation.
In regard to training Math teachers, there are research works on the training

of teaching method such as: research by Nguyen Duong Hoang (2008) focused on
the issue of organizing teaching and learning activities for subjects of mathematics
teaching methodology to enhance the training of teaching skills for students, in
which the author presented a fairly profound representation of teaching skill and
proposed solutions aimed at organizing and improving the effectiveness and quality
of the teaching method training through teaching math teaching method-related
subjects. The study of Pham Van Cuong (2010) presented issues relating to skills,
teaching skills, builded up (proposed) standards of mathematics teaching skills for
students majoring in primary education, and proposed solutions to train
mathematics teaching skills for elementary education students.
In 2012, Nguyen Chien Thang proposed the basic components of
professional skills that need to be trained in the process of studying in the university
through teaching the courses of primary mathematics and mathematics teaching
methods in the university (including 9 skills); the author pointed out: "Measures to


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train some of the fundamental skill-related components for undergraduates
specilizing in mathematics pedagogy through teaching mathematics at elementary
level and mathematics teaching methodology at university level". It can be seen
that, by approaching the professional skills of mathematics teachers, Nguyen Thang
has proposed a system of measures more reasonably. However, the study of skills or
professional skills should be approached in a more modern, insightful and
comprehensive way.
In the study, namely "Development of Math teaching competence for
students in pedagogical colleges” by Do Thi Trinh (2014), the author considered
students’ competence of teaching math includes: the ability to understand students
in the process of teaching and education, teachers’ knowledge and understanding;
capacity to processing learning materials; capacity to master teaching techniques;
and language proficiency. According to the author, teachers’ competence includes

components of competence: preparatory competence and competency. The
preparatory competence is considered as “choosing reference documents”,
identifying "requirements for knowledge, and teaching skills"; predicting situations
and providing solutions”.
The study of Tran Viet Cuong (2012) also aimed to "contribute to training
pedagogical competence for students at Faculty of Maths but approached in the way
of organizing project-based teaching and learning for the course of Math teaching
methodology (specific content). The author has presented solutions to develop
students’ teaching competence by organizing project-based learning.
The concept of competency is fairly new in our country; however, if training
teachers’ teaching skill is considered a core measure to enhance the competency for
pedagogical students, there are a number of studies by scientists who have
investigated, synthesized and introduced a relatively diverse skill system. During
the process of teacher training, it can be seen that there are two approaches in
training, which are clearly presented, and are currently in use:
Trend 1. Focusing on training scientific knowledge and pedagogical
knowledge (a system of subjects and credit points for such content account for the
majority in the training program); Actively preparing for the formation of
professional skills for teachers.
Trend 2. Approach to vocational training, i.e. focusing more on the formation
and development of professional skills along with the preparation of scientific
knowledge and pedagogy. It can be understood that this approach focuses on the
development of the competency.
The author presents some research on the issue of vocational training in
competency-based eduction as a trend in vocational training, in which teacher
training is one of the professions of society. This trend will impact on program
design, learning outcome standard, training content, structure of training content,
form of training and testing, assessment during the training process. In addition, it
has the impact on teachers’ teaching method, teaching materials and textbooks,
interaction between teachers and students during the process of training.

Dang Thanh Hung (2006), based on the results of previous research of the
authors, such as Saransev (1998), Makhmutov (1975), Lerner I. Ia (1974), Allan C.
Omstein (1990), introduced important technique groups for teacher as questioning
techniques, behavioral techniques, in-class speaking techniques, blackboard


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presentation techniques. Nguyen Duc Tri (1993) presented the basic issues of
vocational training with approach of implementation competence. Subsequently,
Nguyen Van Tuan (2008) has systematically presented training issues in
competency-based education, clarified the concept, theory framework, advantages,
limitations, and especifically indicated the difference between training in
competency-based education and convention training. There are also some other
studies on the issue of competency-based training of Nguyen Huu Lam (2004),
Dang Ba Lam (2006), Dinh Cong Thuyet et al. (2008), etc. However, these works
only presented theoretical framework of the vocational training model, the
competency-based model or the competency. Pedagogically, there are some studies
on the issue of competency-based vocational training as: the research by Nguyen
Ngoc Hung (2006) on the issue of vocational training for technical pedagogical
students, and the study by Vu Xuan Hung (2011) on the training of teaching
capability for technical pedagogical students in pedagogical practice also followed
the competency-based approach.
1.2. Pedagogical competence of mathematics teachers in high schools
1.2.1. Teachers’ pedagogical competence
As mentioned, pedagogical competence must be assessed through the results
of successful implementation of pre-defined teaching objectives. Thus, presenting
structure of teaching competence need to approach learning process and teaching
objectives.
Although there are many different perspectives, analyzing mathematics
teachers’ professional knowledge canbe divided as follows: content knowledge,

teaching knowledge, psychological and eductional knowledge, organization,
consultation knowledge. They are specified as follows:
The Organisation of the National Professional Standards for Teachers has
launched national professional criteria for teachers.
Minister of Ministry of Education and Training issued Circular No.
20/2018/TT-BGDTEL dated 22/8/2018 on professional standards of teachers in
secondary schools, and teacher evaluation with standards includes basic content
with 5 standards and 15 criteria.
1.2.2. Pedagogical competence based on students’ learning outcome standard
Some standards of learning outcome for pedagogical students have been
introduced in some foreign and Vietnamese institutions:
The learning outcome standard was announced by the Victoria Institute of
Teaching, Austrailia, which used the Australian teacher professional standards to
evaluate teacher, and also regarded as students’ learning outcome standards. This
problem was also clarified by Nguyen Thi Kim Dung et al. (2015).
New Zealand's teacher council have built learning outcome standards based
on the professional standards for teachers to meet the quality of graduates from
various teacher training programs. The learning outcome standard for the German
pedagogical students includes four sectors (teaching, education, assessment,
innovation) and 11 types of competence that are specified into standards. The
Singaporean teacher competence framework identifies the following elements:
occupational practice; cooperative and managerial relations; personal management.
According to the Dinh Quang Bao et al. (2016), the learning outcome
standard for pedagogical competence includes 5 types of competence and 28


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criteria; 5 types of competence are: teaching competece; educational capacity;
orientation competence of individual development; competence to develop
vocational community and society; individual development competence.

1.2.3. Relationship between professional standards for teachers and learning
outcome standards in teacher training
According to Dinh Quang Bao (2016): " Professional standards for teachers
often describe the competence at the skill and technique level of implementing a
certain task, while pedagogical competence for graduates should be perfomed in
their professional knowledge with indicators of both the knowledge and the skills
performing the task. " Thus, it can be understood that pedagogical students must
achieve the lowest level of the professional standards for teachers after graduation
or students can reach higher than the required level of some criteria.
The compatibility between the professional standards for teachers and the
learning outcome standards in the teacher training is both necessary and dialectic.
The learning outcome standard can be based on the professional standard for
teachers in general. On the other hand, it can be based on movement and change of
educational system. In general, the professional standards for teachers tend to be
more backward than the learning outcome standard because they are often
dominated by administrative regulations.
As aforementioned, in this dissertation, the author fouces on students’
teaching competence rather than concentrates on education competence (through the
subject), personal development competence, and social and professional community
development competence of student teachers. Moreover, towards the competency,
which is manifested through the results and process of actvities, the author uses
"skills" to describe and evaluate the students’ competency. Although competence of
using information technology during the process of teaching is shown in
curriculum, the author does not focus on training such the competence when
conducting this research.
Furthermore, in the process of teaching subjects relating to mathematics
teaching methodology, teachers apply activities to help their students develop
professional competence, teaching competence in general or competency.
1.3.Competency of mathematics pedagogical students
1.3.1. Competency

If competence is the standard that each individual needs to have to do a task,
that is, what task demands, competency is what individuals have to do a task well.
The term is translated into Vietnamese as competency. In Vietnamese-language
materials, based on research and analysis of many reliable international sources, B.
Meier and Nguyen Van Cuong (2014) defines "Competency, in terms of
professional competence, is the ability to effectively and responsibly do tasks and
solve problems in the professional, social, or personal fields on the basis of
knowledge, skills, techniques and experience as well as the willingness to act.
There are four types of skills of competency relating to professional
activities, including: skills to carry out specific and distinct job; management skills
of work; management skills of incidents and acting skills in the working
environment.
Therefore, the author believes that teachers’ competencies should be
presented through knowledge, attitudes and key skills including skills of program


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analysis and design of learning materials; teaching skills. Therefore, the author
basically agrees with the research on the competency and the main component of
the competence is skills. Moreover, in the process of teaching, testing and
assessment, the author focuses on the teaching skills rather than concentrates on
teachers’ attitudes. Although the author still agrees with Shian Leou (1998)
presentation, the thesis will present in more detail about skills and components of
skills of the competency.
1.3.2. Mathematics students’ competency
In the author’s opinion, it is possible to define skill components of math
teachers’ competencies as follows (based on teaching competency assessment items
for school Mathematics teachers by Shian Leou (1998):
Table 1.3. Group 1 – Skills of program analysis and learning material design
Components of

skills
1.1.
Analyze
program, especially
define
teaching
objectives

Code

Descriptions (criteria)

1.1.1

Analyze the scientific base of teaching to draw out
experience and self-study in the teaching process

1.1.2

Define the teaching objectives based on program and
textbooks (competence of analysing program)

1.2.1
1.2. Plan proper
contents and good
organization (Skills
of designing teaching
plan)

1.2.2

Arrange proper materials in order to create students’
cognition and learning ability.
Design a teaching plan effectively

1.2.3

Rearrange lessons based on the content and learning
activities

1.2.4

Predict the suitability of lessons based on the teaching
content and learning activities

Table 1.4. Group 2 – Teaching skills
Components of
skills
2.1.Present
effectively

lectures

Code

Descriptions (criteria)

2.1.1

Instruct contents correctly

2.1.2

Give
handouts/notes
understanding

2.1.3

Apply teaching methods effectively

2.2. Help students 2.2.1
understand
the
connection
and 2.2.2
application
of
mathematics
2.2.3
2.3. Clearly point out 2.3.1
the
learning
objectives
and
2.3.2
procedures for each

to

enhance

students’

Help students understand the connection between math
concept
Stress the connection between math and other
disciplines
Stress the application of math to life
Show the aims clearly before teaching
Inform students the main learning procedures for
topics (chapter, unit, etc…)


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Components of
Code
skills
topic
(subjects,
lessons, etc.) to 2.3.3
students
2.4. Choose proper
teaching strategies 2.4.1
which will help
students grasp the
2.4.5
mathematics
concepts
2.5.1

2.5.Lead
students
into some deep 2.5.2
thinking
2.5.3
2.6.
Explain
2.6.1
students’
misconception
at
2.6.2
right time
2.7.1
2.7. Apply teaching
2.7.2
activities effectively
2.7.3
2.8.1
2.8.
Evaluate
teaching assessment
2.8.2
in each period to
make a necessary
change to meet the 2.8.3
learner’s ability
2.8.4
2.9.1
2.9. Be able to

2.9.2
express idea clearly

Descriptions (criteria)
Present learning objectives and contents of each topic
Apply effective teaching strategies reflecting different
contents and features
Apply proper teaching strategies related to students’
learning ability and understanding
Give proper questions to students leading to clear
thinking
Use related materials to help them do positive thinking
Offer thinking process to help students do mathematics
creation
Give clear explanation when students misunderstand
Clarify the confusing ideas for students
Arrange the procedures and pace for each class
Math the teaching situation and arrange the order of
activities
Give a complete conclusion when a topic has been
completely taught
Understand students’ background through proper
evaluation through teaching process
Give a quiz to test learner’s understanding during the
teaching proceedings
Give a complete test at the end of a finished lesson
Record student assessment during and after a fisnished
lesson
Use the right terms indicating the concepts of
mathematics

Give lectures in a logical order

2.9.3

Teach lessons with normal speed and voice

2.10.1

Have ability to draw correct charts and graphics for
teaching purposes

2.10. Board-writing
2.10.2
skills
2.10.3

Be responsible for neat writing
Arrange contents on board properly


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1.4. Designing teaching situations for the subjects related to mathematics
teaching methodology in order to enhance students’ competencies
1.4.1. Teaching situations in teacher training at universities
In this thesis, the author conceptualizes that the teaching situations (in
teacher training) contains activities that are designed for students to study and
practice. The thesis basically bases on theory about professional education towards
competency-based education as an important basis in designing teaching situations.
Traditional method of teacher training focused on content which demanded
to train experts in each field. This resulted in content-based education, including the

content (mathematics) and pedagogical knowledge (T. Kleickmann et al., 2012).
Such these experts can hardly meet the requirements of teaching in the context of a
knowledge economy, which "teaching force must be prepared to respond to
complex approaches, to continually innovate, and to meet regular reforms in
education "(Gatlin, D., 2009): Learning opportunities to assess knowledge are
increasingly expanding; the orientation of educational philosophy basically
develops learner’s competence in which knowledge and learning experience is
completely insufficient (Jones et al., 2002). Professional training in general and
mathematics teacher training in particular is gradually directed to competency-based
education (CBE).
In training teachers, there are important teaching strategies that have been
discussed in the studies, such as: video analysis, microteaching. project-based
learning, role-play, etc.
1.4.2. Teaching situations aiming at developing mathematics pedagogical
student’s competency
From the aforementioned studies, the requirements of each teaching situation
in order to enhance pedagogical student’s competency as follows:
- The situation must require students do simple or complex activities in order
to practice their skills and mainly develop a specified teaching competence.
- The situation must ensure that there are enough activities for students to
self-study and cooperate with each other in the implementation process.
- The structure of each teaching situation will consist of three parts: opening,
content, assessment.

Opening

Teacher’s activities
Divide students into groups
or individuals to assign
tasks

Students’ activities
Groups, individuals take on
the tasks

Support, observe, check and
assess the the teaching and
learning process

Work individually or work
in groups to fullfil the tasks

Organize the report or
presentation of results or
practice and application

Report, present the results of
the tasks, practice and apply

Content


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Assess and give students’
Draw on experience and
feedback to help them revise
Assessment
complete the results of the
and
complete

the
tasks
report/presentation
Diagram 1.2. Common structures of each teaching situation to enhance
mathematics student’s competency
In this thesis, the author presents some common features of a teaching
situation in order to improve student’s competency as follows:
First, students’ physical or mental activities with the effort to do
professional-related tasks (in teaching practice at schools) is the focus of every
teaching situation.
Second, the author organizes teaching situations with theoretical and
practical requirements at the same time for students to deal with while teaching all
subjects. In response to each teaching situation, there are different tasks and
requirements of the knowledge and skills. Therefore, each situation varies, and
students are required to simultaneously study the theory and practice when
implementing the activities.
Third, self-studying is fundamental in every situation.
Fourth, cooperation learning activities and research are mandatory, frequent
and are one of criterion to evaluate students.
Fifth, the author encourages students to use computers, Internet, social
networks, etc. to efficiently exploit, process, and transform information to perform
assigned tasks in each group, each situation.
The author recommended the following principles in order to ensure
consistency and effectiveness of teaching situations:
First, situations should have a consistent structure which clearly clarifies
teacher and student’s main activities and students plays a major role in the process
of training and developing the competency.
Second, the situations must be organized during or after teaching subjects
related to math teaching theories and method.
Third, the situations will possibly take place in the classrooms at high

schools or in other places, such as pedagogical competition, contest, self-study at
home, etc.
Fourth, the knowledge that students have learned, including the knowledge
of skills and teaching competence, must be detected, debated and seft-studied by
students.
Fifth, teaching skills must be trained and formed in the situations.
Sixth, each situation must include students’ self-assessment and teacher's
assessment.
1.5. The reality of developing the competency for university student
specializing in mathematics teaching through the subjects of mathematics
teaching methodology
1.5.1. Subjects of math teaching theories and methodology in the pedagogical
school
In general, the proportion of credit points in math teaching methodology
accounts for 12,9% to 13,3% in reputable teacher training institutions. There is no


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big difference between content and percentages compared to the total number of
credits. However, the author thinks that the course of "Math program and textbook
in high school" (in the framework of Vinh University's Mathematical teacher
training program) plays a necessary and important role. Two other subjects are
"Quorum and Analysis teaching methodology", “Geometry teaching methodology"
as in the design and description (in the framework of the mathematics teacher
training program of Vinh University and Hong Duc University) are very practical
for students after graduation. Furthermore, these two subjects help students practice
their teaching skills associated with teaching content.
There is the course of Practicum in the training programs; however, the
author thinks that, in the teaching process, the subjects related to mathematics
teaching methodology must develop student’s competence, and well prepare good

conditions, and improve important skills for students to develop and continue being
trained in pedagogical internship process.
1.5.2. The survey results on the reality of teaching the mathematics teaching
methodology courses in competency-based education
- Survey objectives: to assess the perspectives of the teachers who are
training mathematics pre-service teacher at some pedagogical universities on
student’s competency; measures to develop student’s competency
- Survey subjects: 66 teachers who have been teaching the courses of
mathematics teaching methodology in several universities.
- Survey results:
Relating to assessing the importance of the components of skill of the
competency, the results show that the majority of teachers evaluated the skill of
program analysis, especially defining the teaching objectives (1.1) and skill of
planning and arranging content and organizing proper teaching (1.2) are equally
important although they evaluate the skill 1.2 is more important than the skill 1.1.
The results of the survey also reported that the teachers evaluated the
components of skills as shown earlier at the necessary and very necessary levels.
However, fewer teachers thought the skill 1.2.3. was an important skill.
The results of the survey on the importance of teaching skills: the majority of
teachers stated the skill of choosing the proper teaching strategies to help students
understand the concepts of mathematics (2.4) and lead students to positive thinking
(2.5) are the most important. The second place is for the groups of skills 2.1; 2.6;
2.8; to evaluate the role of activities stating the objectives and programs (plan) of
learning for each topic (subject, chapter, lesson, etc.) for the students (skill 2.3), the
teachers are less concerned about helping the students grasp the lesson objectives,
the activities’ objectives, or the chapter’s objectives before the teaching process.
Similarly, the teachers did not appreciate the role of helping students
understand the connections between concepts and the application of mathematics
(Skill 2.2) (6th place). This can be explained that the time devoted to learning and
understanding the concepts is much less than that of organizing activities for

students to solve math exercises. Doing math exercises will contribute to helping
the students understand the concepts or the use of concepts.
From the synthesis of the teachers’ assessment, the author has readjusted the
skills of competency for math teachers in the following table


13
Table 1.8. Description of mathematics pedagogical students’ competencies
No.

The components of
skills

1

Analyze
program,
especially
define
teaching objectives

2

Plan proper
contents and good
organization (Skills
of
designing
teaching plan)

3

Present
effectively

4

Help
students
understand
the
connection between
new
and
old
knowledge as well as
its application

5

6

7

lectures

Clearly point out the
learning objectives
and
procedures

(plan) for each topic
(subjects, chapters,
lessons, etc.) to
students
Choose
proper
teaching strategies
which will help
students grasp the
mathematics
concepts

Indicators
- Write down the teaching objectives;
- Analyze textbook, workbook, teacher book to present the
teaching objectives;
- Clearly and exactly define the teaching objectives and
provide descriptions (examples, tests, etc.) in comparison
with program and other subjects.
- Make basic teaching plan (structure, content, procedures,
etc.);
- Design teaching plans in details with new ideas;
- Specify (interprete) why the organization of knowledge
and activities based on designed procedures;
- Design the teaching plan well: to deeply identify teaching
ideas, cognitive barriers, difficulties and support measures
for the teachers in the teaching process.
- Instruct contents correctly in accordance with the
designed lectures (basic activities, time, etc.);
- Combine contents and types of lessons in classes; flexibly

use and combine instruction forms (even board-writing
skills)
- Help students understand, classify, and arrange the
concepts and the learned knowledge with new knowledge
and start connecting the lesson knowledge and other
knowledge;
- Organize and support students to create knowledge, the
learned knowledge with new knowledge, help the students
connect the knowledge of lessons with other knowledge (in
mathematics, other subjects, in practice);
- Introduce the learning objectves of lessons to students;
- Help students define objectives for each lesson, each
chapter or each topic;
- Organize and support students to understand and define
the learning content and objectives for each lesson, each
topic, and each chapter.
- Appy proper teaching strategies and method in order to
help student understand the mathematics concept clearly;
- Build up proper teaching strategies with the lesson
content and students.

- Organize some activities that help students do some basic
thinking during the learning process;
- Organize the teaching process leading students to positive
Lead students into
thinking to solve mathematics problems;
some deep thinking
- Organize activities that require students to activily think
and do thinking to solve problems during the learning
process.

14
No.

The components of
skills

8

Explain
students’
misconception
at
right time

9

Assess
learning
outcomes to make
necessary adjustment
to meet students’
competence

Indicators
- Give clear explanations when students raise questions and
miscunderstand;
- Anticipate, actively detect, and explain the cause of such
misunderstanding and difficulties and support the students

when there are mistakes, difficulties at right times and in
the proper way.
- Draw on experience after each lesson;
- Evaluate, and adjust in-class teaching activities during the
teaching process;
- Make plan professionally to evaluate students before,
during, and after the teaching process in class; proactively
adjust the in-class supporting activities for studnents.

In order to develop the competencies for students specializing in math
teaching, the author concluded that it is necessary to train 9 groups of skills in the
process of teaching the courses of mathematics teaching methodology.
Survey on the feasibility of a number of organizational techniques of
teaching to develop the competencies for mathematics pedagogical students pointed
out that teachers primarily evaluated 4 forms of teaching organization
(microteaching; program analysis, especially determining the teaching objectives;
design of teaching plans and analysis of teaching practice (video analysis)) that are
necessary and feasible. Moreover, due to the reform of the current teaching
program, the author believes that the organization for students to design some
specialized courses in teaching mathematics will contribute to helping children with
documentation for the development of the school program, the future classroom
program, and develop the competency of program analysis and design a teaching
plan. Therefore, these activities will be researched, integrated, and experimented in
Chapter 2.
CHAPTER 2. SOME TEACHING SITUATIONS OF MATHS TEACHING
METHOD MODULES AT UNIVERSITIES WITHIN THE
IMPLEMETATION CAPACITY APPROACH
2.1. Building up situations
2.1.1. Situations focused on developing some component teaching competencies
in implementation capacity: The proposed situations must create an environment

and enough conditions so that students have opportunities to train and develop their
teaching competencies .
2.1.2. Follow the objectives and contents of the Math teacher training
curriculum: The organization of situations must always ensure and aim at the goal
of training Math teachers.
2.1.3. Ensure feasibility and effectiveness: Situations are built in the context in
conformity with the current requirements and regulations of the teacher training
institutes, under the regulations of the Ministry of Education and Training, it must
also come from the Teacher training reality, required training outcome or the
requirements for teachers' abilities, from students’ awareness level, difficulties,
obstacles, and advantages, from the strengths and shortcomings of students.


15
2.1.4. Ensure the systematic and logical characteristics: Situations need to be
systematic and logical in a certain level of flexibility. That is to say, designed
situations must take into account the conditions , procedure, contents and timing of
implementation, ...
2.2. Some situations of Math teaching method modules to develop
implementing capacity for students
2.2.1. Situation 1: The teaching situation of program analysis and designing
teaching agendas for students
In this situation, we focus on training students for some important activities
in designing active teaching situations: Determining teaching objectives; designing
knowledge discovery and creation activities; operational requirements to assess the
implementation of teaching objectives.
2.2.2. Situation 2: The teaching situation of video analysis of teachers' math
lessons in high schools
The process of video analysis consists of three steps as follows:
- Step 1: Determining teaching objectives.

- Step 2: Observing teaching and learning activities from videos.
- Step 3: Evaluating the advantages and disadvantages, proposing ways to
adjust and draw out knowledge of designing and implementing teaching plans.
2.2.3. Situation 3: Micro-teaching practice of some contents of Mathematics
course: The micro-teaching situation is organized to help students practice basic
teaching skills in class. Teachers organize "mini lessons" for students to teach in a
small class, of which from 5 to 10 students play the role of secondary students. This
approach helps students practice teaching in a less challenging learning
environment. Micro teaching is considered as an effective form of teaching in the
initial training for teacher students so that they can grasp separate skills, forming the
component competence of the teaching profession. Micro teaching is actually the
teaching in which the complexity of teaching in normal classrooms is simplified to
focus on training students to complete skill exercises, at the same time to enhance
the practice supervision and collect information in time.
For example. The lecturer divides the class into 04 groups, asks the groups
to implement the following requirements: Each group selects a conceptual teaching
content below, the teacher requires the groups to carry out within one week,
planning teaching agenda (one phase), sending it in advance to the lecturer via
email, trying it out in a maximum period of 30 minutes, video recording (selfrecording group), submitting the video to the lecturer (after submitting the lesson
plan), the class will meet in the lab, giving comment on teaching concepts, the
implementation of teaching activities in class (based on the videos).
Step 1. Planning: Individual Students and groups design a lesson phase.
Teaching plans are in the following forms:
Form 1. Idea of conceptual teaching of the Number sequence with limit 0
(Mathematical Analysis grade 11)
+) Group 1:
Teaching objectives: the concept of number sequence having a limit of 0;
Knowing how to use the theorem and the previous results to prove a range with
limit 0.
Teaching content: The series has a limit of 0

16
Teaching process:
Timing

Activity of the Teacher
Activity 1. Learn about a sequence of
numbers with limit of 0: The sequence
n
−1)
(
un =
n
Teacher: Please tell me when n gets
bigger, how will un value change?
Teacher: Is it possible that un is equal to
0?
10
minutes Teacher: What is the absolute value of
un?
Teacher: When n approaches infinity,
what is the absolute value of un?
1000
Teacher: If given v n =
, does vn
n
have the same feature as the un sequence
above?
Activity 2. Teacher notifies concept

As the example above, we see that, un is
smaller when n is larger, it can be
described as follows: "for all arbitrary
small positive numbers ε, then from a
certain number in the sequence onwards,
all numbers of the sequence have a
distance to 0 of less than ε.” Then we
can say, the un sequence is a sequence of
numbers with the limit of 0.
There is another way to write: The un
sequence is called to have a limit of 0 if
20
minutes  ε (ε > 0),  N0 N* :  n > N0
un  ε.. Then we write limun = 0

Activities of students
Students: bigger n is, the smaller the
un becomes, gradually approaching 0
Students: Never
Students: We have un =

( −1)
n

n

=

1
n

Students: The absolute value of un
will then advance to zero
Students: Similarly, VN also moves
to 0 when it reaches infinity

Students: Writingd down concepts in
mathematical language, writing down
examples, finding ways to prove
(similar to the teacher’s proof)

Teacher: Prove that the sequence
n
−1)
(
un =
has a limit of 0.
n
For example: The following sequences
are those with a limit of 0:
1000
1
1
vn = ; t n = 2 ; w n =
n
n
n
Please prove it.

+) Group 2:

Teaching objectives: Students can express the concept of sequence of numbers
with a limit of 0; Knowing how to use the theorem and previous results to prove a
sequence of number of 0 limit ; solving some simple exercises, in the textbook
Teaching content: The sequence has a limit of 0


17
Teaching process:
Activity 1. Motivate students
Teacher: Given the following sequence of numbers, do you have any
comments about the value of the sequence when n is bigger?

n +1
−1
1
10
(−1) n
un =
wn =
vn = xn =
yn =
zn = 3 n + 1
n ,
n ;
n;
n ;
n;

Students: Realizing that the first four sequences gradually approach 0 and the
remaining two sequences do not approach 0.

Teacher: What does it mean to approach to 0?
Students: Gradually getting smaller, to 0.
Teacher: What about the case of sequence xn?
Students: To say it again, the absolute value of each element of the sequence
progresses to 0.
GV: Progressing to 0, is the value of the sequence element equal to zero?
Students: No.
Teacher: How does it progress?
Students: For every arbitrary smll positive number ε, there is some N0 so that,
every number of the sequence has a distance to 0 of less than ε.
GV: Can you make it brief?
Students: Shortening it down as defined in the textbook.
Activity 2. Giving definition
Teacher: Giving definitions as in textbooks
Students: Write down in notebooks, write down examples.
Teacher: Find the number N0 for the sequences un , vn , xn when given ε =
0.0001.
Students: Find N0.
Teacher: Supporting and helping with each desk.
Students: Complete, edit, and report.
Activity 3. Conclusion and homework assignment (Students do not present
because it is only done after forming concepts)
Form 2. The teaching idea of a pyramid interface cut by a plane
+) Group 3:
Teaching objectives: The teaching determines the interface of a pyramid cut
by a plane through some simple cases (the plane is defined by three points, one
point and one line).
Major teaching and learning activities:
Timing

Teacher’s activities
Students’ activities
Activity 1. Determine the
interface of the pyramid
Teacher: Organize students to Students: Work individually, or solve the
solve exercises in the whole class: problem in groups
Exercise: Given the pyramid
S .A BCD with the A BCD
parallelogram at the bottom. Call
M , N the midpoints of the sides


18
Timing

Teacher’s activities
A B , A D , respectively and P is
a point at side SC as shown.
Determine the area of the pyramid
interface cut by the plane.
Teacher: Guide and support
students to identify intersections,
... and call a student to the board
to explain about the solutions.

Students’ activities

S
P

D

C

N
B
Activity 2. Teaching rules to
define the interface by original
lines of intersection
Teacher:
Ask
students
to
comment on his solution. Ask
some open-ended questions:
+) Which plane can be defined
immediately?
+) From those lines of
intersection, can you identify the
intersections with other planes?
How?
+) So, which intersection with the
plane should be determined first
next time?
Teacher: In conclusion, the line of
intersection with the bottom plane
in the above problem is called the
original line of intersection, since
it can help to determine the lines
of intersection with other planes

of the pyramid. This method is
called the original lines of
intersection method
So, can you describe the steps of
proving?
Activity 3. Practice
Teacher: Assign homework to
students

M

A

Students: Comment and answer some
questions of the teacher:
+) Determine the lines intersection with the
front side plane.
+) It is possible, to lengthen MN, which will
cut the sides of the parallelogram at the
bottom, thereby determining the lines of
intersection with other sides.
+) With the front side plane

Students: Memorizing, writing the name of
the original lines of intersection method.
Students: Step 1. Determine the original
lines of intersection (the intersection with
the bottom of the pyramid)
Step 2. Identify the lines of intersection with
the remaining sides

Step 3. Connect the intersection points on
the sides of the pyramid we get the
necessary interface.

Students: Solving exercises, from simple to
complex
according
to
teachers'
requirements.

+) Group 4:
Teaching objectives: Teaching process of determining the interface of pyramid
cut by a plane through a number of simple cases.
Major teaching and learning activities:
Activity 1. Doing exercise
Teacher: Ask the whole class to solve two problems as follows:


19
Lesson 1. Let the pyramid with the bottom A BCD not a trapezoid and P be a
point of the SA edge as shown. Determine the area of the pyramid cut by the plane.
S
S
P
P

A

D

A

D
B
C

B
C

Lesson 2. Let the pyramid S .A BCD with the bottom A BCD not trapezoid
and P be a point of the SA edge as shown. Determine the area of the pyramid cut by
the plane.
Activity 2. Develop a process for defining a profile
Teacher: Call the two students to the board and draw in the A0 size paper
(printed with the above figure) and then present the solution in the form of tables:
Solution of exercise 1
Solution of exercise 2
Figure of exercise 1
Figure of exercise 2
Answer:................................................. Answer:....................................................
..
..
Student: Go to the board
Teacher: Call one or more to comment on the similarities and differences
between the two solutions above, thereby determining the steps (which
students have done).
Student: Comment, draw out three steps:
+) Step 1. Determine the original lines of intersection (the intersection with the
bottom of the pyramid);

+) Step 2. Identify the intersections with the sides of the pyramid;
+) Step 3. Connect the intersection points on the sides of the pyramid we get
the interface we are looking for.
Activity 3. Applying to solve exercise
Teacher: Assigning students to solve some exercises in the textbook.
Some notices in the teaching process: Teachers should draw the pictures on
A0 paper in advance to save time in class. Classes should be divided into groups in
order to have cooperation and competition among groups during the process of
solving exercises.
Step 2. Teaching: Teachers organize students to teach a lesson based on the
lesson plan, not more than 30 minutes for a group. The lesson takes place with the


20
participation of students and is recorded. In class, students will analyze the video to
evaluate the results of teaching and teaching skills of students.
Step 3. Evaluation - Feedback: We received feedback from students and
teachers as follows:
Feedback from the first lesson: +) Students can visualize the "progressing to
0" of the sequence but still misunderstand it. For example, students may not
understand that the number of elements a sequence of numbers has. +) Some

( −1) it is
=
n

contents are not accurate: for example, in the first sequence, un

n

impossible to conclude that with the larger n, the un becomes smaller, and
approaching 0 but we can only draw the conclusions that are un gradually
approaches 0. +) It is difficult for students to determine the number N0 if the teacher
does not give some examples, or ε should be given as a specific number, then it will
be easier for students in finding N0, and understand the problem. +) If possible, it is
better to help students find the absolute value of the sequence in a natural way than
to require students to do it.
Feedback from the second lesson: +) This lesson is quite good, the questions
are quite appropriate, with smooth gradation. However, it should be corrected in
Activity 1, because there are two sequences of which one has a limit of 1, the other
has no limits, furthermore, showing a sequence with a limit other than 0 and a
sequence of infinite limits (or no limit) at the current level of students is a difficult
job! +) There should still be given an example of ε that is a specific number, it will
be easier for students in the process of finding N0, understanding the problem and
some such numbers should be given, which get smaller to help to find out the N0
variations in each case. +) If possible, it should be represented by a graph or a
certain image of the "advance to 0" of the sequence!
Feedback from the third lesson: +) The problem should be, if possible,
modified, and the class should be divided into groups, given four similar problems,
with only changing point P: corresponding to each group, position P will be the
midpoint of SC (or SB, SA, SD, respectively). Thus, students can use a drawing or
each group draw 4 different shapes, but generally it does not affect the process of
defining the interface, of which the degree of difficulty is equal. After that, the
teacher may also have suggestions about drawing pictures in the space in such a
way that it is easy to see and imagine. +) It can be shortened from three steps into
two steps defining the interface for the sake of brevity. +) There should be more
specific questions (smoother gradation) suitable for each group.
Feedback from the fourth lesson: +) The lesson plan is quite good, detailed
and positive, to motivate students' learning activities. +) Teachers are not yet learn
the lesson plan carefully, they do not follow the lesson plans properly. +) The the

lesson plan needs to give more details in Activity 2, especially the expectations or
situations, the possible answers that the author can anticipate during the lesson, to
make appropriate adjustments. +) Considering if defining the interface should
include two steps or three steps. +) The focus on the teaching process is good, but


21
the content needs to be more complete, more attention should be paid to the learning
practice of students.
Some general remarks about the teaching on videos:
+) Students’ ability to organize the board in general is not good, it should be
paid more attention to in presenting, it is necessary to divide the table into columns
to record and save important information the teacher wants to convey to students. +)
The ability to follow the lesson plan of the students is not good, some are too
dependent on the lesson plan, leading to a lack of natural and flexible lesson. +) The
role of students in the teaching process is not good, not practical, the reason is that
the students had perceived the knowledge beforehand so it was difficult to pretend
as if they had not known. +) The teaching objective section is generally good, but it
needs to be more specific, on the other hand, it needs to be developed in the
direction of competency development, it must show that after the lesson, what
students can do, such as: be able to solve similar problems.
Step 4. Reconstructing lesson plans
Step 5. Re-teach
Step 6. Re-evaluation
2.2.4. Situation 4: Guiding students to develop specific topics for teaching
mathematics in high school
In the context of educational innovation nowadays, teaching by topic, by
building teaching topics will be an important requirement for teachers. The
objective is: Teachers build up and develop the teaching programs, in order to meet
the requirements of integration in teaching, associating math with real life, etc. in

order to be suitable for students (in differentiated instruction). The basic idea is,
teachers organize group activities for students to design teaching topics as an
activity to develop learning programs, contributing to the development of the school
program. This is a complicated activity that requires the cooperation of students and
the support of teachers to have good results. This situation is aimed at developing
competency in developing curriculum and differentiated instruction capacity for
students.
2.3. Using teaching situations in teaching method modules for students base on
competency approach at universities
2.3.1. The general process of using situations in the teaching method module:
The process of using a teaching situation is as follows: Stage 1: Modeling; Stage 2:
students perform under the guidance of the teacher; Stage 3: Students perform by
themselves, lecturers evaluate and feedback.
2.3.2. Simultaneously using situations in Math Teaching Method modules of to
develop implementation capacity of Math students
The author proposes the process of synchronous use of situations in teaching
modules of Math Teaching Methods to develop the implementation capacity of
Math teacher students as shown in the following diagram:


22
Teachers select one to two units belonging to a chapter of high school
math textbook related to the content of the Math teaching method
module (algebra, mathematical analysis, geometry, etc.)

Analyzing then lesson content, determining teaching objectives
and developing teaching plans for selected units

Not obainting teaching skills

Observing and analyzing teaching hours of selected units

Developing lesson plans of selected units

Teaching in groups, practising the prepared lesson plans
Obtaining teaching skills

Developing teaching topics related to the Maths textbook contents in
the selected high school

CHAPTER 3. PEDAGOGICAL EXPERIMENT
3.1. Purpose of pedagogical experiment: Results of pedagogical experiment through
teaching to collect and analyze data on teaching capacity of students qualitatively
and quantitatively to answer the following two questions:
- How does students’ ability to analyze curriculum and design learning
materials develop?
- How do the teaching situations affect the teaching skills of students?
3.2. Process of pedagogical experiment: The pedagogical experiment process was
carried out through the following steps: Developing criteria for evaluating
pedagogical experiment results; choosing pedagogical experiment method;
determining content of experiments, collecting and evaluating results of
experiments.
3.3. Method of evaluating pedagogical experimental results
3.3.1. Qualitative evaluation criteria
3.3.2. Quantitative evaluation criteria
3.4. The content of pedagogical experiment
3.4.1. Pedagogical experiment documents: In order to implement the pedagogical
experiment, we prepared the following documents: The frame of performance
competency for university students in Mathematics major; teaching situations;
teaching plans of some Math teaching method modules; some sample teaching

23
videos; a set of criteria for evaluating the performance competency of university
students in the field of Mathematics (standardized); questionnaires for lecturers and,
students etc.
3.4.2. The procedure of pedagogical experiment
3.4.2.1. Phase 1: Initially experimenting the research results
3.4.2.2. Stage 2: Experiment on students at universities training Math teacher
students.
3.5. Pedagogical experiment process and obtained results
3.5.1. Experiment phase 1
3.5.2. Experiment phase 2
3.5.2.1. Time, location, sample selection for phase 2
Consulting 19 experts, including scientists working at universities, research
institutes and lecturers in specialized fields of Theory and Teaching Methodology,
who are teaching at universities which train math teacher students.
3.5.2.2. Results from consulting experts
After analyzing the comments of experts, we put them altogether to
standardize the criteria to evaluate the elements of skills in Math teacher students’
performance competency at some points: Adding a quantitative evaluation index in
some criteria for easier evaluation, in which: adding content levels which "fully
describe the objectives of knowledge, skills and attitudes" in skill 1; adding a
quantitative description of skill 6 from level 3 onwards: Combining at least 2 or
more active teaching techniques in one teaching period. At the same time,
modifying contents in situations 3 of micro teaching in activity 1, instead of
"Organizing for groups of students to design some typical teaching situations (in
common sense) in Teaching Maths and implementing teaching in groups, then
asking students to record and submit them to the teacher ", it is changed into"
Organizing and instructing groups of students to design some typical teaching

situations (in common sense) in Teaching math and teaching in groups, then asking
students to record and submit videos to the teacher".
3.5.2.3. The result of pedagogical experiment phase 2 on students
The results of experimental data analysis phase 2 are as follows:
a) Experimental results through qualitative data analysis
Before organizing the pedagogical experiment, through the survey, we
collected information that the majority of students did not have elemental skills of
performance competency for Math teacher students or some students initially knew
how to design teaching plans; how to organize teaching activities but mainly at low
levels. Regarding theoretical knowledge, students have basically gained knowledge
of program analysis and teaching objectives; active teaching methods; the way
young students perceive maths etc. but when asking students to design products,
most of them are confused and their skills are at a low level.
We integrated teaching situations in the lessons of teaching methods and the
former were used mainly in practical lessons. The situations were taught in 4
different sessions (3 hours each), In session 1 we applied integration in theoretical
lessons to instruct students basic skills, for the remaining three sessions we
organized practicing activities for students, the sessions could be separated by 2-7
days depending on the program of the school to help students have time to study by
themselves and study at home: In 3 periods of the first session, The author


24
organized for students to discuss basic skills of mathematical competence, and
assigned specific tasks to train those skills in the next 3 sessions.
Specifically, in situation 1, when we instructed students to analyze the
objectives and teaching plan of specific lessons based on the analysis of the subject
curriculum at high schools; based on the Ministry of Education and Training's
output standards; Based on the references, students were very excited to discuss.
The groups worked enthusiastically, showed motivation and drew out system of

goals in the sample lessons.
However, at the 2nd session (the next 3 hours), the author asked students to
determine teaching objectives and formulate teaching plans in lessons 1 and 2 on
"The linear equation in the plane" (Geometry 10 - section 1.2), just over 30% of
students were excited to participate in the required lectures, the rest stayed
indifferent or did personal work when teachers did not observe. Next, the author
asked students to report on the prepared lesson objectives and the proposed
teaching plans; organizing for students to discuss, showing the right and wrong in
their work.
In the last lesson (3 hours of teaching), when the instructor asked students to
continue to define teaching objectives and plan the lesson "cosine theorem", the
number of students participating and interested in implementing the task increased,
students in the group discussed enthusiastically and organized the task, however, we
observed that there were still 7 students who almost did not participate in the task,
through analysis and interview, among 7 students, there were 4 students whose
study reports were at average and under average level, their ability to cooperate was
not good; There are 03 Laotian so their language competence was limited and it was
difficult to join the groupwork activities.
The author directly discussed with the group leaders of the above students,
asking them to organize extracurricular group learning after school, re-teaching the
under average and average level students to ensure that they could grasp the
program analysis skills.; determining teaching objectives and developing teaching
plans.
To the final practice session, the lecturers asked students to discuss to build up
teaching objectives and plan teaching lessons of "Interchange, Arrangement and
Combination", then 25 out of 26 students were interested in participating and
completing the task, and 1 student was more active in doing of the task, and still
submitted the product but still kept the indifferent attitude.
When carrying out situations 2,3,4, we drew out experience from teaching
situation 1, we distributed the documents in advance and asked groups of students

to self-study and read the materials themselves beforehand so when analyzing
videos, more students participated, most students actively took part in the
discussion, only 3 Laotian students had difficulty due to language barrier, but when
analyzing the last lesson video lesson "Interchange, Arrangement and
Combination", these students basically analyzed better and reached the average
level.
In the process of implementing situation 3 on micro teaching , the groups had
been familiar with the skills, so they were quite active, coordinating and helping
each other in the process of practicing teaching skills. However, through
observation, the number of students who achieved skill 6 in handling wrong


25
situations of school students did not achieve very high results. There were some
students who still depended on the lesson plans, and still were not creative yet.
In case of situation 4, when we asked students to discuss teaching topics
related to the above 4 lessons, 100% students were active, enthusiastic in the
discussion process and each student submitted their complete assignment according
to the teacher's request in a responsible way.
Thus, by observing the learning process of students, it is shown that they are
very active and interested in teaching situations organized by lecturers;
enthusiastically participating and elemental skills of math teaching skills of
students are developed.
b) Experimental results through quantitative data analysis
Table 3.7. Results of performance competency of the experimental group before
and after the pedagogical experiment
Skills The levels students obtained before The levels students obtained after
the experiment
the experiment
Level Level Level Level Level Level Level Level Level Level

1
2
3
4
5
1
2
3
4
5
Skills
1
Skills
2
Skills
3
Skills
4
Skills
5
Skills
6
Skills
7
Skills
8
Skills
9

19

0

0

0

0

9

15

2

0

0

12

0

0

0

0

3

8

13

2

0

3

2

0

0

0

8

10

5

3

0

5

1

0

0

0

14

7

4

1

0

4

1

0

0

0

22

2

1

1

0

5

0

0

0

0

8

14

2

2

0

5

1

0

0

0

17

4

4

1

0

2

2

0

0

0

16

6

4

0

0

0

0

0

0

0

21

2

0

0

0

The table shows that the skills of students have developed to a higher level

after the pedagogical experiment process, especially in skills 1, 2 and 3, it is shown
that the number of students achieving a high level is quite large:
- The author initially affirmed that after the pedagogical experiment process,
the skills of "program analysis and preparation of learning materials (especially
defining teaching objectives)"; the skills of "designing teaching plans"; the skills of
"Presenting lessons effectively" and that of "Helping students understand the
relationship between new knowledge and previous knowledge and their application"
were well-developed, before the pedagogical experiment students were at level 1
but after the pedagogical experiment they reached level 2, 3 and especially, there
are some students reaching level 4 (accounting for about 5-10%).
- Skills 5, 6, 7, 8 of the experimental students are developed from level 1, 2 to
level 3 and 4, however, the rate is not high, the number of students reaching level 1