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Survey on actual training of Math teachers at universities, especially in the current situation of training under the credit system, it is clear that the situation of training teaching s

INTRODUCTION

1 Justification of the study

The Resolution of the 8th Central Conference of the 12th term on the fundamental and comprehensive innovation of education and training emphasized

" Strongly shifting the education process from mainly equipping knowledge to comprehensively developing capacity and quality of learners, etc Thus, universities need to form and develop the necessary competencies for students in the training process so that students can achieve professional competence in their teaching University graduates must integrate, adapt and meet the requirements of the society and life

Currently, implementation capacity training is becoming a popular trend in the world This method has been researched and implemented effectively in many countries around the world such as the US, UK, Australia, etc In Vietnam, some schools have started to apply implementation capactity in training, however, the application is difficult due to the lack of a theoretical system based on implementation capacity

In the field of Math teacher training in Vietnam within the implementation capacity approach, there are also some related research and books such as those by Tran Viet Cuong (2012), Nguyen Chien Thang (2012), Do Thi Trinh (2014), Tran Trung, Tran Viet Cuong (2014), Bui Van Nghi et al (2016), Le Thi Tuyet Trinh (2017), Le Minh Cuong (2017), etc However, we have not found any Ph.D dissertation focusing on implementation capacity development for students in the Pedagogical school This is also a gap that needs to be exploited, explored and given opportunities for theoretical and practical contributions

Survey on actual training of Math teachers at universities, especially in the current situation of training under the credit system, it is clear that the situation of training teaching skills for students is still not systematic, lack of in-depth contents , the time students spend on lesson planning, teaching practice is little, the process of practicing practical skills, practice in high schools is still limited Most teacher training universities have not yet built up the process of training teaching skills for maths for students, practical activities for students are not adequate

From the above reasons, the author chose the topic: "Designing the teaching situations of Math teaching method modules for Math teacher students

at universities within the implementation capacity approach" as the PhD

dissertation in education science

2 Research aims: Designing some teaching situations to develop teaching capacity

for students of Mathematics major; organizing teaching according to the situations designed in instructing math teaching methods at the university within the implementation capacity approach to contribute to improving the quality of teacher training at universities currently

3 Subjects, objects and scope of the research

3.1 Subjects of the study: Some situations of math teaching method modules at

universities based on implementation capacity approach

3.2 Object of research: The process of teaching the modules of math teaching

methods at universities based on the implementation capacity approach

3.3 Scope of the research: The research was carried out at the following

universities: Hanoi Pedagogical University, Pedagogical College - Thai Nguyen

University, Hanoi Pedagogical University N02, Tay Bac University, Vinh University, Hong Duc University, Tay Nguyen University, Dong Thap University

4 Scientific hypothesis: It is possible to practice and develop the implementation

capacity for math teacher students in teaching theory and math teaching method modules through using situations because the implementation capacity can be formed and developed through individual and groupwork activities of students under the organization and support of teachers

5 Research task

5.1 Studying the theoretical background of math teaching methods of Maths

at universities to train teachers in the implementation capacity approach

5.2 Surveying and assessing the situation of teaching the math teaching method modules at universities which train teacher students in the direction of implementation capacity

5.3 Designing and organizing teaching activities based on the designed situations in math teaching method modules at universities within the implementation capacity approach

5.4 Conducting pedagogical experiment to assess the feasibility and necessity of designed teaching situations

- Can the teaching of Maths teaching method modules at universities based

on the implementation capacity approach as the proposed procedure mentions ensure the feasibility and necessity?

7 Research method

7.1.Theoretical research

7.2 Practical methods

7.3 Experimental method

8 The significance of the thesis

- Identifying the current situation of teaching Maths teaching method modules at universities within the implementation capacity approach at the current teacher training universities

- Building a capacity framework, criteria to evaluate the performance of university students in Math Pedagogy, including 9 skills and 5 levels

- Developing the structure of 3-part teaching situations, with 5 characteristics and proposing 6 principles to ensure the consistency of teaching situations

- Designing and organizing the implementation of 4 situations in teaching modules of Math teaching methods to develop implementation capacity for university students in Math Pedagogy

9 Design of the dissertation

In addition to the Introduction and Conclusion, the dissertation consists of 3 chapters:

Chapter 1 Literature review

Chapter 2 Designing situations of Maths teaching method modules at universities within the implementation capacity approach at universities

Chapter 3 Pedagogical experiment

References and appendices

CHAPTER 1: LITERATURE REVIEW

1.1 Overview

1.1.1 Previous research in the world

The definition of competence should be viewed as a holistic concept – a dynamic combination of knowledge, understanding and skills (or in Vietnam competence is now regarded as a combination of knowledge, skills, attitudes and it

is reflected through activities) There are various definitions of the concept of competence González and Wagenaar (2005) defined competence as " something that can be demonstrated to a certain level of achievement along a continuum" or Rychen and Salganik (2003) considered competence as “the ability to meet complex demands, by drawing on and mobilising psychosocial resources in context – i.e a complex action system encompassing knowledge (also tacit); cognitive and practical skills; attitudes such as motivation, value orientations, emotions” According to Koster and Dengerink (2008), competency can be defined as the combination of knowledge, skills, attitude, values and personal characteristics, empowering the teacher to act professionally and appropriately in a situation, deploying them in coherent way

Many other international scholars have agreed and shared the aforementioned definitions They believe that competence - as the basic requirements for teaching - articulated in knowledge, craft skills and dispositions Such definition focuses on the potentialities of continuous development and achievement, associated with aims and objectives in a lifelong learning perspective, and it specifies requirements for each of the three areas The recent review by

Williamson et al (2008), which sums up relevant existing studies, mentions the

following features in the knowledge area: subject matter knowledge; pedagogical subject knowledge (for example, Math); pedagogical knowledge (in general); curricular knowledge, educational sciences foundations (intercultural, historical, philosophical, psychological, sociological knowledge); contextual, institutional, organizational aspects of educational policies; issues of inclusion and diversity; new technologies; developmental psychology; group processes and dynamics; learning theories, motivational issues; evaluation and assessment processes and methods

Deakin Crick (2008) proposed the definition of competence as a complex combination of knowledge, skills, understanding, values, attitudes and desire which lead to effective, embodied human action in the world, in a particular domain Weinert (2001) simply considered competence as the capacity and cognitive skill that is inherent in individuals or can be learned to solve problems in life

Gharajedaghi (2006) defined competence as a combination of physiological factors, knowledge and skills of each individual that bring high efficiency in resolving specific situations By the end of the 20th century, John Erpenbeck stated that the basis of competence is knowledge that is used as the ability defined by value, strengthened by the experience and implemented through

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

1.1.2 Previous research in Vietnam

According to Nguyen Van Giao (2001): "Competence - defined as capacity -

is built up and developed to allow a person to succeed in a physical, intellectual, or professional activity The capacity is performed through the ability to perform an activity or do a task " Nguyen Vu Bich Hien et al (2015) supported the idea that

"competence can be understood as the ability to fullfill the task or work performance that is proven through the actual results of activity and it involves knowledge, skills, attitudes and personal characteristics"; Pham Minh Hac thought that "competence is a combination of the psychological characteristics of a human/personality" Bernd Meier and Nguyen Van Cuong (2014) viewed competence as the synthesis of knowledge, skills, as well as perspectives and attitudes that an individual managed to act successfully in new situations Defined

in the Psychology Dictionary by Vu Dung (2000), "competence is qualities of personal psychology with a role as an internal condition, facilitating the

implementation of a certain activity" According to Nguyen Thi Kim Dung et al

(2015): "Competence is the combination of knowledge, skills, attitudes and personal experience enabling a person to take responsibilities, act effectively, carry out all tasks, and solve problems in various professional, social, or personal situations"

Although the aforementioned definitions are different, there are some common perspectives among them and they can also be separated into two types of concept:

Firstly, in terms of psychology, competence is considered as a psychological attribute or a personality trait Secondly, the competence is included and displayed through skills Each type of competence is analysed and shown in the form of specific skills, and different levels of performance will present different level of competence development In this way, the competence can be developed and trained through skill training; Competence can be professionally developed and be reflected not only in knowledge but also in skills and specific activity Therefore, it is necessary to evaluate the competence through practical activities; to be specific, it can be measured and assessed through skill evaluation

In regard to training Math teachers, there are research works on the training

of teaching method such as: research by Nguyen Duong Hoang (2008) focused on the issue of organizing teaching and learning activities for subjects of mathematics teaching methodology to enhance the training of teaching skills for students, in which the author presented a fairly profound representation of teaching skill and proposed solutions aimed at organizing and improving the effectiveness and quality

of the teaching method training through teaching math teaching method-related subjects The study of Pham Van Cuong (2010) presented issues relating to skills, teaching skills, builded up (proposed) standards of mathematics teaching skills for students majoring in primary education, and proposed solutions to train mathematics teaching skills for elementary education students

In 2012, Nguyen Chien Thang proposed the basic components of professional skills that need to be trained in the process of studying in the university through teaching the courses of primary mathematics and mathematics teaching methods in the university (including 9 skills); the author pointed out: "Measures to

train some of the fundamental skill-related components for undergraduates specilizing in mathematics pedagogy through teaching mathematics at elementary level and mathematics teaching methodology at university level" It can be seen that, by approaching the professional skills of mathematics teachers, Nguyen Thang has proposed a system of measures more reasonably However, the study of skills or professional skills should be approached in a more modern, insightful and comprehensive way

In the study, namely "Development of Math teaching competence for students in pedagogical colleges” by Do Thi Trinh (2014), the author considered students’ competence of teaching math includes: the ability to understand students

in the process of teaching and education, teachers’ knowledge and understanding; capacity to processing learning materials; capacity to master teaching techniques; and language proficiency According to the author, teachers’ competence includes components of competence: preparatory competence and competency The preparatory competence is considered as “choosing reference documents”, identifying "requirements for knowledge, and teaching skills"; predicting situations and providing solutions”

The study of Tran Viet Cuong (2012) also aimed to "contribute to training pedagogical competence for students at Faculty of Maths but approached in the way

of organizing project-based teaching and learning for the course of Math teaching methodology (specific content) The author has presented solutions to develop students’ teaching competence by organizing project-based learning

The concept of competency is fairly new in our country; however, if training teachers’ teaching skill is considered a core measure to enhance the competency for pedagogical students, there are a number of studies by scientists who have investigated, synthesized and introduced a relatively diverse skill system During the process of teacher training, it can be seen that there are two approaches in training, which are clearly presented, and are currently in use:

Trend 1 Focusing on training scientific knowledge and pedagogical

knowledge (a system of subjects and credit points for such content account for the majority in the training program); Actively preparing for the formation of professional skills for teachers

Trend 2 Approach to vocational training, i.e focusing more on the formation

and development of professional skills along with the preparation of scientific knowledge and pedagogy It can be understood that this approach focuses on the development of the competency

The author presents some research on the issue of vocational training in competency-based eduction as a trend in vocational training, in which teacher training is one of the professions of society This trend will impact on program design, learning outcome standard, training content, structure of training content, form of training and testing, assessment during the training process In addition, it has the impact on teachers’ teaching method, teaching materials and textbooks, interaction between teachers and students during the process of training

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

presentation techniques Nguyen Duc Tri (1993) presented the basic issues of vocational training with approach of implementation competence Subsequently, Nguyen Van Tuan (2008) has systematically presented training issues in competency-based education, clarified the concept, theory framework, advantages, limitations, and especifically indicated the difference between training in competency-based education and convention training There are also some other studies on the issue of competency-based training of Nguyen Huu Lam (2004),

Dang Ba Lam (2006), Dinh Cong Thuyet et al (2008), etc However, these works

only presented theoretical framework of the vocational training model, the competency-based model or the competency Pedagogically, there are some studies

on the issue of competency-based vocational training as: the research by Nguyen Ngoc Hung (2006) on the issue of vocational training for technical pedagogical students, and the study by Vu Xuan Hung (2011) on the training of teaching capability for technical pedagogical students in pedagogical practice also followed the competency-based approach

1.2 Pedagogical competence of mathematics teachers in high schools

1.2.1 Teachers’ pedagogical competence

As mentioned, pedagogical competence must be assessed through the results

of successful implementation of pre-defined teaching objectives Thus, presenting structure of teaching competence need to approach learning process and teaching objectives

Although there are many different perspectives, analyzing mathematics teachers’ professional knowledge canbe divided as follows: content knowledge, teaching knowledge, psychological and eductional knowledge, organization, consultation knowledge They are specified as follows:

The Organisation of the National Professional Standards for Teachers has launched national professional criteria for teachers

Minister of Ministry of Education and Training issued Circular No 20/2018/TT-BGDTEL dated 22/8/2018 on professional standards of teachers in secondary schools, and teacher evaluation with standards includes basic content with 5 standards and 15 criteria

1.2.2 Pedagogical competence based on students’ learning outcome standard

Some standards of learning outcome for pedagogical students have been introduced in some foreign and Vietnamese institutions:

The learning outcome standard was announced by the Victoria Institute of Teaching, Austrailia, which used the Australian teacher professional standards to evaluate teacher, and also regarded as students’ learning outcome standards This

problem was also clarified by Nguyen Thi Kim Dung et al (2015)

New Zealand's teacher council have built learning outcome standards based

on the professional standards for teachers to meet the quality of graduates from various teacher training programs The learning outcome standard for the German pedagogical students includes four sectors (teaching, education, assessment, innovation) and 11 types of competence that are specified into standards The Singaporean teacher competence framework identifies the following elements: occupational practice; cooperative and managerial relations; personal management

According to the Dinh Quang Bao et al (2016), the learning outcome

standard for pedagogical competence includes 5 types of competence and 28

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

1.2.3 Relationship between professional standards for teachers and learning outcome standards in teacher training

According to Dinh Quang Bao (2016): " Professional standards for teachers often describe the competence at the skill and technique level of implementing a certain task, while pedagogical competence for graduates should be perfomed in their professional knowledge with indicators of both the knowledge and the skills performing the task " Thus, it can be understood that pedagogical students must achieve the lowest level of the professional standards for teachers after graduation

or students can reach higher than the required level of some criteria

The compatibility between the professional standards for teachers and the learning outcome standards in the teacher training is both necessary and dialectic The learning outcome standard can be based on the professional standard for teachers in general On the other hand, it can be based on movement and change of educational system In general, the professional standards for teachers tend to be more backward than the learning outcome standard because they are often dominated by administrative regulations

As aforementioned, in this dissertation, the author fouces on students’ teaching competence rather than concentrates on education competence (through the subject), personal development competence, and social and professional community development competence of student teachers Moreover, towards the competency, which is manifested through the results and process of actvities, the author uses

"skills" to describe and evaluate the students’ competency Although competence of using information technology during the process of teaching is shown in curriculum, the author does not focus on training such the competence when conducting this research

Furthermore, in the process of teaching subjects relating to mathematics teaching methodology, teachers apply activities to help their students develop professional competence, teaching competence in general or competency

1.3.Competency of mathematics pedagogical students

1.3.1 Competency

If competence is the standard that each individual needs to have to do a task, that is, what task demands, competency is what individuals have to do a task well The term is translated into Vietnamese as competency In Vietnamese-language materials, based on research and analysis of many reliable international sources, B Meier and Nguyen Van Cuong (2014) defines "Competency, in terms of professional competence, is the ability to effectively and responsibly do tasks and solve problems in the professional, social, or personal fields on the basis of knowledge, skills, techniques and experience as well as the willingness to act

There are four types of skills of competency relating to professional activities, including: skills to carry out specific and distinct job; management skills

of work; management skills of incidents and acting skills in the working environment

Therefore, the author believes that teachers’ competencies should be presented through knowledge, attitudes and key skills including skills of program

analysis and design of learning materials; teaching skills Therefore, the author basically agrees with the research on the competency and the main component of the competence is skills Moreover, in the process of teaching, testing and assessment, the author focuses on the teaching skills rather than concentrates on teachers’ attitudes Although the author still agrees with Shian Leou (1998) presentation, the thesis will present in more detail about skills and components of skills of the competency

1.3.2 Mathematics students’ competency

In the author’s opinion, it is possible to define skill components of math teachers’ competencies as follows (based on teaching competency assessment items for school Mathematics teachers by Shian Leou (1998):

Table 1.3 Group 1 – Skills of program analysis and learning material design Components of

1.1 Analyze

program, especially

define teaching

objectives

1.1.1 Analyze the scientific base of teaching to draw out

experience and self-study in the teaching process

1.1.2 Define the teaching objectives based on program and

textbooks (competence of analysing program)

1.2.1 Arrange proper materials in order to create students’

cognition and learning ability

1.2.2 Design a teaching plan effectively

1.2.3 Rearrange lessons based on the content and learning

activities

1.2.4 Predict the suitability of lessons based on the teaching

content and learning activities

Table 1.4 Group 2 – Teaching skills Components of

2.1.Present lectures

effectively

2.1.1 Instruct contents correctly

2.1.2 Give handouts/notes to enhance students’

understanding 2.1.3 Apply teaching methods effectively

disciplines 2.2.3 Stress the application of math to life

2.3 Clearly point out

the learning

objectives and

procedures for each

2.3.1 Show the aims clearly before teaching

2.3.2 Inform students the main learning procedures for

topics (chapter, unit, etc…)

which will help

students grasp the

mathematics

concepts

2.4.1 Apply effective teaching strategies reflecting different

contents and features

2.4.5 Apply proper teaching strategies related to students’

learning ability and understanding

2.5.3 Offer thinking process to help students do mathematics

2.6.1 Give clear explanation when students misunderstand

2.6.2 Clarify the confusing ideas for students

2.7 Apply teaching

activities effectively

2.7.1 Arrange the procedures and pace for each class

2.7.2 Math the teaching situation and arrange the order of

activities 2.7.3 Give a complete conclusion when a topic has been

2.8.1 Understand students’ background through proper

evaluation through teaching process 2.8.2 Give a quiz to test learner’s understanding during the

teaching proceedings 2.8.3 Give a complete test at the end of a finished lesson

2.8.4 Record student assessment during and after a fisnished

lesson

2.9 Be able to

express idea clearly

2.9.1 Use the right terms indicating the concepts of

mathematics 2.9.2 Give lectures in a logical order

2.9.3 Teach lessons with normal speed and voice

2.10 Board-writing

skills

2.10.1 Have ability to draw correct charts and graphics for

teaching purposes 2.10.2 Be responsible for neat writing

2.10.3 Arrange contents on board properly

1.4 Designing teaching situations for the subjects related to mathematics teaching methodology in order to enhance students’ competencies

1.4.1 Teaching situations in teacher training at universities

In this thesis, the author conceptualizes that the teaching situations (in teacher training) contains activities that are designed for students to study and practice The thesis basically bases on theory about professional education towards competency-based education as an important basis in designing teaching situations

Traditional method of teacher training focused on content which demanded

to train experts in each field This resulted in content-based education, including the

content (mathematics) and pedagogical knowledge (T Kleickmann et al., 2012)

Such these experts can hardly meet the requirements of teaching in the context of a knowledge economy, which "teaching force must be prepared to respond to complex approaches, to continually innovate, and to meet regular reforms in education "(Gatlin, D., 2009): Learning opportunities to assess knowledge are increasingly expanding; the orientation of educational philosophy basically develops learner’s competence in which knowledge and learning experience is

completely insufficient (Jones et al., 2002) Professional training in general and

mathematics teacher training in particular is gradually directed to competency-based education (CBE)

In training teachers, there are important teaching strategies that have been discussed in the studies, such as: video analysis, microteaching project-based learning, role-play, etc

1.4.2 Teaching situations aiming at developing mathematics pedagogical student’s competency

From the aforementioned studies, the requirements of each teaching situation

in order to enhance pedagogical student’s competency as follows:

- The situation must require students do simple or complex activities in order

to practice their skills and mainly develop a specified teaching competence

- The situation must ensure that there are enough activities for students to self-study and cooperate with each other in the implementation process

- The structure of each teaching situation will consist of three parts: opening, content, assessment

Teacher’s activities Students’ activities Opening

Divide students into groups

or individuals to assign tasks

Groups, individuals take on the tasks

Content

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

Work individually or work

in groups to fullfil the tasks

Organize the report or presentation of results or practice and application

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

Assessment

Assess and give students’

feedback to help them revise

report/presentation

Draw on experience and complete the results of the tasks

Diagram 1.2 Common structures of each teaching situation to enhance

mathematics student’s competency

In this thesis, the author presents some common features of a teaching situation in order to improve student’s competency as follows:

First, students’ physical or mental activities with the effort to do

professional-related tasks (in teaching practice at schools) is the focus of every teaching situation

Second, the author organizes teaching situations with theoretical and

practical requirements at the same time for students to deal with while teaching all subjects In response to each teaching situation, there are different tasks and requirements of the knowledge and skills Therefore, each situation varies, and students are required to simultaneously study the theory and practice when implementing the activities

Third, self-studying is fundamental in every situation

Fourth, cooperation learning activities and research are mandatory, frequent

and are one of criterion to evaluate students

Fifth, the author encourages students to use computers, Internet, social

networks, etc to efficiently exploit, process, and transform information to perform assigned tasks in each group, each situation

The author recommended the following principles in order to ensure consistency and effectiveness of teaching situations:

First, situations should have a consistent structure which clearly clarifies

teacher and student’s main activities and students plays a major role in the process

of training and developing the competency

Second, the situations must be organized during or after teaching subjects

related to math teaching theories and method

Third, the situations will possibly take place in the classrooms at high

schools or in other places, such as pedagogical competition, contest, self-study at home, etc

Fourth, the knowledge that students have learned, including the knowledge

of skills and teaching competence, must be detected, debated and seft-studied by students

Fifth, teaching skills must be trained and formed in the situations

Sixth, each situation must include students’ self-assessment and teacher's

assessment

1.5 The reality of developing the competency for university student specializing in mathematics teaching through the subjects of mathematics teaching methodology

1.5.1 Subjects of math teaching theories and methodology in the pedagogical school

In general, the proportion of credit points in math teaching methodology accounts for 12,9% to 13,3% in reputable teacher training institutions There is no

big difference between content and percentages compared to the total number of credits However, the author thinks that the course of "Math program and textbook

in high school" (in the framework of Vinh University's Mathematical teacher training program) plays a necessary and important role Two other subjects are

"Quorum and Analysis teaching methodology", “Geometry teaching methodology"

as in the design and description (in the framework of the mathematics teacher training program of Vinh University and Hong Duc University) are very practical for students after graduation Furthermore, these two subjects help students practice their teaching skills associated with teaching content

There is the course of Practicum in the training programs; however, the author thinks that, in the teaching process, the subjects related to mathematics teaching methodology must develop student’s competence, and well prepare good conditions, and improve important skills for students to develop and continue being trained in pedagogical internship process

1.5.2 The survey results on the reality of teaching the mathematics teaching methodology courses in competency-based education

- Survey objectives: to assess the perspectives of the teachers who are

training mathematics pre-service teacher at some pedagogical universities on student’s competency; measures to develop student’s competency

- Survey subjects: 66 teachers who have been teaching the courses of

mathematics teaching methodology in several universities

- Survey results:

Relating to assessing the importance of the components of skill of the competency, the results show that the majority of teachers evaluated the skill of program analysis, especially defining the teaching objectives (1.1) and skill of planning and arranging content and organizing proper teaching (1.2) are equally important although they evaluate the skill 1.2 is more important than the skill 1.1

The results of the survey also reported that the teachers evaluated the components of skills as shown earlier at the necessary and very necessary levels However, fewer teachers thought the skill 1.2.3 was an important skill

The results of the survey on the importance of teaching skills: the majority of teachers stated the skill of choosing the proper teaching strategies to help students understand the concepts of mathematics (2.4) and lead students to positive thinking (2.5) are the most important The second place is for the groups of skills 2.1; 2.6; 2.8; to evaluate the role of activities stating the objectives and programs (plan) of learning for each topic (subject, chapter, lesson, etc.) for the students (skill 2.3), the teachers are less concerned about helping the students grasp the lesson objectives, the activities’ objectives, or the chapter’s objectives before the teaching process Similarly, the teachers did not appreciate the role of helping students understand the connections between concepts and the application of mathematics (Skill 2.2) (6th place) This can be explained that the time devoted to learning and understanding the concepts is much less than that of organizing activities for students to solve math exercises Doing math exercises will contribute to helping the students understand the concepts or the use of concepts

From the synthesis of the teachers’ assessment, the author has readjusted the skills of competency for math teachers in the following table

Table 1.8 Description of mathematics pedagogical students’ competencies

No The components of

- Write down the teaching objectives;

- Analyze textbook, workbook, teacher book to present the teaching objectives;

- Clearly and exactly define the teaching objectives and provide descriptions (examples, tests, etc.) in comparison with program and other subjects

- Design teaching plans in details with new ideas;

- Specify (interprete) why the organization of knowledge and activities based on designed procedures;

- Design the teaching plan well: to deeply identify teaching ideas, cognitive barriers, difficulties and support measures for the teachers in the teaching process

3 Present lectures

effectively

- Instruct contents correctly in accordance with the

designed lectures (basic activities, time, etc.);

- Combine contents and types of lessons in classes; flexibly

use and combine instruction forms (even board-writing

- Organize and support students to create knowledge, the learned knowledge with new knowledge, help the students connect the knowledge of lessons with other knowledge (in mathematics, other subjects, in practice);

- Introduce the learning objectves of lessons to students;

- Help students define objectives for each lesson, each chapter or each topic;

- Organize and support students to understand and define the learning content and objectives for each lesson, each topic, and each chapter

6

Choose proper

teaching strategies

which will help

students grasp the

7 Lead students into

some deep thinking

- Organize some activities that help students do some basic thinking during the learning process;

- Organize the teaching process leading students to positive thinking to solve mathematics problems;

- Organize activities that require students to activily think and do thinking to solve problems during the learning process

No The components of

- Draw on experience after each lesson;

- Evaluate, and adjust in-class teaching activities during the teaching process;

- Make plan professionally to evaluate students before, during, and after the teaching process in class; proactively adjust the in-class supporting activities for studnents

In order to develop the competencies for students specializing in math teaching, the author concluded that it is necessary to train 9 groups of skills in the process of teaching the courses of mathematics teaching methodology

Survey on the feasibility of a number of organizational techniques of teaching to develop the competencies for mathematics pedagogical students pointed out that teachers primarily evaluated 4 forms of teaching organization (microteaching; program analysis, especially determining the teaching objectives; design of teaching plans and analysis of teaching practice (video analysis)) that are necessary and feasible Moreover, due to the reform of the current teaching program, the author believes that the organization for students to design some specialized courses in teaching mathematics will contribute to helping children with documentation for the development of the school program, the future classroom program, and develop the competency of program analysis and design a teaching plan Therefore, these activities will be researched, integrated, and experimented in Chapter 2

CHAPTER 2 SOME TEACHING SITUATIONS OF MATHS TEACHING

METHOD MODULES AT UNIVERSITIES WITHIN THE

IMPLEMETATION CAPACITY APPROACH 2.1 Building up situations

2.1.1 Situations focused on developing some component teaching competencies

in implementation capacity: The proposed situations must create an environment

and enough conditions so that students have opportunities to train and develop their teaching competencies

2.1.2 Follow the objectives and contents of the Math teacher training curriculum: The organization of situations must always ensure and aim at the goal

of training Math teachers

2.1.3 Ensure feasibility and effectiveness: Situations are built in the context in

conformity with the current requirements and regulations of the teacher training institutes, under the regulations of the Ministry of Education and Training, it must also come from the Teacher training reality, required training outcome or the requirements for teachers' abilities, from students’ awareness level, difficulties, obstacles, and advantages, from the strengths and shortcomings of students