Summary of Doctoral Thesis of Scientific Education: Developing teaching competence for university students in Mathematics Pedagogy with the support of information and communication technology

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 inter- connected 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

Chapter 1. Theoretical and practical basis Chapter 2. Solutions to develop teaching competence for math pedagogical students

In addition to the Introduction, Conclusions and References, the thesis content has 3 chapters: 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.

to develop

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 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 Co- operation 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.

- Preparation capability includes operations, - The ability to implement a teaching plan is shown in the process of practicing

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. 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 ".

Designing content of teaching mathematics

Check and evaluate

Math teaching competency of pedagogical students

Mathematics thinking and reasoning

Logical design to form Mathematics competency of Students

Use tools and means to learn mathematics

Math modeling

Using Math teaching facilities

Mathematics Competency

Math competency of pupils

Solve math problems

Math communicatio n

Managing mathematics teaching activities

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

Competency to conduct teaching

Teaching Design Competency

Competency to manage teaching

Competency of testing and evaluating 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

Indicators Competency components Demonstration of competency

1. DESIGN COMPETENCY OF MATHEMATICS IN HIGH SCHOOL

curriculum

in

1.1. Studying knowledge content and mathematics program in high school (4 indicators)

the Mastering of knowledge mathematics in high school, ensuring the content of teaching is accurate, systematic, rationally applying interdisciplinary knowledge to meet the the goals of education general program.

Create a plan for to teaching Math the meet 1.1.1. Present the knowledge system of Mathematics, which is related and extended with other subjects and practice 1.1.2. Describe and the distribution of Math curriculum to ensure the objectives of mathematics education 1.1.3. Identify the process of developing mathematical teaching competencies mathematics in high schools by the general education program. 1.1.4. Identify characteristics of teaching, methods, means and forms of teaching mathematics in the direction of developing students' competency to meet educational objectives 1.2.1. Find out characteristics, student objects, facilities, resources to plan for teaching Math 1.2. Planning math teaching in high school

Indicators

Competency components (6 indicators)

to

in accordance with

Demonstration of competency requirements of the and teaching goals education according the curriculum Math general for education, consistent with the of characteristics students and the educational environment.

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 the high schools 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

implementation of

2.1. Organize students' learning activities according to the high school Math teaching plan teaching (3 indicators) methods, Using techniques and teaching facilities to implement students' learning and math activities to achieve the teaching and educational goals.

clear to and

concise, ensures of

2.2.Communicate, use Math language

intonation, have (2 indicators) a

Knowing how use accurate expressions Mathematics, thoughts coherent of feelings and verbal as well as facial expressions, acts, gestures

resolve that have occurred positive, facilitately, collaborately, 2.3. Handling pedagogical situations 2.1.1. Organize the teaching activities according to the set plan 2.1.2. Guide and manage learning activities in class, group, ensuring the process and duration of teaching reach the teaching objectives set out. facilities, 2.1.3. Use Math equipment, software to support learning and Math self-study for students effectively 2.2.1. Know how to use language that contains a high density of information, the presentation of accurately expresses logical Mathematics, information 2.2.2. Know how to use simple, vivid, rich clarity, images, expressiveness coherent with pronunciation in which there are no mistakes in rhetoric, grammar, and phonetics. 2.2.1. Know anticipation and situations cooperately, securedly and be healthy

(2 indicators)

2.2.2. Know how to deal with student friendly and democratically Solve pedagogical arisen situations that meet the learners 'requirements and keep the teachers' reputation

Identify methods, 3.1.1. Describing the methods, forms of 3. INSPECTION – EVALUATION COMPETENCY IN MATHEMATICS 3.1. Test –

Indicators Competency components

Demonstration of competency forms, testing tools - assess the quality and competency of students the

evaluation planning in accordance with the teaching plan and school education program

(4 indicators)

organization tools forms, to assess and

testing and evaluation specifically in Math teaching 3.1.2. Designing questions, test exercises, assess 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 3.2.1. Knowing of the examination - assessment to ensure the openness, accuracy, objectivity, comprehensiveness and fairness. 3.2.2. Using means and technologies to store and manage test and evaluation results

3.2. Organization of examination - evaluation

and adjust and (3 indicators)

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

4. COMPETENCY OF MATHEMATICS TEACHING MANAGEMENT

4.1.1. Knowing how to design a notebook, tracking record and recording all comments on characteristics, performance of students during class time ...

4.1. Manage the implementation process of teaching to ensure the teaching meets the set goals.

4.1.2. Knowing how to use information to make plans, schedules, and timelines for teaching activities (2 indicators) Mobilizing, distributing, organizing resources, managing classrooms to well implement teaching activities

to use student

4.2. Self-test and evaluation to draw experience for teaching

Self-assessment, successes and limitations of each lecture and propose remedies (2 indicators) 4.2.1. Knowing how test- assessments, comparing with identified goals to assess learning experience for teaching 4.2.2. Suggesting solutions to overcome the 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

Indicators Average

Standard deviation

Element of competency Demonstration of competency

1. COMPETENCY OF MATHEMATICS DESIGN IN HIGH SCHOOL

3.64 0.902

3.64 1.136

of

3.59 1.008

1.1. Studying knowledge content and mathematics program in high school (4 indicators)

Mastering the knowledge of Maths in high school, ensuring the teaching content is accurate, systematic, rationally applying interdisciplinary knowledge to meet the goals of the general education program.

3.55 0.912

3.55 0.912 1.2. Planning math teaching in high school (6 indicators) 1.1.1. Presentation of Mathematics the knowledge system, which is related and expanded with other subjects and practices the 1.1.2. Describing curriculum and distribution of Math to ensure the objectives of mathematics education 1.1.3. Determining the path developing mathematical competence in teaching mathematics at high schools by the general education program. 1.1.4. Identifying characteristics of teaching, methods, means and forms of teaching mathematics in the direction of developing students' competency to meet educational objectives 1.2.1. Finding out characteristics, student objects, facilities, resources to plan for teaching Math Making a plan of teaching Math to meet the requirements of the teaching and education

Indicators Average

Standard deviation

Element of competency

3.45 0.852

Demonstration of competency objectives according to the Maths general education curriculum, suitable to the characteristics of students and the educational environment. 3.35 0.934

3.55 1.057

3.50 1.102

3.45 1.011

Selecting, tools, study ensure for the in 1.2.2. Determine teaching objectives that meet the requirements Math of the student curriculum, and characteristics school facilities Identifying 1.2.3. teaching methods of Math in high schools in accordance with the objectives and teaching content 1.2.4. Designing content and situations teaching in mathematics in schools to ensure the goal of competency development for students 1.2.5. Designing Math in teaching activities accordance with teaching objectives 1.2.6. designing facilities, and to cards convenience students awareness process

2. COMPETENCY OF ORGANIZING MATHEMATICS TEACHING IN HIGH SCHOOL

Organize activities 3.27 1.032

in to ensure 3.27 0.985

2.1.Organizing students' learning activities according to the high school Math teaching plan (3 indicators)

3.27 0.703 Using methods, techniques, teaching facilities to implement Math learning and training activities of students to achieve the teaching and educational goals. 2.1.1. teaching according to the plan 2.1.2. Instructing and administering learning class, activities group the teaching process and duration meet the teaching objectives set out. 2.1.3. Using Math teaching aids, equipment, software to

Indicators Average

Standard deviation

Element of competency Demonstration of competency

3.27 1.162

2.2.Communicating, using Math language (2 indicators)

3.27 0.985

Using clear, precise expressions of Mathematics, coherent with your thoughts and feelings with words as well as facial expressions and gestures

3.23 0.752

2.3. Handling pedagogical situations

the (2 indicators)

Solving pedagogical situations that arise to meet the learners 'requirements and keep teachers' reputation 3.23 0.685 learning and support Math self-study effectively for students 2.2.1. Language contains large information density, accurate and concise description of Mathematics, ensuring logical information 2.2.2. The language is simple, vivid, rich in intonation, images, expressive a with coherent pronunciation in which there are no mistakes rhetoric, in grammar, and phonetics. 2.3.1. Anticipating and situations addressing that occurred have positively, cooperatively, collaboratively, smoothly, safely, and healthily 2.3.2. Dealing with students democratically and friendly

3. INSPECTION – EVALUATION COMPETENCY IN MATHEMATICS

3.18 0.958

3.14 0.774

Identifying methods, forms, testing tools to the assess quality and competency of students 3.1. Test – evaluation planning in accordance with the teaching plan and school education program

3.64 0.902

the 3.1.1. Describing of forms methods, testing and evaluation specifically in Math teaching Designing 3.1.2. questions, test exercises, assessing the level of mastery of Math knowledge and skills of students 3.1.3. Designing plan questions, to use exercises testing, in assessing competencies teaching in mathematics 3.1.4. Developing test 3.64 1.136

Indicators Average

Standard deviation

Element of competency Demonstration of competency

assessment plan the and education

3.59 1.008

3.55 0.858 test

3.2. Thực hiện kiểm tra - đánh giá (3 chỉ báo) Perform tests - assessments (3 indicators)

results and 3.55 0.912

results Sử dụng các hình thức, pháp, phương công cụ kiểm tra, đánh giá lực học năng sinh một cách chính xác, khách quan, công bằng để điều chỉnh hoạt động dạy học, giáo dục thúc đẩy sự phấn đấu vươn lên của học sinh. and – consistent with plan teaching school program 3.2.1. Organizing the inspection - evaluation to ensure the openness, accuracy, objectivity, comprehensiveness and fairness 3.2.2. Using facilities and technology to store and manage - evaluation results 3.2.3 Using appropriate notify ways to to assessment other students using stakeholders, assessment to adjust improve teaching activities.

4. COMPETENCY OF MATHEMATICS TEACHING MANAGEMENT

3.55 0.912 of

to implement 4.1. Managing the implementation process of teaching to ensure the teaching meets the set goals

Mobilizing, distributing, organizing resources, managing classrooms well teaching activities 3.50 1.102

3.45 1.011

4.2. Self-test, self - evaluation to draw experience for teaching Self-assessment, and successes of limitations each lecture and proposing remedies

3.45 0.858

4.1.1. Designing books, teaching tracking sheets and recording all comments on characteristics, performance of students during class time ... 4.1.2. Using information to make plans, schedules, and timelines for teaching activities 4.2.1. Using test information - student assessments, comparing with identified goals to assess learning experience for teaching 4.2.2. Proposing solutions to overcome 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 INFORMATION AND WITH THE SUPPORT OF FOR STUDENTS 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:

E-learning portal

INTERFACE LEVEL

User (Managers, lecturers, Students)

EXTENDED LEARNING MANAGEMENT (Extended LMS)

LEARNING MANAGEMENT (LMS)

LEARNING MANAGEMEN T LEVEL

Digital library

Online exam management system (*)

Scientific management system

Student assessment system (*)

Online conference (*)

virtual classroo m (*)

Integrated learning, cooperation (*)

Object management system (*)

Learning content management system (LCMS)

CONTENT, OBJECT MANAGEMEN T LEVEL

CSDL LEVEL

Study

Other CSDL

Finance

Library

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

Expected result

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)

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

Content

Pupil activity - Indicating how to determine the image of a point through a sequence - Observing images:

order among those points ”, the lecturer instructs students to use GeoGebra software to organize teaching for pupils as follows: Teacher activity - Open the file "VD3.ggb" to show the following elements: ray center I, ray ratio and three straight points A, B, C (B is between A and C). - Appearing points A ', B' and C 'respectively which are photos of through homothetic A, B, C transformation V (I, k) Activity 1. Determining a point image through homothetic transformation V (I, k)

Using the software's function to change the positions of points A, B and C

Activity 2. Observing the relative position 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:

3

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 points into straightly and preserve the order among those points Activity 3. Prediction checking

through points ? Let’s state the property of 3 collinear 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

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

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

Activity 1. Determining the image of point a through a center symmetry

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)

Activity 2. Observing the trace image of M 'point

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 3.

Activity 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.

+ When you need to help students to practice certain skills, through having to

complete many exercises, organizing automated assessment and evaluation on computers. + The need to simulate movements, to create problematic situations to stimulate learning interest in students.

+ The need to change conditions, parameters. + Content that students often make mistakes, need a model, sample solution for reference, lessons learned.

+ Content to be summarized in the lesson, summarized at the end of the chapter. + Multiple choice exercises, crossword exercises in the form of games to help consolidate and quick test of lesson knowledge.

+ Need to save time in class (Drawing complex shape drawing). Thus, it can be considered that integrated teaching is not only a way of designing the teaching process, but also a restructuring of the teaching model, which needs to be seen as a holistic approach both in terms of pedagogical principle and physical space of teaching organization.

2.2.2.3. Solution content * Activity 1. Organizing teaching activities associated with the process of training teaching competency for Math pedagogical students

Based on the general approach following pedagogical principles and physical space, lectures in Math pedagogical student training program at university can be designed and implemented in the following two methods:

* Activity 2. Using virtual model by exploiting teaching software to organize students - Method 1. Turnaround - Next: learning modules are implemented in the face-to- face and online format respectively, according to the plan. The face-to-face format mostly supports introductory activities, guidance, personal planning orientation, discussion of issues and problem-solving directions. The implementation of individual learning plan can be done online including exchange, feedback, testing ... through the network and learning management system - LMS: to explore knowledge and discover new knowledge Lectures create opportunities for students to practice using IT to support some stages of organizing cognitive activities in teaching Math.

Example 16: Lecturers instruct students to organize teaching for pupils as follows: Using GeoGebra software to suggest problems for the following problem: “Prove that in a tetrahedron, four straight lines connect the vertices of the tetrahedron with the centroid of opposite face converges at 1/4 of each line (from the centroid of opposite face). Are the four height lines of the tetrahedron converging? ”

Lecturer: We know in a plane that three median lines in an triangle are converging at 1/3 of each line (from the midpoint of opposite edge). So the same property in tetrahedra are correct? Lecturer: Giving picture and changing positions for pupils to observe drawing on dynamic geometry software. Through observation pupils predict AG1, BG2, CG3 and DG4 converged and want to clarify that. Lecturer: After students have demonstrated 4 lines converged, the lecturer asks to study the

position of G point to see what's special.

Lecturer: Using the measurement function, the result shows that in this case, the point of intersection G is 1/4 of each line. For changing a few other positions, the ratio is unchanged. lecturer asks the question: "Is it possible that in the tetrahedra, 4 straight lines

connect the vertex with the opposite centroid converging at 1/4 of each line?". Here students will find a way to prove their judgment. At the same time, lectures create situations for students to practice using virtual models to consolidate mathematical teaching knowledge for students.

Example 17: With the problem "Given two points A, B and the circle center O has no common points with line AB. Through each point M runs on a circle (O), construct a parallelogram MABN. Prove that point N belongs to a definite circle ”. In face-to-face class, lecturers instruct students to use GeoGebra software to organize

teaching for pupils as follows:

Content

Teacher activity Open file "VD2.ggb" for pupils to observe the picture:

Pupil activity Pupils picture, observe drawing picture and identify elements; mobile fixed element and locus element

Acivity 1. Understanding the problem

Using the software function, give point M to change some positions on the circle and leave traces of point N for pupils to observe:

- Observing the position of point N during the process of point M changes on the circle (O) - Predicting the locus N is a circle Activity 2. Predicting locus

function, Using the software's

determining point O ’= (O).

- O ’is a fixed point. - OM = O’N Conclusion: The distance between N and O' is a unchanged distance OM. Therefore, the locus of N is a circle with diameter OM Commenting on the position of point O ', comparing the lengths of OM there, drawing and O’N. From conclusions about the locus of point N:

Activity 3. Developing problem solving program

Making specific requirements when proving the pros and cons

the guidance of Under lecturer, logical by reasoning, pupils proceed to prove the pros and cons and the locus conclusion.

Using the software's function, Pupils observe visually the Activity 4. Implementing the problem solving program Activity 5.

Content Surveying the found solution Teacher activity determining the locus of point N when M runs on the circle (O):

Pupil activity locus image on screen and find that the locus of point N completely coincides with the result that pupils have shown in the activity is the image of circle (O) through following the translation

* Activity 3. Applying knowledge into practice Example 18: Determining regular tetrahedra in the following pictures:

- Activity 1 : Let's predict where is the regular tetrahedron ? From there, using GeoGebra software to check.

Clearly, visual images easily make pupils think that the tetrahedron A2B2C2D2 is

regular tetrahedron and the tetrahedron A1B1C1D1 is not. But when pupils use the measurement function of GeoGebra software, they quickly recognize this mistake and correct it.

- Activity 2 : Teacher gives pupils comment on the general representation of a regular tetrahedron. Lecture needs to emphasize to pupils that: based on the representation of space cubes only, it is difficult to accurately determine the picture. Neither can we measure, nor survey, on drawing accurately except on the real thing or the model of real thing. Therefore, when solving spatial geometry problems, on the one hand, it is necessary to draw pictures to support thinking, on the other hand to avoid subjectivity and misperception that leads to unfortunate mistakes. Need to combine with logical thinking to clarify the speculation.

- Activity 3 : Teacher must also create a situation that helps pupils identify equilateral triangles and regular tetrahedra by opening the file containing regular tetrahedra and equilateral triangular pyramid, asking pupils to use the perpendicular tool and measure the length of the line to determine which is a equilateral triangular pyramid and which is a regular tetrahedron. These are two very confusing concepts for pupils. The equilateral triangular pyramid is the shape whose bottom is an equilateral triangle, with a top point coinciding with the bottom centroid. And the regular tetrahedra is a equilateral triangular pyramid with all equal sides. Thus, the regular tetrahedra is a equilateral triangle pyramid, but the opposite is not true.

Online courses for Math pedagogical students are built on the LMS Moodle system. The system allows the organization of flexible courses, thematic format or each week of study.

The learning activities are organized in a flexible and seamless to meet the learners'

individual needs, including:

- Searching for learning materials: Digitized learning materials in PDF format or packaged electronic lectures according to SCORM standards are included in the course's resource section and linked with icons on the main screen. . Students can click the icons to read on the computer or downloading to read on the computer when there is no internet connection - Exchanging and discussing: by forums or chat room, students can give questions, answers, or attaching files for discussion, group work in class.

- Taking tests: Tests can be in the form of quizzes or essay format which is uploaded to the file (Upload file). Students can do essay exercises on word files, PDF... and upload files to the web The process of developing a mixed teaching plan in teaching for pedagogical

university students is as follows:

- Step 1: Determining the purpose of applying mixed teaching; - Step 2: Selecting the appropriate model; - Step 3: Analyzing the context; - Step 4: Developing a detailed teaching target system; - Step 5: Developing appropriate content topics; - Step 6: Digitizing content and learning materials; - Step 7: Making a plan to organize teaching activities in detail by topic or by week; - Step 8: Designing activities, assessments and evaluation tools; - Step 9: Selecting appropriate tools and technology platforms; - Step 10: Trial operation and evaluation. 2.2.3. Solution 3: Applying micro-teaching methodology to develop teaching competency for Mathematics pedagogical students with the support of video analysis software associated with seminar organizations to exploit some stages of math teaching organization using software 2.2.3.1. Purpose of the solution

This solution is to develop elements of the teaching competency framework that needs to be developed for mathematics pedagogical students and it has been proposed in chapter 1, which focuses on the content analysis, curriculum and planning skills of math teaching plan in high school.

The solution will contribute to strengthening the implementation of teaching activities for math pedagogical students at the university and the ability to integrate technology, pedagogy and content through a number of practical teaching activities and using video analytics software to support lesson research by micro methods, in association with organizing seminars for students on the content of using teaching software, in which focusing on discussing exploitation of some organizational steps to teach math using appropriate software. The competencies formed and developed through solution 3 are shown in Table 2.3.

Table 2.3. The competencies formed and developed through solution 3

Indicators Competency elements Demonstration of competence Student learning activities

2.1.1. Organizing teaching activities according to the plan Using methods, techniques, teaching Self-practice, video recording, 2. COMPETENCY OF ORGANIZING MATHEMATICS TEACHING IN HIGH SCHOOL 2.1. Organizing students' learning

Indicators Competency elements Demonstration of competence Student learning activities to in discussion class and online

Instructing

activities according to the high school math teaching plan (3 indicators)

learning training of to the and

Self-practice, video recording, in discussion class and online facilities implement math and activities students achieve teaching educational goals. 2.1.2. and learning administering activities in class, group, ensuring teaching the process and duration meet the teaching objectives set out.

2.1.3. Using math teaching aids, equipments, software to support learning and math self-studying effectively for students Self-practice, video recording, in discussion class and online

clear,

2.2.1. Language contains information density, large accurate of description mathematics, concise and logical information Self-practice, video recording, discussion in class and online

language

2.2. Communicating, using math language (2 indicators)

Using precise expressions of mathematics, coherent with your thoughts and feelings as well as facial expressions, gestures Self-practice, video recording, discussion in class and online grammar, 2.2.2. The is simple, vivid and rich in images, intonation, bright, expressive with a coherent pronunciation in which there are no mistakes in and rhetoric, phonetics.

smoothly, Self-practice, video recording, discussion in class and online and 2.2.1. Anticipating that addressing situations have occurred positively, cooperatively, collaboratively, safely, and healthily

2.3. Handling pedagogical situations (2 indicators) 2.2.2. Dealing with students democratically and friendly. Solving pedagogical situations that arise to meet learners 'requirements and keep teachers' reputation

2.2.3.2. Scientific basis of the solution Micro teaching or "excerpt teaching" means that a regular lesson can be divided into small, short periods.

Micro teaching is most clear at lecturing practice stage, lecturer needs to split activities. Each student should practice only one to two activities (For example activities: checking old lessons and introducing new lessons; ...). Each student can choose short sections of 15-20 minutes in lessons - with the intention of training students with a skill, the ability to determine in the pedagogical competency system of the training program.

2.2.3.3. Content of the solution

* Organizing practice of teaching under micro-teaching and evaluation with the help

of video analysis software Example 19: Lecturer gives students observation of 1 math lesson video in high

school, in which the teacher uses GeoGebra software to organize teaching for pupils with the following problem: "Give ABCD trapezoid with big bottom line BC and inscribed circle center O. Let P be a changable point on the line BC and outside of the segment BC so that PA is not tangent to the circle (O). The circle with diameter PD cuts (O) at E (E ≠ D). Let M be the intersection of BC with DE, N is another intersection of PA with (O) beside A. Prove that the line MN passes through a fixed point. " Through video, students analyze the teaching activities of math teachers in high school:

To solve this problem, there are two difficult issues that pupils need to overcome: (i) Predicting fixed point. (ii) Discovering the orientation to prove the fixed point.

With the support of the software, teachers can organize activities to support pupils to solve the problem as follows: Activity 1: Teacher draws picture clearly showing the given elements of the problem for students to observe:

Activity 2: Teacher changes picture, helping students accurately identify fixed factors and changing factors of the problem. Activity 3: Teacher can use the system of open questions combined with support of the software to find solutions to the problem as following:

Suggestive questions of teacher and

Pupil’s prediction detection MN cuts the fixed circle (O)

? 1 The fixed point to look for is usually the intersection of two fixed lines. Is the change of MN line related to any fixed line?

Suggestive questions of teacher and

Teacher sets point A' is the intersection of MN with (O), changing position of point P Pupil’s prediction detection It seems that point A’ does not change position when MN changes

? 2 Let’s observe the position of point A' when MN changes

seems that A’

? 3 Let’s observe and predict the relationship between point A’ and point A

is It symmetrical with point A through center O Need to prove that M, N, A’ are always in line

is DA's ? 4 Set A' is the symmetrical point of A through O, so A' is fixed. What needs to be done to prove that MN always goes through A’ ? Teacher: Connect A' with D, call F intersection with BC DE is the radical axis of (O) and (γ1) the diameter PD

? 5 DE is the radical axis of which two circles?

so NA’ is the NA 'is the radical axis of (O) and (γ2) diameter PA' ? 6 Because of the angle radical axis of which two circles?

? 7 Since DA' cuts BC at F, thats why angle BC is the radical axis of (γ1) and (γ2) . It means the angel . So, BC is the radical axis of which two circles?

và NA'

? 8 Because the radical axes converge at the radical center, what should we infer?

are DE, BC concurrent at point M. So M, N, A ’are collinear (What must be proven)

After allowing pupils to present the solution, teacher gives point P to change position so that the pupils observe the image of straight line MN always passing through point A' :

Currently, there are many softwares to help analyzing video such as BORIS software, this is free software, which can be downloaded at http://www.boris.unito.it/. BORIS software helps to encode that information into quantitative and computable variables with data analysis software such as Excel, SPSS ... Using BORIS software to analyze video files for micro analysis requires the following component files: - Video file of teaching hours. - Project file: Describing in detail the behaviors, events, and attributes of variables which you want to use for coding.

The BORIS software analyzes video files by marking the video parts and encoding them into events. There are two types of behavior are State, called time interval variables and Point called moment variables). Interval variables allow time values to be calculated, with point variables not for time values but for the point value at the marked position.

2.3. Pedagogical requirements in using teaching competency development solutions for math pedagogical students at universities with the support of information and communication technology New technologies, especially the appearance of "E-education", bring the ability to meet education requirements and teaching without limitation (anywhere, anytime, every object, every information content, knowledge, every means ...). On the other hand, ICT environment also requires students to develop more than some specific skills.

Lecturers who play an active role in pedagogical solutions should be well equipped in operating the method as those who design the content of materials and as a guide for students. For learning process, in addition to learning skills in the traditional classroom, students need to equip learning skills in the ICT environment. In addition, some assessment techniques in teaching math for pedagogical students also improve the reliability if using IT.

- Through electronic testing (E-testing) - Through operation - Through conversations on the forum or chat room - Through the performance exercises (performance task) - Through electronic learning records (e-portfolio) In addition to the evaluation techniques through the above channels, there are other evaluation channels such as through reports or personal diaries. Teachers need to clearly identify the expected results of each lesson and subject.

2.4. Conclusion of chapter 2 Accessing teaching activities of mathematics teacher in high school, studying professional standards of high school teacher in Vietnam and some countries in the world, on the basis of applying the Know-Do-Be model, the thesis determines the teaching competency that needs to be formed and developed in math pedagogical students including 9 elemental competencies in Chapter 1 including: understanding the content of knowledge and mathematics program in high school; understanding theories, methods of teaching mathematics and developing mathematics teaching programs in high school; knowledge of tests and assessments in teaching math; planning mathematics for teaching in high school; implementing the plan of teaching mathematics in high school; build learning environment for mathematics; use of IT in teaching math; using foreign languages in research and teaching math.

Building these competencies requires direct or indirect contributions from many subjects and ICT support. Based on the analysis of training math pedagogical students at some pedagogical universities, the thesis proposes 3 solutions to develop teaching competency for math pedagogical students with the support of ICT: Building an e-learning online system "Developing teaching competency for mathematics pedagogy students", identifying technical tools to design and build online courses for students; organizing the use of online learning system combined with b-learning; exploiting video analysis software to combine with micro-teaching in developing teaching competency for math pedagogical students. The above solutions supplement the diverse teaching methods in pedagogic universities, helping students develop the ability to teach math.

Chapter 3: PEDAGOGICAL EXPERIMENT

3.1. Purpose of pedagogical experiment Pedagogical experiment is conducted to test scientific hypothesis through teaching practice, and at the same time, evaluating the feasibility and effectiveness of a number of proposed pedagogical solutions to contribute to the development of mathematical self - studying skills for students with the support of ICT.

3.2. Pedagogical experimental method The thesis uses the following methods in pedagogical experiment: - Research design based on action - Research using pre- and post-intervention analysis - Survey method, in-depth interview (using questionnaire, student interview question),

- Evaluating the preparation and planning of teaching. (appendix 4a) - Teaching micro-learning (using video observation checklist) (appendix 4b) - Teaching practice in class (with another students playing the role of pupils) (appendix 4c)

- Evaluating through "Teaching records" which students built. (appendix 4d) 3.3. Preparing pedagogical experiment In order to create favorable conditions for pedagogical experiment, a number of preparatory works have been carried out: - Exchanging ideas with the subject departments, teachers to do experiments on the purpose, content, experimental methods.

- Arranging a practice room with two working spaces: A co-working space with a high-speed Internet classroom, a projector (requiring students to prepare laptop). Teaching and video recording practice space with computer and projector layout, chalkboard, mobile phone holder (for video recording) for groups of students to practice teaching, video recording and analysis of teaching hours . 3.4. Pedagogyical experimental process Because the thesis author is working at Vinh University, the module that the author designed to organize pedagogyical experimental is "Algebra and analytic teaching method" in the bachelor's program of mathematics pedagogy of Vinh University. Pedagogyical experimental 's location is Vinh University.

Experiment in developing mathematical teaching skill for students during teaching the module "Algebra and Analysis method" for 4th year students. It is worth noting that after 3 years of studying, students have gained some knowledge and skills in psychology, education, and reasoning for teaching mathematics, however, because the structure, content and time of each module are not enough for lecturers to focus on developing mathematical teaching skills for students carefully. Therefore, the thesis author wants to try to continue training and developing mathematical teaching competency for students with the use of solutions proposed in chapter 2 through teaching the module " Algebra and analytic teaching method" (This is also the module that students will have to teach in pedagogy intership).

3.5. Pedagogical experiment result 3.5.1. Result of consulting with experts (Pedagogyical experiment stage 1) - Purpose, content of 3 solutions (Solution 1: Building an e-learning online learning system "Developing teaching competency for mathematics pedagogy students"; Solution 2: Organizing learning activities of mathematics pedagogical students based on blended learning model to create opportunities for practicing using IT to support some stages of organizing cognitive activities for students in teaching mathematics; Solution 3: Applying micro-methods to develop teaching competency for Mathematics pedagogical students with the support of video analysis software associated with seminar organizations to exploit some stages of organizing teaching mathematics using software ); The solutions are edited and presented in the content of chapter 2 of the thesis.

The synthesizing result of expert opinions on the structure of a high school preparatory Math teaching practice report for Mathematics pedagogical students; Criteria for evaluating teaching records of students; Criteria for evaluating teaching performance of students; Criteria for evaluating videos of students' lessons:

3.5.2. Experimental result of pedagogy stage 2 * For module 1: - About the preparation of students: - About practice of teaching a specific Math content: - About class discussion activities: * In module 2 and the following: - About the preparation of students - About teaching practice - About general knowledge of Mathematics and understanding of Math curriculum - About lesson planning and implementation of teaching plan Observing the presentation and evaluation of teaching files, the thesis author has commented: - Teaching hours are designed by students very diverse, with many creative points, clear presentation. - About the lesson file: Most students develop a teaching plan, write clear goals, identify teaching activities that are appropriate to the goals.

However, the planning of using study cards, facilities, technology in teaching of students is still mechanical, stereotyped according to the teacher manuals and materials on lesson design which are being sold on market. 3.5.3. Experimental result of pedagogy stage 3 After pedagogical experiment stage 2, due to recognizing the difficulties encountered by pedagogical students in the process of applying synchronously the proposed solutions, direct impact on the teaching process of the module "Algebra and analytic teaching method”, the thesis author revised the interface and content of the module on e-learning system; enhancing documents and sample lectures on the system so that students can refer to many documents; arranging more computers in school during self-study time so that student groups can study following B-learning model

Drawing on experience from stage 2, the author organizes guidelines for students to log in and use functions on e-learning system; guiding students to prepare practical lesson plans; guiding students to discuss in groups, play the role of teachers and students to practice teaching and informing evaluation criteria so that students can assess themselves; peer assessment among students.

Three stages of pedagogical experiment, including two stages of pedagogical experiment directly with the object of students in the fourth year of mathematics pedagogy at Vinh University show that basic solutions are appropriate and help developing well the elements of teaching competency. Particularly, only teaching competency element No. 9, "Using foreign language in researching and teaching Mathematics" is a thesis that has not been tested due to limitations of students' ability to use foreign languages in teaching and bachelor’s programs have not had a module of teaching Maths in foreign languages.

3.6. Conclusion of chapter 3 Some lessons of pedagogical experiment process with the number of experimental samples have initially confirmed the value of the proposed author's solutions. Proposing solutions based on the view of comprehensive competency development and exploitation of IT support has helped students to be active, self-reliant, creative and effective in developing teaching competency when teaching some modules of Mathematics teaching method.

Pedagogyical experiment result helps the author to draw some conclusions:

The proposed thesis solutions are appropriate and feasible in deploying the development of teaching competency for Mathematics pedagogical students; The assessment tools have been developed to evaluate the components of teaching competency with reliability, have been standardized and consistent with the teaching characteristics of Mathematics pedagogical students; The results of pedagogical experiment help the author confirm that the purpose of thesis research is appropriate in the context of the need to renovate the current teacher training towards a competency-based approach; Proven scientific hypotheses that the author has completed the research task and the thesis results can be applied in the training of math teachers at universities.

CONCLUSION

Math plays an important role in developing students' thinking. Therefore, in order to teach mathematics well in high school, mathematics pedagogical students need to be capable of teaching mathematics. Within the scope of the topic, the author proposes solutions to develop mathematics teaching competency in high school with the support of IT application. Compared with the purpose and research tasks of the topic, the author has achieved the following results:

1) Theoretical system of teaching competency development for mathematics pedagogical students, based on the theory of teaching competency development, general teaching competency components, teacher career standards of other countries and Vietnam, from which the author identifies the teaching competencies and components of mathematics pedagogical students including 9 competency components with 24 expressions. At the same time, based on the career standards of high school teachers and on the basis of analyzing Math teaching activities, describing in detail the competencies needed to form in Math pedagogical students. (Table 1.2)

2) Conducting research, surveying and analyzing the situation of developing teaching competency for Math pedagogical students. From the viewpoint of competency development and comprehensive innovation with the support of IT, the topic has proposed three solutions to shape and develop teaching competency for math pedagogical students. Specific solutions are: Building an e-learning system "Developing teaching competency for Mathematics pedagogy students"; Organizing the learning activities of Math pedagogical students under the blended learning model; Applying micro methods to develop teaching competency for Mathematics pedagogy students with the support of ICT (Section 2.2).

3) Researching and implementing the proposed solutions into a number of modules on teaching method of Mathematics, based on the position, role of teaching method of Mathematics and the practical conditions of teaching at the training institutions, appling techniques to build online courses on Moodle. Building processes and identifying methods, forms of teaching organization. Applying methods and forms of micro-teaching, building a system of criteria and tools to support teaching competencyof Math pedagogical students. The initial pedagogical experiment results show the feasibility and effectiveness of the proposed solutions for the development of teaching competency of Math pedagogical students with the support of ICT.

With the above results, the thesis has achieved its purpose and confirmed the initial scientific hypothesis. In the process of researching the topic, the author realized that the implementation of solutions to develop teaching competency for Math pedagogical students should be systematically implemented with all the contents in these modules, strengthening the self-study and self-research activities of students. To equip complete and integrated

information technology equipment for pedagogical universities to have conditions to deploy the above solutions. At the same time, there are solutions to encourage teachers to apply IT in teaching.

CATEGORY

PUBLISHED ARTICLES RELATED TO THE THESIS

I. ARTICLES PUBLISHED IN MAGAZINES: {1}. Tran Trung, Phan Anh Hung (2 12), “ ng dụng e-learning trong r n luyện nghiệp vụ sư phạm cho sinh viên ng nh sư phạm Toán trư ng đại học”, Education Journal, số 298 (page 51 -53 và page 48).

{2}. Tran Viet Cuong, Phan Anh Hung (2 12), “T chức dạy học theo dự án các môn phương pháp dạy học góp phần r n luyện nghiệp vụ sư phạm cho sinh viên sư phạm Toán”, Journal of Science & Technology, Thai Nguyen university, Episode 98, No. 10 (page 115- 120). {3}. Phan Anh Hung (2 12), “Quy trình thực tập sư phạm gắn với chuẩn nghề nghiệp giáo viên tại Trư ng đại học Vinh”, Education Journal, special number in 11/2012 (page 59 - 60).

{4}. Tran Trung, Phan Anh Hung (2 13), “Đánh giá k t quả học tập môn Toán của học sinh theo hướng ti p cận năng lực”, Science Journal, Hanoi Pedagogical University, no. 58 (page 190-196).

{5}. Trung Tran, Hung Phan Anh, Duc Bui Minh, Giang Nguyen Ngoc (2 14), “Discovery learning with the help of the GeoGebra dynamic geometry software”, International Journal of Learning, Teaching and Education Research, vol 7(1), page 44-57.

{6}. Pham Anh Giang, Phan Anh Hung (2016), “Xây dựng đề cương học phần Phương pháp dạy học Toán trư ng sư phạm theo hướng ti p cận năng lực thực hiện cho sinh viên sư phạm”, Journal of Educational Science, The Vietnam National Institute of Educational Sciences, special number in 1/2016: (page 43-44). {7}. Phan Anh Hung (2 1 ), “Phát triển năng lực dạy học cho sinh viên ng nh Sư phạm Toán”, Journal of Educational Science, no. 139, 4/2017 (page 49-52).

II. ARTICLES ANNOUNCED AT CONFERENCE: {1}. Tran Trung, Trinh Thanh Hai, Phan Anh Hung, Do Duc Thong (2 12), “ ng dụng công nghệ thông tin trong dạy học trư ng ph thông theo hướng tích hợp”, Yearbook of Workshop on Information Technology in Vietnam Education: Integration or conversion, 12/2012, Publisher Pedagogical University, (page 197 - 203).

{2}. Phan Anh Huung, Nguyeen Ngoc Giang (2 13), “Dạy học đ nh l Pi-ta-go với sự trợ giúp của phần mềm Cabri theo phương pháp khám phá”, Yearbook of The 3rd Youth National Science Conference of Pedagogical Universities, 4/2013, Publisher Da nang (page 485 - 489).

{3}. Phan Anh Hung, Nguyen Yen Thang, Nguyen Tuan Hung, Tran Viet Cuong (2014), “Research on pedagogical models supporting e-learning”, Kỷ yếu Hội thảo khoa học cán bộ trẻ các trường đại học sư phạm toàn quốc lần thứ IV, Publisher Pedagogical University (page 713-722).

{4}. Phan Anh Hung, Nguyen Thanh My (2 19), “Phát triển năng lực dạy học cho sinh viên sư phạm với sự hỗ trợ của CNTT”, Yearbook of International Science Conference on program development, teacher training organization and educational managers towards competency- based approach, publisher Vinh University, (page summary 125-126).