Phát triển năng lực dạy học cho sinh viên đại học ngành sư phạm toán với sự hỗ trợ của công nghệ thông tin và truyền thông tt tiếng anbh

MINISTRY OF EDUCATION AND TRAINING
VINH UNIVERSITY

PHAN ANH HUNG

DEVELOPING TEACHING COMPETENCE FOR
UNIVERSITY STUDENTS IN MATHEMATICS
PEDAGOGY WITH THE SUPPORT OF INFORMATION
AND COMMUNICATION TECHNOLOGY

SUMMARY OF DOCTORAL THESIS OF SCIENTIFIC
EDUCATION

Specialization: Theory and Teaching Methodology of Mathematics
Code: 9.14.01.11

Science instructor:
1. Assoc.Prof., Dr. Tran Trung
2. Assoc.Prof., Dr. Tran Kieu

NGHE AN, 2019


The thesis was completed at Vinh University
Science instructor:
1. Assoc.Prof., Dr. Tran Trung
2. Assoc.Prof., Dr. Tran Kieu

Reviewer 1: Assoc. Prof., Dr. Dao Thai Lai – The Vietnam National Institute of
Educational Sciences
Reviewer 2: Assoc. Prof., Dr. Nguyen Anh Tuan - Hanoi National University of

Education
Reviewer 3: Assoc. Prof., Dr. Nguyen Danh Nam - Thai Nguyen University of
Education

The thesis is defended in front of the University-level doctoral
thesis-grading council, Location: Vinh University,
Time: At , date month

year 2020

The thesis can be found at Vietnam National Library,
Nguyen Thuc Hao Library - Vinh University.


INTRODUCTION
1. The reason to choose this subject
In order to meet the requirements of industrialization and modernization of the
country in the conditions of socialist-oriented market economy and international
integration, the Party Central Committee adopted the Resolution No. 29 / NQ-TW.
November 4th, 2013 on radical innovation, comprehensive education and training.
In order to create fundamental and strong changes in the quality and
effectiveness of education and training; To better meet the work of building, defending
the Fatherland and learning needs of the people, Resolution 29 / NQ-TW has set the
requirements of renovating the education system in an open, flexible and interconnected way between modes of education and training. The goals set out are:
“Building open education, practical learning, practical education, good teaching, good
learning, good management; have reasonable education structure and methods,
associated with building a learning society; ensure conditions for quality improvement;
standardize, modernize, democratize, socialize and internationalize the education and
training system ".
On December 26th, 2018, the Ministry of Education and Training issued the

General Education Program according to Circular No. 32/2018 / TT-BGDĐT of the
Minister of Education and Training. The new general education program is built in the
direction of developing students' qualities and competencies, ensuring close connections
between classes, grades and connecting with vocational education and higher education
program.
In order to effectively implement the general education program, a key
determinant is the teachers in the schools and their pedagogical competence, which
requires the Pedagogical schools and teacher training institutions to innovate training
content and methods to develop students' professional competence, associated with
professional activities in practice of teachers in high schools.
Mathematics is a science that has many applications in life, basic mathematical
knowledge and skills that have helped people solve real-life problems in a systematic
and accurate manner, contributing to promote social development.
To carry out teaching Math in high school towards developing Math competency
for future students, Math pedagogical students need not only master the Math
knowledge system in high school but also develop Math teaching competence.
Therefore, pedagogical schools and training institutions for Math teachers need to apply
Competency Based Education and training.
Thus, in order to develop the competence of teaching mathematics for students,
pedagogical schools and training facilities for Math teachers need to build an open
training system, enhancing the activities of experience, and well managing students'
learning activities which have a modern educational structure and method, attached to
building a learning society; ensuring conditions for quality improvement; standardizing
and modernizing according to the spirit of Resolution 29 / NQ-TW.
Today, Information and Communication Technology (ICT) plays a huge role in
the process of teaching and training at all levels, majors, contributing to a positive
innovation in teaching and learning. ICT promotes an open education, giving people
quick access to information, multi-dimensional information, shortening all distances,
narrowing every space, time. ICT enables people to self-study anywhere, anytime,
contributing to a learning society in which everyone can learn for life.

In order to improve the training quality for math teachers in high schools, the
research is based on the view of competence development and comprehensive
innovation of education, training, exploitation of IT applications to propose solutions to


develop teaching competence for math pedagogical students with the support of ICT
which is necessary and urgent.
Start from the above reasons we study the thesis “Developing teaching
competence for university students in Mathematics Pedagogy with the support of
information and communication technology”.
2. Research objectives: Applying theoretical views to develop competence,
meaning and value of ICT application in Education and Training to propose solutions to
develop Math teaching competence for Math pedagogical students with the support of
ICT.
3. Object and scope of the study
3.1. Research object
The process of teaching competence development of Math pedagogical students at
university with the support of ICT.
3.2. Research philosophy
The process of training Math pedagogical students at the university.
3.3. Scope of the study
Application of ICT contributes to train teaching competence in the process of
training Math teachers at high schools and at pedagogical universities, through specialized
subjects and mainly forging practice pedagogy.
4. Scientific hypothesis
If the measures are developed and mastering well the viewpoint of teaching and
competence development, along with the reasonable method of exploiting ICT applications,
the application of those solutions will contribute to the development of teaching competence of
math pedagogical students.
5. Research mission

5.1. Systematize theoretical basis for training, developing teaching competence of
mathematics pedagogy students. Identify the component competencies and manifestations of
the major math teaching competencies that need to be developed for undergraduate
mathematics pedagogical students.
5.2. Identify roles, functions and applications of ICT in training teaching
competence for math pedagogical students; pedagogical requirements, ICT application
process to support teaching competence training for math pedagogical students at
university.
5.3. Surveying the current situation of applying ICT in training teaching competence
for math pedagogical students at some pedagogical universities which have training of math
teachers.
5.4. Identify solutions to train teaching competence for math pedagogical students
with the support of ICT.
5.5. Pedagogical experiment to test the feasibility and effectiveness of ICT
applications in organizing teaching competence for math pedagogical students at university.
6. Research Methods
6.1. Theoretical research Method
Studying documents, research works on competence development teaching theory,
documents on ICT application in teacher training in general and training of teaching
competence for math pedagogical students in particular, materials on vocational training
programs and training teaching competence for math pedagogical students at universities
with the support of ICT.
6.2. Investigation and observation Methods
Using the questionnaire, observing student activities related to the requirements for
forming, developing competence and using ICT.
Communicating with experts and lecturers at universities and observing some teaching


competence training activities for math pedagogical students at universities; At the same
time, learn about the practical application of ICT in training teaching competence for math

pedagogical students nowadays.
6.3. Experimental method of pedagogy
Organize pedagogical experiments to confirm the rationality and feasibility of the
pedagogical solutions proposed and test scientific hypotheses. Handling pedagogical
experiment results by mathematical statistical methods.
7. Theoretical and practical meanings of the topic
- The thesis has systematized and contributed to the theory of formation and
development of teaching competence of math pedagogical students at university with the
support of ICT.
- The research results of the thesis can be applied in teaching activities to formulate
and develop teaching competence for Math pedagogical students at pedagogical universities
and current training facilities of Math teachers.
8. The thesis contributions
- Contribute to the determination of the competence frame for teaching mathematics,
component competencies and competence expression of university math pedagogical
students.
- There is a grounded analysis about the current situation of ICT application of
students in developing teaching competence for Math pedagogical students at pedagogical
universities at present.
- Proposing a number of pedagogical solutions to exploit the application of ICT in
training teaching competence for math pedagogical students at university, approaching the
current career standards of high school teachers.
9. The thesis structures
In addition to the Introduction, Conclusions and References, the thesis content has 3 chapters:
Chapter 1. Theoretical and practical basis
Chapter 2. Solutions to develop teaching competence for math pedagogical students
with the support of ICT in university
Chapter 3. Pedagogical experiment.
Chapter 1: THEORETICAL AND PRACTICAL BASIS
1.1. Overview of the problem research history

1.1.1. Studies in the world
- Research on developing training competence for teaching mathematics
In Western countries, the concept of training math teachers is clearly formed and early.
The role and task of forming pedagogical skills are always a topic of interest in research
topics and seminars on the field of education. Many research works focus on teacher
training.
Entering the 70s of the twentieth century and the following years, the research works in
the Soviet Union and Eastern Europe were promoted in the direction of in-depth study of
scientific labor organization - the teaching process. The birth of the Teacher Training
Research Department at Pedagogical School has facilitated the introduction of a series of
studies.
- Research on the application of information and communication technology in training
pedagogical students
In the late 70s of the twentieth century, information technology was widely used in
professional and scientific documents around the world. Since 2000, the term "information


and communication technology" (abbreviated as ICT) began to be popularly used to reflect
the trend of integration of ICT in different areas of social life, including education.
The advantages as well as limitations of the research works of foreign scholars help the
thesis author define the basic steps of forming skills and techniques for students in the
conditions of higher education through the time and in different social regimes. These are
good grounds for a good reference when studying the current situation and prospects of
higher education in Vietnam.
1.1.2. The researches in Vietnam
- Research on training and developing competence for teaching mathematics
Until the twentieth century, the educational research results of Vietnam were still
inclined to study classical theories, the research trends have only really begun from the
middle of the 1990s until now. When discussing teaching competence, teaching skills are
considered as solutions, tricks to implement teaching method to achieve high results. A

number of textbooks, documents, authors have gone into the instruction of teaching skills,
new teaching methods, and teaching practice skills. Many authors have presented in a
systematic, relatively comprehensive way to pedagogical skills in order to promote activities
of pedagogical skill training, pedagogical skills for students with better quality.
- Research on ICT application in math pedagogical student training
In Vietnam, research on the applications of ICT in teaching mathematics and training
of math pedagogical students appeared from the late 1990s and early 2000s. Initial studies
focused on the applications of IT in teaching mathematics in high school and IT training for
Math pedagogical students.
According to the above studies, in the age of information explosion, higher education
in the world has been having many development opportunities, and at the same time faces
many great challenges, especially the problem of solving the relationships between training
scale and effectiveness, between training and scientific research, services, between needs
and resources for development.
By studying the situation of development research on teaching competence for
pedagogical students of domestic and foreign authors related to the topic that the thesis is
aiming to, the author realized, developing teaching competence for Math pedagogical
students are mentioned at the general level with the general research object in the research
works. Application of ICT in training Mathematics pedagogical students should be
continually researched and deployed. In Vietnam, the evaluation perspective and the trend
of conducting research on the type of training to develop teaching competence under an
innovative program to integrate with regional and world education have been implemented,
but the the number of in-depth research works is not much, especially directly related to the
subjects of Mathematics pedagogy at Pedagogical schools. However, these research results
reflect a variety of problems in developing teaching competence for math pedagogical
students at pedagogical schools and make an important contribution to that development.
On the basis of an overview of relevant research works, this thesis will focus on
addressing the issues: systematizing the competencies needed to form in math pedagogical
students based on the view of modern university education, professional standards of high
school teachers in Vietnam and some developed countries, research works on teaching

competence; propose pedagogical experiment and solutions to develop teaching
competence for Math pedagogical students with the support of ICT.
1.2. Education follows competence development approach
1.2.1. The definition of “education follows competence development approach”
Today the concept of competency is understood in many different meanings. From
different approaches to the concept of competency, researchers around the world have used
different competency models according to their approach:
- The model is based on the personal characteristics and behaviors of individuals


pursuing definite way "how people need to be to perform their roles";
- The model is based on the knowledge and skills that are required to pursue the
identification of “what knowledge and skills people need” to perform their roles well;
- The model is based on the outcomes and output standards pursuing identifying people
"what needs to be achieved in the workplace".
Thus, competency is understood as the proficiency, the ability of an individual to
perform a job. Competence concept is associated with the ability to act. Competence to act is
a kind of competence, but when it comes to developing competence, people also understand
it as well as developing competence for action. Therefore, in the field of pedagogy,
competence is also understood as the ability to perform responsibly and effectively actions,
solve tasks and problems in different situations in many fields, social or individual based on
knowledge, skill, trick and experience as well as willingness to act.
According to the author of the thesis: Competence is also understood as the ability to
perform responsibly and effectively actions, solve tasks and problems in different situations
in many fields, social or individual based on knowledge, skill, trick and experience as well
as willingness to act. At the same time, these factors must be observed, measured and
allowed to distinguish those who exhibit the best competency with others.
1.2.2. Characteristics of training according to the competence development approach
Competence formation and development need to identify their components and
structures. There are many different types of competencies, and the description of structures

and components of competencies is also different.
From the perspective of the German pedagogist, the general structure of action
competence is described as a combination of 4 component competency components:
professional competency, methodological competency, social competency, individual
competency. The detail follows:
In the current educational program of OECD countries (Organization for Economic Cooperation and Development), the competency model is divided into two main groups,
including general competence (also called main competence, specific competence) and
professional competencies (also called specialized competencies). The above competence
structure model can be concretized in each different professional field. On the other hand, in
each career field, there are also different types of competencies. For example, the
competencies of teachers include the following basic groups: Teaching competency,
educational competency, diagnostic and advisory competencies, professional development
and school development competencies.
Because of the characteristics and advantages of a competency-based approach, competency
models and competency standards are identified and used as tools for the development of many
educational programs, different training and development around the world.
1.3. Teaching competence of Math teachers in high school
1.3.1. Mathematics competency of high school students
Math has more and more applications in life, helping people solve problems in reality in
a systematic and accurate way, contributing to the development of society. Math in high
school contributes to the formation and development of students' character and personality;
develop key knowledge and skills and create opportunities for students to experience and
apply Mathematics in real life; build a connection between mathematical ideas, between
mathematics and practice, between mathematics and other subjects, especially with STEM
education subjects.
Teacher's competence is closely related to students' Math competency because it is the
goal of Math teaching. .
According to the Ministry of Education and Training's 2018 General Education
Program, the Mathematics Program implements interdisciplinary integration through related

content, topics or mathematical knowledge exploited and used in other subjects. . Making
good use of the above-mentioned interdisciplinary factors has brought efficiency to all
subjects, while contributing to consolidating the knowledge of Mathematics, as well as
contributing to train students the ability to apply Mathematics into practice.
1.3.2. Teaching competence of Math teacher
From the perspectives and approaches on education and training based on competence,
the thesis conception: Teaching competence is to mobilize and use necessary knowledge,
skills and attitudes, combined smoothly and inseparably to carry out specific teaching tasks
and jobs according to set standards, under certain conditions.
Professional competency standards are an important basis for teacher training
institutions to develop training plans and evaluate teachers' development. Occupational
competencies (teaching job) are closely related to national occupational standards.
- Preparation capability includes operations,
- The ability to implement a teaching plan is shown in the process of practicing
teaching and education, including skills,
- The ability to use language is an ability that has important meaning,
- The ability to use teaching equipment and facilities,
- The ability for social activities inside and outside the school,
- Evaluation ability
Thus, teaching competence is a combination of many competencies and is an
important competence in pedagogical competence. With a process-based approach, the
structure of teaching competence includes competency groups such as: teaching design
competence; competence to conduct teaching; competence to test and evaluate the
learning results of learners and teaching process management competence. Within each
group of competencies, there are many competency components. For example, in the
competence to prepare for teaching, there will be the competence to design lessons, the
ability to prepare equipment, teaching aids, the competence to prepare equipment,
materials, practical materials, etc.
One of the methods that can be applied to build teaching competence framework

is DACUM (Develop A Curriculum). By describing of teachers who have extensive
experience in the profession, the DACUM method allows detailed depiction of a
teacher's career painting.
1.3.3. Teaching competence needs to develop for Mathematics pedagogical
students
1.3.3.1. Characteristics of math pedagogical students associated with the formation
and development of teaching competence
Fennema and Franke's research on mathematical teachers 'knowledge and
competencies has built a model for developing teachers' knowledge and teaching
organization.
Math pedagogical students are trained from high school who have the following basic
knowledge and competencies in Math:
a) Mathematic competency includes the following core components: mathematical
thinking and reasoning competency; mathematical modeling competency; mathematical
problem solving competency; mathematical communication competency; competency in
using mathematical tools and means.
b) The main qualities and common competence at the levels appropriate to the
subjects and grades specified in the overall program.
c) Have basic, essential mathematical skills and knowledge; develop interdisciplinary
integrated problem solving between Math and other subjects such as Physics, Chemistry,
Biology, Geography, Informatics, Technology, History, Art, ... ; Students can experience
and apply math in practice.


d) Have a relatively general understanding of the usefulness of mathematics for each
of the relevant professions as a basis for career orientation, as well as have the minimum
capacity to self-investigate issues related to Math throughout life.
These knowledge and competencies have been expanded and developed at the
university level, especially for math pedagogical students, who are capable of teaching
Maths based on specialized mathematical knowledge and skills.

Determining the mathematics teaching competency to form for students while still in
school chair must be derived from the tasks and required teaching competency of math
teachers:
- The formation and development of students' mathematical competencies from
studying mathematical knowledge contents, students develop mathematical "thinking and
reasoning competencies", from which "mathematical modeling" and apply" mathematical
problem solving ".

Check and
evaluate

Using
Math
teaching
facilities

Math teaching
competency of
pedagogical
students

Designing
content of
teaching
mathematics
Mathematics
thinking and
reasoning

Use

tools and means to
learn mathematics

Mathematics
Competency

Math
communicatio
n
Managing
mathematics
teaching
activities

Math
modeling

Logical design
to form
Mathematics
competency of
Students

Math
competency
of pupils

Solve math
problems
Organize Math

awareness
activities of
students

Organize
Math teaching
activities

Diagram of developing teaching competency for Mathematics

(Explain: Student math competency is centered; presenting the competency
components specified in the general school programs; the necessary teaching competencies
to develop the skills which is outlined in )
Math teaching competency of math pedagogical students is inextricably linked to pupils'
Math competency, deepened and expanded with higher levels at university level, and at the
same time closely connected with teaching competency in general. The above-mentioned
competence components are not separated but combined with each other, support for each
other into the competency of an overall and integrity nature.
1.3.3.2. Proposing a teaching competency framework for Mathematics pedagogical
students
Mathematics pedagogy students are the future math teachers and will generally work in
high schools. Even during the training process at university level, they need to form and
develop teaching competency. That raises the requirement for universities that have trained
math teachers in finding ways so that in the process of organizing teaching and evaluating


student results, they must meet the above standards and criterias. In principle, Math teachers
should also have the same teaching competencies as teachers who teach other subjects.

Approach to teaching tasks - DACUM method:

Teaching Competency

Teaching
Design
Competency

Competency to
conduct
teaching

Competency of
testing and
evaluating
teaching

Competency to
manage
teaching

Teaching competency structure
Based on the study of teaching competency structure (Diagrams above), models,
processes, methods of developing teacher professional standards, the philosophy of
DACUM methodology, from the requirements to build teaching competency framework, the
relationship between the factors that make up the peculiarities of professional activities of
teachers in general and teaching Math in particular, the thesis author proposes a teaching
competency framework to train students whose major in Math pedagogy includes 4
competencies, 10 components, 28 indicators, these competency components for students as
Table 1.2:
Table 1.2. The teaching competency framework needs training for Math pedagogical

students
Competency
Demonstration of
Indicators
components
competency
1. DESIGN COMPETENCY OF MATHEMATICS IN HIGH SCHOOL
1.1.1. Present the knowledge system of
Mastering
the Mathematics, which is related and extended
knowledge
of with other subjects and practice
mathematics in high 1.1.2. Describe the curriculum and
1.1. Studying
school, ensuring the distribution of Math curriculum to ensure the
knowledge
content of teaching objectives of mathematics education
content and
is
accurate, 1.1.3. Identify the process of developing
mathematics
systematic,
mathematical competencies in teaching
program in high rationally applying mathematics in high schools by the general
school
interdisciplinary
education program.
knowledge
to
meet

(4 indicators)
1.1.4. Identify characteristics of teaching,
the goals of the methods, means and forms of teaching
general
education mathematics in the direction of developing
program.
students' competency to meet educational
objectives
Create a plan for 1.2.1. Find out characteristics, student
1.2. Planning
math teaching in teaching Math to objects, facilities, resources to plan for
meet
the teaching Math
high school


Competency
components
(6 indicators)

Demonstration of
competency
requirements of the
teaching
and
education
goals
according to the
Math
curriculum

for
general
education,
consistent with the
characteristics
of
students and the
educational
environment.

Indicators

1.2.2. Determine teaching objectives that meet
the requirements of the Math curriculum,
student characteristics and school facilities
1.2.3. Identify methods of teaching Math in
high schools in accordance with the
objectives and content of teaching
1.2.4. Designing content and situations in
teaching mathematics in schools to ensure
the goal of competency development for
students
1.2.5. Designing Math teaching activities in
accordance with teaching objectives
1.2.6. Select and design tools, facilities and
learning cards to ensure convenience for
students in the awareness process
2. COMPETENCY OF ORGANIZING MATHEMATICS TEACHING IN HIGH
SCHOOL
2.1.1. Organize the implementation of

Using
methods,
teaching activities according to the set plan
2.1. Organize
techniques
and
students' learning
2.1.2. Guide and manage learning activities in
teaching
facilities
to
activities
class, group, ensuring the process and duration
implement students'
according to the
of teaching reach the teaching objectives set
high school Math learning and math out.
activities to achieve
teaching plan
the teaching and 2.1.3. Use Math teaching facilities,
(3 indicators)
equipment, software to support learning and
educational goals.
Math self-study for students effectively
Knowing how to 2.2.1. Know how to use language that
use
clear
and contains a high density of information,
accurately expresses the presentation of
2.2.Communicate, accurate

expressions
of Mathematics, concise, ensures logical
use Math
information
Mathematics,
language
coherent thoughts 2.2.2. Know how to use simple, vivid, rich
(2 indicators)
and feelings of images,
have
intonation,
clarity,
verbal as well as expressiveness
with
a
coherent
facial expressions, pronunciation in which there are no mistakes
acts, gestures
in rhetoric, grammar, and phonetics.
Solve pedagogical 2.2.1. Know anticipation and resolve
2.3. Handling
situations
arisen situations that have occurred positive,
pedagogical
that
meet
the cooperately,
collaborately,
facilitately,
situations

learners
securedly and be healthy
'requirements and
(2 indicators)
keep the teachers' 2.2.2. Know how to deal with student
friendly and democratically
reputation
3. INSPECTION – EVALUATION COMPETENCY IN MATHEMATICS
Identify methods, 3.1.1. Describing the methods, forms of
3.1. Test –


Competency
components
evaluation
planning in
accordance with
the teaching plan
and school
education
program
(4 indicators)

3.2. Organization
of examination evaluation
(3 indicators)

Demonstration of
competency
forms, testing tools

- assess the quality
and competency of
students

Indicators

testing and evaluation specifically in Math
teaching
3.1.2. Designing questions, test exercises,
assess the level of mastery of Math
knowledge and skills of students
3.1.3. Designing a plan to use questions,
exercises in tests, assessing competencies in
teaching Maths
3.1.4. Developing testing – evaluation plan
in accordance with the teaching plan and
school education program
Using
forms, 3.2.1. Knowing the organization of
methods, tools to examination - assessment to ensure the
test and assess openness,
objectivity,
accuracy,
students
comprehensiveness and fairness.
'competencies
3.2.2. Using means and technologies to store
accurately,
and manage test and evaluation results
objectively

and
fairly to adjust
teaching
and 3.2.3. Using appropriate ways to notify
educational
assessment results to students and other
activities
to stakeholders, and use assessment results to
promote students' adjust and improve teaching activities.
striving
for
improvement .

4. COMPETENCY OF MATHEMATICS TEACHING MANAGEMENT
Mobilizing,
4.1.1. Knowing how to design a notebook,
4.1. Manage the
distributing,
tracking record and recording all comments
implementation
organizing
on characteristics, performance of students
process of
during class time ...
teaching to ensure resources,
the teaching meets managing
classrooms to well 4.1.2. Knowing how to use information to
the set goals.
implement teaching make plans, schedules, and timelines for
teaching activities

(2 indicators)
activities
4.2.1. Knowing how to use student test4.2. Self-test and Self-assessment,
evaluation to
successes
and assessments, comparing with identified goals to
draw experience limitations of each assess learning experience for teaching
for teaching
lecture and propose 4.2.2. Suggesting solutions to overcome the
remedies
(2 indicators)
limitations in each lecture
From the above teaching competency framework, the thesis will study the proposal
of fostering, training and development for math pedagogical students at universities,
becoming a basis for the process of organizing training activities, to train pedagogical skills
and seeking pedagogical solutions to organize implementation.
1.3.3.3. Evaluate the teaching competency framework of proposed Math pedagogical
students
In order to determine the proposed teaching competency framework of Math


pedagogical students, the author consulted experts and teachers about the standards, criteria, and
indicators of the teaching competency of Math pedagogical students in terms of easy to
understand expression; conformity with practice; conformity of indicators with expression;
conformity of expression with element.
Survey results: Result from collecting opinions of pedagogical teachers and math
teachers at high schools through questionnaires with 29 lecturers at universities, 52 math
teachers and the results are as follows:

Table 1.4. Result from collecting opinions of pedagogical teachers and general

teachers on the teaching competency framework of Math pedagogical students
Element of
Demonstration
Standard
Indicators
Average deviation
competency
of competency
1. COMPETENCY OF MATHEMATICS DESIGN IN HIGH SCHOOL
1.1.1. Presentation of
the
Mathematics
knowledge
system,
3.64
0.902
which is related and
expanded with other
subjects and practices
Mastering the
1.1.2. Describing the
knowledge of
curriculum
and
Maths in high
distribution of Math to 3.64
1.136
school, ensuring
ensure the objectives of
the teaching

mathematics education
content is
1.1. Studying
1.1.3. Determining the
knowledge content accurate,
path of developing
and mathematics systematic,
mathematical
program in high rationally
competence in teaching 3.59
1.008
applying
school
mathematics at high
interdisciplinary
(4 indicators)
schools by the general
knowledge to
education program.
meet the goals
1.1.4. Identifying
of the general
characteristics of
education
teaching, methods,
program.
means and forms of
teaching mathematics
3.55
0.912

in the direction of
developing students'
competency to meet
educational objectives
Making a plan
1.2.1. Finding out
1.2. Planning math of teaching Math characteristics,
to meet the
student objects,
teaching in high
3.55
0.912
requirements of facilities, resources to
school
the teaching and plan for teaching
(6 indicators)
education
Math


Element of
competency

Demonstration
of competency
objectives
according to the
Maths general
education
curriculum,

suitable to the
characteristics of
students and the
educational
environment.

Indicators

1.2.2.
Determine
teaching objectives that
meet the requirements
of
the
Math
curriculum,
student
characteristics
and
school facilities
1.2.3.
Identifying
methods of teaching
Math in high schools in
accordance with the
objectives and teaching
content
1.2.4.
Designing
content and situations

in
teaching
mathematics
in
schools to ensure the
goal of competency
development
for
students
1.2.5. Designing Math
teaching activities in
accordance
with
teaching objectives
1.2.6.
Selecting,
designing
tools,
facilities, and study
cards
to
ensure
convenience
for
students
in
the
awareness process
2. COMPETENCY OF ORGANIZING MATHEMATICS
HIGH SCHOOL

2.1.1.
Organize
Using methods,
teaching
activities
techniques,
according to the plan
teaching
2.1.2. Instructing and
facilities to
administering learning
2.1.Organizing
implement Math
activities in class,
students' learning
learning and
group to ensure the
activities according
training
teaching process and
to the high school
activities of
duration
meet
the
Math teaching plan
students to
teaching objectives set
(3 indicators)
achieve the

out.
teaching and
2.1.3. Using Math
educational
teaching
aids,
goals.
equipment, software to

Standard

Average deviation

3.45

0.852

3.35

0.934

3.55

1.057

3.50

1.102

3.45

1.011

TEACHING IN

3.27

1.032

3.27

0.985

3.27

0.703


Element of
competency

Demonstration
of competency

Indicators

Standard

Average deviation

support learning and
Math
self-study
effectively for students
2.2.1. Language
contains large
information density,
Using clear,
accurate and concise
precise
3.27
1.162
description of
expressions of
Mathematics, ensuring
Mathematics,
2.2.Communicating,
logical information
coherent with
using Math
your thoughts
2.2.2. The language is
language
and feelings
simple, vivid, rich in
(2 indicators)
with words as
images,
intonation,
well as facial

expressive
with
a
3.27
0.985
expressions and coherent pronunciation
gestures
in which there are no
mistakes in rhetoric,
grammar, and phonetics.
2.3.1. Anticipating and
addressing situations
Solving
that have occurred
pedagogical
situations
that positively,
2.3. Handling
3.23
0.752
arise to meet the cooperatively,
pedagogical
collaboratively,
learners
situations
smoothly, safely, and
'requirements
(2 indicators)
and keep the healthily
teachers'

2.3.2. Dealing with
reputation
students democratically 3.23
0.685
and friendly
3. INSPECTION – EVALUATION COMPETENCY IN MATHEMATICS
3.1.1. Describing the
methods, forms of
testing and evaluation 3.18
0.958
specifically in Math
teaching
3.1.2.
Designing
Identifying
3.1. Test –
questions,
test
evaluation planning methods, forms,
exercises, assessing the
3.14
0.774
in accordance with testing tools to
level of mastery of
assess
the
the teaching plan
Math knowledge and
quality
and

and school
skills of students
education program competency of
3.1.3. Designing plan
students
to
use
questions,
exercises in testing,
3.64
0.902
assessing competencies
in
teaching
mathematics
3.1.4. Developing test 3.64
1.136


Element of
competency

Demonstration
of competency

Indicators

Standard

Average deviation

– assessment plan
consistent with the
teaching plan and
school
education
program
3.2.1. Organizing the
inspection - evaluation
Sử dụng các
to ensure the openness,
3.59
1.008
hình
thức,
objectivity, accuracy,
phương
pháp,
comprehensiveness and
công cụ kiểm
fairness
tra, đánh giá
3.2.2. Using facilities
3.2. Thực hiện kiểm
năng lực học
and technology to store
tra - đánh giá
sinh một cách
3.55
0.858

and manage test (3 chỉ báo)
chính xác, khách
Perform tests evaluation results
quan, công bằng
assessments
3.2.3 Using appropriate
để điều chỉnh
(3 indicators)
ways
to
notify
hoạt động dạy
assessment results to
học, giáo dục
students and other
thúc đẩy sự phấn
3.55
0.912
stakeholders,
using
đấu vươn lên
assessment results to
của học sinh.
adjust and improve
teaching activities.
4. COMPETENCY OF MATHEMATICS TEACHING MANAGEMENT
4.1.1. Designing books,
teaching tracking
sheets and recording all
Mobilizing,

comments on
distributing,
3.55
0.912
4.1. Managing the
organizing
of characteristics,
implementation
performance of
resources,
process of teaching
students during class
managing
to ensure the
classrooms
to time ...
teaching meets the
well implement 4.1.2. Using
set goals
teaching
information to make
activities
plans, schedules, and
3.50
1.102
timelines for teaching
activities
4.2.1. Using test
information - student
assessments,

Self-assessment,
comparing with
3.45
1.011
and
4.2. Self-test, self - successes
identified goals to
of
evaluation to draw limitations
assess learning
each lecture and
experience for
experience for teaching
proposing
teaching
4.2.2. Proposing
remedies
solutions to overcome
3.45
0.858
the limitations in each
lecture


1.4. Process of training and assessing teaching competency of Math pedagogical
students
1.4.1. The training process of teaching competency
The training process of teaching competency of pedagogical students based on the
approach of the performance through specific teaching activities which is designed with 7
stages

Stage 1: Students choose the lesson.
Selecting the main lesson is the period when students study materials, textbooks, looking for
Math knowledge, selecting lessons.
Stage 2: Teaching design (practice according to the teaching content).
Stage 3: Examining and evaluating the preparatory work (checking Math knowledge,
teaching plan, preparing teaching facilities). If passed: proceeding to the next stage, if failed:
repeating stage 2;
Stage 4: Class observation to learn experience. (this phase is performed many times);
Stage 5: Teaching practice.
Teaching practice is the stage where learners teach on hypothetical subjects, before teaching
on real subjects, so this stage only carries out the Teaching section.
Stage 6: At the end of the training period, students must present lecture to check and
evaluate;
Stage 7: If passed: the learner will go to class on the real practice as planned. If not,
learner continues to practice until they are proficient and well-trained. The essence of phase
8 is also phase 7.
The process is repeated for the next lesson.
Thus, in the aforementioned general process, a stage may also be a task or a job in
the occupational analysis scheme. It is a sequence (Angorit) of tasks and jobs defined in a
reasonable sequence, ensuring the efficiency of the training process.
1.4.2. Evaluating teaching competency of Math pedagogical students
One of the most important tasks in teacher training innovation is to measure and
evaluate research in both learning and performance of student.
Because the learning time is limited, students still have to study many other subjects.
The building of teaching documents involves many contents in many pedagogical subjects, so
that students can get used to the real tasks that math teacher in high school needs to perform.
Many skills are required in students when teaching. Assessing these skills for students
in practice is complex because of the absence of the main subject for teaching process which
is student. Therefore, it is necessary to combine evaluation methods such as objective test and
essay test, interview, implementation in hypothetical situations, observation, document

analysis and video tapes, etc.
1.5. Application of information technology in developing teaching competency for
math pedagogical students at university
1.5.1. The role of information technology in teacher training at universities
In most developed countries and some developing countries, the use of IT is widespread
and includes many activities that teachers can and need to participate in.
A question to ask when using IT in teaching Math is: When teachers decide to use
technology in teaching and how to use the software, they need to consider the content of
Mathematics that they will teach, the technology they will use and the pedagogy that will be
used. This requires teachers to think about the importance of the relationship between
content, technology and pedagogy.
Example: To develop competencies “1.2.4. Designing content and situations in
teaching mathematics at school to ensure the goal of developing competency for students”
as in the case of teaching the quadratic functionin grade 10 - Math program, to develop
student solving competency which can show iron chain image as mathematical situations.


(Picture 1.5).
The question is:
- Under the influence of gravity, what is the shape of the iron chain? How to determine
the mathematical equation that describes the shape of this chain?
- What measurements need to be taken to begin solving this problem? Is there any
information that can be exploited in the picture?
- In practice, who might need this information?
- How will IT application help students learn?

Picture 1.5. The shape of an iron chain is under gravity.
Lecturers can guide students to use Cabri Geometry 2 Plus or The Gemeter, Sketchpad,
GeoGebra and maybe some questions are asked on the website. The steps performed on
GeoGebra software are as follows:

- First, the axes are moved to an appropriate position and then placed in equal
proportions.
- Then the picture of the iron chain is inserted as a background and dragged to the
appropriate position.
- Use the "points" tool to mark points along the sequence and change colors to make
them clearer.

Picture 1.6. Using GeoGebra software to mark the shape of the iron chain.
The angle measuring tool can be used to find the angle created by the arc in the parabol
center. Some softwares that graphs coordinates for points on an iron chain picture.


Picture 1.7. Drawing the coordinates of points on the iron chain.
From matching experimental points with the quadratic function’s graph line
identifying the function to describe the shape of iron chain.
As such, the application of IT can enable students to model real-world phenomena,
creating problematic situations, using software to solve those problems. IT becomes a
powerful tool and allows organizing student activities to solve problems.
- Support self-practice for Math teaching in high school (support to implement the
process)
- Support testing - evaluation (support to analyze practice video recording, build
assessment tools, grading and score management)
- Building an open and flexible learning environment
1.6. Current situation of applying information and communication technology in
teaching competency development of math pedagogical students at university
1.6.1. Survey purpose
1.6.2. Object, survey time
1.6.3. Survey content
1.6.4. Survey result
* Survey results for teachers of pedagogical schools:

+ Regardingt the accessibility of IT equipment in teaching of lecturers.
+ Regarding the level of using IT equipment in teaching of lecturers:
+ Regarding the use of teaching websites of lecturers:
+ About the skill of using IT in teaching of lecturers:
* Survey results for students of pedagogical schools:
+ About IT equipment used in learning
- For lecturers:
- For students:
1.7. Conclusion of chapter 1
Math in high school contributes to the formation and development of student quality and
character. The application of mathematics in real life, creating a connection between
mathematical ideas, between mathematics and practice, between mathematics and other subjects,
especially with subjects in the field of STEM education is an important requirement. Students of
Mathematics pedagogy need to be formed and develop teaching competency right in the training
process at university level to meet the requirements of the new general education program. That
requirement poses for universities that train Math teachers to research and find ways to develop
Math teaching competency for students.
In the context of Industry 4.0, the application of IT in teacher training has many
opportunities and challenges. TPACK model (Technology, Pedagogy, and Content Knowledge),
based on basic requirements related to technology, pedagogy and subject knowledge, is likely to be
applied effectively in training future teachers. . The investigation of the situation of IT application in
training students in general and Math pedagogical students in particular at teacher training
establishments shows that the application of IT in teacher training is still limited.


Chapter 2: SOLUTIONS FOR DEVELOPING TEACHING COMPETENCY
FOR STUDENTS
WITH THE SUPPORT OF INFORMATION AND
COMMUNICATION TECHNOLOGY
2.1. Orientation to propose solutions to develop teaching competency for Math

pedagogical students with the support of information and communication technology
- Solutions must be directed to meet the output standards of the training institutions
and the high school teachers' professional standards
- Solutions must ensure the feasibility
- Focusing on training teaching competency for students in the IT environment
through practical situations of teaching mathematics in high schools.
2.2. Solutions to develop teaching competency for math pedagogical students
with the support of information and communication technology
2.2.1. Solution 1: Building an e-learning online learning system "Developing
teaching competency for math pedagogical students"
2.2.1.1. Purpose of the solution
This solution is dual-purpose in training for pedagogical Math students at the university.
It is the goal of both teaching the content of "Application of Information Technology in
teaching mathematics" for students, as well as developing the element of "using IT" in the
teaching competency framework that needs to be fostered for math pedagogical students
through practical experience.
The method focuses on building the online course structure and content for Math
pedagogical students, creating an environment of exchange and interaction between students
and lecturers, teachers and other students throughout the country. The e-learning system
contains e-learning materials to train and develop teaching competency for math
pedagogical students at university. At the same time, creating a virtual environment to
practice teaching content in high school, accessing to pedagogical requirements under the
high school Math program issued in 2018.
2.2.1.2. Scientific basis of the solution
E-learning in Vietnam as well as in the world has been applied by many schools so far.
E-learning is closely linked to online courses, in which learning activities take place via
the internet and the web, allowing a large number of people to participate, without
restrictions on space and time, increase connectivity, integrate data, software, learning
materials, management tools, assessment, ...
In the elearning environment, there exists a group of learning methods in the virtual

community. Therefore, learning in an online environment is oriented towards tasks, towards
finding information and asking questions to answer or discuss, instead of just transmitting
knowledge simply.
2.2.1.3. The solution contents
Mô hình elearning t ng thể để phát triển năng lực dạy học cho sinh viên sư phạm Toán
được tác giả xây dựng (Hình 2.1) có những chức năng chính của hệ thống cần có sau đây:
The overall e-learning model to developing teaching competency for Math pedagogical
students built by the author (Figure 2.1) has the following main system functions:


INTERFACE
LEVEL

User
(Managers, lecturers, Students)

E-learning portal

LEARNING MANAGEMENT
(LMS)
LEARNING
MANAGEMEN
T LEVEL

CONTENT,
OBJECT
MANAGEMEN
T LEVEL

Scientific

management
system

Online exam
management
system (*)

Student
assessment
system (*)

EXTENDED LEARNING
MANAGEMENT (Extended LMS)
Integrated
learning,
cooperation
(*)

Learning content management system
(LCMS)

Online
conference
(*)

virtual
classroo
m (*)

Digital

library

Object management system (*)

CSDL LEVEL

Study

Finance

Library

Other CSDL

Picture 2.1. Overall model of e-learning system for Math pedagogical students
Learning activities are divided into 3 forms: self-study activities, thematic learning
activities, group activities. Online training courses can be conducted by the following
channels (Picture 2.2):
- Provide learning content including lectures, exercises, reference materials, class
plan, assessment criteria, exam plans and tests.
- Exchange, discuss between teachers, students such as exchanging (chat text / video)
with lecturers or with other students.
- Manage learning activities: attendance trạcking with the user activity control feature
of the system.
- Testing and evaluation: Through the system of test questions in many forms such as
objective test, essay test or essays in the form of file upload, group exercises using Wilki ...

Picture 2.2. E-learning course structure
The process of building content of courses is branched in e-learning system to help
students get acquainted with Math teaching activities in high school and can be described as

follows:


Step 1: Developing a course script
The course script should identify the interaction activities between students and
computers, "programize" teaching activities, detailing the activities of teachers and students.
Activities may include: Providing information about electronic lectures, video, audio,
textual presentations, or simulated contents and presentations on video, flash, etc. Exchange
activities, discussion activities, testing activities: Exercises, quizzes ...
The following is an example of a pedagogical scenario development model:
1. An overview of the course

2. Objective of the subject
- About knowledge:
- About skills:
- About attitude:
3. Expected learning plan
Ord Content
1.

Introduction

2.

Chapter 1

3.
4.

Chapter 1 Exercises

Chapter 2

Study mode
Watch the introduction video,
Read course material.
Online
(video + self-study material)

Expected result

4. Learning materials
- Document / curriculum ...
- Document / outline with attached video ...
- Link...
5. Inspection and evaluation:
- Essay questions...
- Essay...

Step 2. Developing content of e-learning courses
Teaching approach through programming, learning content can be divided into
modules partially. Learner activities are divided into steps. Every learning step requires
feedback and testing. These activities can be problem-raising, lecturing, illustrating,
examining, consolidating, etc. Activities can be carried out as follows:
- Preparation: Can ask students to research documents, answer various questions,
including open questions and short answer;
- Exchanging after watching videos, photos of good practices;
- Solving situations and apply what was learned into real practice through situations
or role play;
- Lecturer explains the module content in image or audio files.
The author has built an online course "Developing competency for teaching mathematics"

at Vinh University. Based on the study of training pedagogical bachelor of Vinh University, the
program structure which consists of knowledge blocks includes:
Math’s knowledge block; Math’s pedagogical knowledge block; Teaching knowledge
block
Based on the analysis of the training program of mathematics pedagogy, the author
chooses the teaching method of Algebra and Analysis, the method of teaching Geometry, and the
practice of teaching Math to build e- learning Website "Developing the competency of teaching
Math" supports student training of Mathematics pedagogy.


Picture 2.3. The online course screen "Developing teaching competency of
Mathematics"
Course structure is as follows:
+ Module 1: Overview of the course
- Providing students with necessary documents before the start of the course,
including: Course outline: detailed outline of the subject, topics and activities related to the
subject, introduction on the methodology, the form of score evaluation, ...
- Study plan: study plan for each lesson includes information about the topics to be
learned and how the activities will be implemented, study schedule, ...
- References: documents related to the subject needed for student.
These materials are posted directly by lecturer on the system, students will download to
their personal computers and use throughout the course.
+ Module 2: Student learning activities
- Self-study: This is the part where students study each module in the subjects, students
can view, listen to lectures through electronic lectures, read learning materials related to the
subject that students will use during learning. Learning study cards, work sheets, exercises,
etc.
- Case study: The typical lecture videos can be a case for students to study as a class
observation activity. Students observe lecture hours (can be viewed multiple times),
individuals make comments or exchange via forum. Electronic lectures will exist throughout

the course, students can watch online or download lectures anytime. The system does not
rate this activity but it is still possible to know if a student has read the lesson or not.
2.2.2. Solution 2: Organize learning activities of Math pedagogy students under the
blended learning model, creating opportunities for practicing using IT to support some
stages of organizing cognitive activities for students in teaching Math
2.2.2. Purpose of the solution
This solution focuses on developing elements of the teaching competency framework
that need to be developed for mathematics pedagogical students at university through
designing teaching activities in the training program of pedagogical universities to develop
the ability of teaching students under the blended learning model to exploit effectively,
appropriately and promote the advantages of traditional teaching in the lecture hall and
online teaching through the e-learning system which was presented above.
2.2.2.2. Scientific basis of the solution
The current e-learning courses are very diverse, not restricted to any institution's
program but follow and meet diverse learning needs, skills, and research capabilities or real
career in society.
A blended learning or hybrid learning model is a combination of "face-to-face"
teaching with "online" teaching models.
Example 15: Teacher designs learning materials in a "mixed learning" model with
online content in e-learning system: Help students learn the homothetic transformation: "The
homothetic transformation turns 3 points straightly into 3 points straightly and preserve the


order among those points ”, the lecturer instructs students to use GeoGebra software to
organize teaching for pupils as follows:
Content
Teacher activity
Pupil activity
- Open the file "VD3.ggb" to - Indicating how to determine
show the following elements: ray the image of a point through a

center I, ray ratio and three sequence
Activity 1.
straight points A, B, C (B is - Observing images:
Determining a between A and C).
point
image - Appearing points A ', B' and C
through
'respectively which are photos of
homothetic
A, B, C through homothetic
transformation transformation V (I, k)
V (I, k)

Activity 2.
Using the software's function to
Observing the
change the positions of points A,
relative position B and C
of 3 points A ’,
B’, C ’
- Using the software function,
checking the alignment of the
three points A ’, B’ and C ’
- Drawing straight lines AC, A’C
’and let point B move on AC:

Observing the result on screen
and make predictions:
- 3 points A ’, B’, C ’are
collinear

- B ’is between A’ and C ’
- 3 points A ’, B’, C ’are
always in line
- Point B 'always between A'
and C '
The
homothetic
transformation turns 3 points
straightly into 3 points
straightly and preserve the
order among those points

Activity 3.
Prediction
checking

? Let’s state the property of 3
collinear points through a
homothetic transformation
Giúp HS tìm hiểu tính chất của phép đối xứng tâm: “Phép đối xứng tâm biến đường
tròn thành đường tròn có cùng bán kính”, giảng viên hướng dẫn SV sử dụng phần mềm
GeoGebra để t chức dạy học cho HS như sau:
Similarly, we can exploit GeoGebra software to help students discover other
properties of the homothetic transformation.
Helping students learn the properties of central symmetry: "Central symmetry
converts a circle into a circle with the same radius", the lecturer instructs students to use
GeoGebra software to organize teaching for pupils as follows:

Content

Lecturer activity

Pupil activity


Content

Lecturer activity
- Opening the file "VD1.ggb" to
show the following elements:
Activity 1.
Determining Center of symmetry I, circle (O;
the image of R) and point M  (O; R)
a
point - Determining M’, O’ respectively
through
a images of M, O through center
symmetry I
center
symmetry

Pupil activity
- Indicating how to determine the
image of a point through center
symmetry.
- Observing image:

Using the function of GeoGebra
software, set the property to leave
a mark for point M 'and to change

the position of point M:

Observing the result on screen
and make a prediction: The
image of circle (O; R) through
center symmetry I is a circle (O ';
R)

Using the function of GeoGebra
software, determining the locus of
M 'point when M changes,
calculating the length of the O’M'
and R segments:

- M's locus is a circle
- O’M’= R.
Central symmetry converts a
circle into a circle with the same
radius

Activity 2.
Observing
the trace
image of M
'point

Activity 3.
Prediction
checking

? Let’s state the property of the
circle through center symmetry
Similarly, teachers can exploit GeoGebra software to help students discover the
properties of center symmetry as well as with any displacements.
After organizing for students to learn with online courses about teaching method of
Mathematics for pupils, teachers teach in traditional classroom the following exercise:
“According to you, in the following lessons, which lesson is allowed to be applied IT in
online courses under the model of "mixed learning" with high efficiency, why?
1) Translations and displacements;
2) Two parallel lines;
3) Two perpendicular planes;
4) Distance.
Lecture organizes for student, student groups to self - research and exchange, discuss
the above exercise. The purpose of this exercise helps students form the ability to select
lesson content and appropriate types of lesson to apply IT to achieve high efficiency. Math
lessons need the support of IT because of high level of knowledge abstraction. The type of
lesson presented in the form of an "online course" is usually a theory lecture. Thereby, the
lecturer noted that students should apply IT in some situations:
+ Teaching scientific concepts and phenomena in which students have difficulty
visualizing scientific concepts and can use simulations to express the above concept in a
more intuitive way.