1 INTRODUCTION 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 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 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 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 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 Research questions - On what theoretical background does Math teaching method situation designing based on implementation capacity approach rely on? - What is the current status of teaching Maths teaching method modules at universities to train teachers within the implementation capacity approach? - What procedures are the situations of teaching Maths teaching method modules at universities based on the implementation capacity approach designed and implemented? - Can the teaching of Maths teaching method modules at universities based on the implementation capacity approach as the proposed procedure mentions ensure the feasibility and necessity? Research method 7.1.Theoretical research 7.2 Practical methods 7.3 Experimental method 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 skills and levels - Developing the structure of 3-part teaching situations, with characteristics and proposing principles to ensure the consistency of teaching situations - Designing and organizing the implementation of situations in teaching modules of Math teaching methods to develop implementation capacity for university students in Math Pedagogy Design of the dissertation In addition to the Introduction and Conclusion, the dissertation consists of chapters: Chapter Literature review Chapter Designing situations of Maths teaching method modules at universities within the implementation capacity approach at universities Chapter Pedagogical experiment References and appendices CHAPTER 1: LITERATURE REVIEW 1.1 Overview 1.1.1 Previous research in the world The definition of competence should be viewed as a holistic concept – a dynamic combination of knowledge, understanding and skills (or in Vietnam competence is now regarded as a combination of knowledge, skills, attitudes and it is reflected through activities) There are various definitions of the concept of competence González and Wagenaar (2005) defined competence as " something that can be demonstrated to a certain level of achievement along a continuum" or Rychen and Salganik (2003) considered competence as “the ability to meet complex demands, by drawing on and mobilising psychosocial resources in context – i.e a complex action system encompassing knowledge (also tacit); cognitive and practical skills; attitudes such as motivation, value orientations, emotions” According to Koster and Dengerink (2008), competency can be defined as the combination of knowledge, skills, attitude, values and personal characteristics, empowering the teacher to act professionally and appropriately in a situation, deploying them in coherent way Many other international scholars have agreed and shared the aforementioned definitions They believe that competence - as the basic requirements for teaching - articulated in knowledge, craft skills and dispositions Such definition focuses on the potentialities of continuous development and achievement, associated with aims and objectives in a lifelong learning perspective, and it specifies requirements for each of the three areas The recent review by Williamson et al (2008), which sums up relevant existing studies, mentions the following features in the knowledge area: subject matter knowledge; pedagogical subject knowledge (for example, Math); pedagogical knowledge (in general); curricular knowledge, educational sciences foundations (intercultural, historical, philosophical, psychological, sociological knowledge); contextual, institutional, organizational aspects of educational policies; issues of inclusion and diversity; new technologies; developmental psychology; group processes and dynamics; learning theories, motivational issues; evaluation and assessment processes and methods Deakin Crick (2008) proposed the definition of competence as a complex combination of knowledge, skills, understanding, values, attitudes and desire which lead to effective, embodied human action in the world, in a particular domain Weinert (2001) simply considered competence as the capacity and cognitive skill that is inherent in individuals or can be learned to solve problems in life Gharajedaghi (2006) defined competence as a combination of psychologicalphysiological factors, knowledge and skills of each individual that bring high efficiency in resolving specific situations By the end of the 20th century, John Erpenbeck stated that the basis of competence is knowledge that is used as the ability defined by value, strengthened by the experience and implemented through 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 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 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 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 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 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 types of competence and 28 criteria; 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 a task, that is, what task demands, competency is what individuals have to 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 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 – Skills of program analysis and learning material design Components of skills 1.1 Analyze program, especially define teaching objectives Code Descriptions (criteria) 1.1.1 Analyze the scientific base of teaching to draw out experience and self-study in the teaching process 1.1.2 Define the teaching objectives based on program and textbooks (competence of analysing program) 1.2.1 1.2 Plan proper contents and good organization (Skills of designing teaching plan) 1.2.2 Arrange proper materials in order to create students’ cognition and learning ability Design a teaching plan effectively 1.2.3 Rearrange lessons based on the content and learning activities 1.2.4 Predict the suitability of lessons based on the teaching content and learning activities Table 1.4 Group – Teaching skills Components of skills 2.1.Present effectively lectures Code Descriptions (criteria) 2.1.1 Instruct contents correctly 2.1.2 Give handouts/notes understanding 2.1.3 Apply teaching methods effectively 2.2 Help students 2.2.1 understand the connection and 2.2.2 application of mathematics 2.2.3 2.3 Clearly point out 2.3.1 the learning objectives and 2.3.2 procedures for each to enhance students’ Help students understand the connection between math concept Stress the connection between math and other disciplines Stress the application of math to life Show the aims clearly before teaching Inform students the main learning procedures for topics (chapter, unit, etc…) Components of Code skills topic (subjects, lessons, etc.) to 2.3.3 students 2.4 Choose proper teaching strategies 2.4.1 which will help students grasp the 2.4.5 mathematics concepts 2.5.1 2.5.Lead students into some deep 2.5.2 thinking 2.5.3 2.6 Explain 2.6.1 students’ misconception at 2.6.2 right time 2.7.1 2.7 Apply teaching 2.7.2 activities effectively 2.7.3 2.8.1 2.8 Evaluate teaching assessment 2.8.2 in each period to make a necessary change to meet the 2.8.3 learner’s ability 2.8.4 2.9.1 2.9 Be able to 2.9.2 express idea clearly Descriptions (criteria) Present learning objectives and contents of each topic Apply effective teaching strategies reflecting different contents and features Apply proper teaching strategies related to students’ learning ability and understanding Give proper questions to students leading to clear thinking Use related materials to help them positive thinking Offer thinking process to help students mathematics creation Give clear explanation when students misunderstand Clarify the confusing ideas for students Arrange the procedures and pace for each class Math the teaching situation and arrange the order of activities Give a complete conclusion when a topic has been completely taught Understand students’ background through proper evaluation through teaching process Give a quiz to test learner’s understanding during the teaching proceedings Give a complete test at the end of a finished lesson Record student assessment during and after a fisnished lesson Use the right terms indicating the concepts of mathematics Give lectures in a logical order 2.9.3 Teach lessons with normal speed and voice 2.10.1 Have ability to draw correct charts and graphics for teaching purposes 2.10 Board-writing 2.10.2 skills 2.10.3 Be responsible for neat writing Arrange contents on board properly 10 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 simple or complex activities in order to practice their skills and mainly develop a specified teaching competence - The situation must ensure that there are enough activities for students to self-study and cooperate with each other in the implementation process - The structure of each teaching situation will consist of three parts: opening, content, assessment Opening Teacher’s activities Divide students into groups or individuals to assign tasks Students’ activities Groups, individuals take on the tasks Support, observe, check and assess the the teaching and learning process Work individually or work in groups to fullfil the tasks Organize the report or presentation of results or practice and application Report, present the results of the tasks, practice and apply Content 14 No The components of skills Explain students’ misconception at right time Assess learning outcomes to make necessary adjustment to meet students’ competence Indicators - Give clear explanations when students raise questions and miscunderstand; - Anticipate, actively detect, and explain the cause of such misunderstanding and difficulties and support the students when there are mistakes, difficulties at right times and in the proper way - Draw on experience after each lesson; - Evaluate, and adjust in-class teaching activities during the teaching process; - Make plan professionally to evaluate students before, during, and after the teaching process in class; proactively adjust the in-class supporting activities for studnents In order to develop the competencies for students specializing in math teaching, the author concluded that it is necessary to train 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 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 CHAPTER SOME TEACHING SITUATIONS OF MATHS TEACHING METHOD MODULES AT UNIVERSITIES WITHIN THE IMPLEMETATION CAPACITY APPROACH 2.1 Building up situations 2.1.1 Situations focused on developing some component teaching competencies in implementation capacity: The proposed situations must create an environment and enough conditions so that students have opportunities to train and develop their teaching competencies 2.1.2 Follow the objectives and contents of the Math teacher training curriculum: The organization of situations must always ensure and aim at the goal of training Math teachers 2.1.3 Ensure feasibility and effectiveness: Situations are built in the context in conformity with the current requirements and regulations of the teacher training institutes, under the regulations of the Ministry of Education and Training, it must also come from the Teacher training reality, required training outcome or the requirements for teachers' abilities, from students’ awareness level, difficulties, obstacles, and advantages, from the strengths and shortcomings of students 15 2.1.4 Ensure the systematic and logical characteristics: Situations need to be systematic and logical in a certain level of flexibility That is to say, designed situations must take into account the conditions , procedure, contents and timing of implementation, 2.2 Some situations of Math teaching method modules to develop implementing capacity for students 2.2.1 Situation 1: The teaching situation of program analysis and designing teaching agendas for students In this situation, we focus on training students for some important activities in designing active teaching situations: Determining teaching objectives; designing knowledge discovery and creation activities; operational requirements to assess the implementation of teaching objectives 2.2.2 Situation 2: The teaching situation of video analysis of teachers' math lessons in high schools The process of video analysis consists of three steps as follows: - Step 1: Determining teaching objectives - Step 2: Observing teaching and learning activities from videos - Step 3: Evaluating the advantages and disadvantages, proposing ways to adjust and draw out knowledge of designing and implementing teaching plans 2.2.3 Situation 3: Micro-teaching practice of some contents of Mathematics course: The micro-teaching situation is organized to help students practice basic teaching skills in class Teachers organize "mini lessons" for students to teach in a small class, of which from to 10 students play the role of secondary students This approach helps students practice teaching in a less challenging learning environment Micro teaching is considered as an effective form of teaching in the initial training for teacher students so that they can grasp separate skills, forming the component competence of the teaching profession Micro teaching is actually the teaching in which the complexity of teaching in normal classrooms is simplified to focus on training students to complete skill exercises, at the same time to enhance the practice supervision and collect information in time For example The lecturer divides the class into 04 groups, asks the groups to implement the following requirements: Each group selects a conceptual teaching content below, the teacher requires the groups to carry out within one week, planning teaching agenda (one phase), sending it in advance to the lecturer via email, trying it out in a maximum period of 30 minutes, video recording (selfrecording group), submitting the video to the lecturer (after submitting the lesson plan), the class will meet in the lab, giving comment on teaching concepts, the implementation of teaching activities in class (based on the videos) Step Planning: Individual Students and groups design a lesson phase Teaching plans are in the following forms: Form Idea of conceptual teaching of the Number sequence with limit (Mathematical Analysis grade 11) +) Group 1: Teaching objectives: the concept of number sequence having a limit of 0; Knowing how to use the theorem and the previous results to prove a range with limit Teaching content: The series has a limit of 16 Teaching process: Timing Activity of the Teacher Activity Learn about a sequence of numbers with limit of 0: The sequence n −1) ( un = n Teacher: Please tell me when n gets bigger, how will un value change? Teacher: Is it possible that un is equal to 0? 10 minutes Teacher: What is the absolute value of un? Teacher: When n approaches infinity, what is the absolute value of un? 1000 Teacher: If given v n = , does n have the same feature as the un sequence above? Activity Teacher notifies concept As the example above, we see that, un is smaller when n is larger, it can be described as follows: "for all arbitrary small positive numbers ε, then from a certain number in the sequence onwards, all numbers of the sequence have a distance to of less than ε.” Then we can say, the un sequence is a sequence of numbers with the limit of There is another way to write: The un sequence is called to have a limit of if 20 minutes  ε (ε > 0),  N0 N* :  n > N0 un  ε Then we write limun = Activities of students Students: bigger n is, the smaller the un becomes, gradually approaching Students: Never Students: We have un = ( −1) n n = n Students: The absolute value of un will then advance to zero Students: Similarly, VN also moves to when it reaches infinity Students: Writingd down concepts in mathematical language, writing down examples, finding ways to prove (similar to the teacher’s proof) Teacher: Prove that the sequence n −1) ( un = has a limit of n For example: The following sequences are those with a limit of 0: 1000 1 = ; t n = ; w n = n n n Please prove it +) Group 2: Teaching objectives: Students can express the concept of sequence of numbers with a limit of 0; Knowing how to use the theorem and previous results to prove a sequence of number of limit ; solving some simple exercises, in the textbook Teaching content: The sequence has a limit of 17 Teaching process: Activity Motivate students Teacher: Given the following sequence of numbers, you have any comments about the value of the sequence when n is bigger? n +1 −1 10 (−1) n un = wn = = xn = yn = zn = n + n , n ; n; n ; n; Students: Realizing that the first four sequences gradually approach and the remaining two sequences not approach Teacher: What does it mean to approach to 0? Students: Gradually getting smaller, to Teacher: What about the case of sequence xn? Students: To say it again, the absolute value of each element of the sequence progresses to GV: Progressing to 0, is the value of the sequence element equal to zero? Students: No Teacher: How does it progress? Students: For every arbitrary smll positive number ε, there is some N0 so that, every number of the sequence has a distance to of less than ε GV: Can you make it brief? Students: Shortening it down as defined in the textbook Activity Giving definition Teacher: Giving definitions as in textbooks Students: Write down in notebooks, write down examples Teacher: Find the number N0 for the sequences un , , xn when given ε = 0.0001 Students: Find N0 Teacher: Supporting and helping with each desk Students: Complete, edit, and report Activity Conclusion and homework assignment (Students not present because it is only done after forming concepts) Form The teaching idea of a pyramid interface cut by a plane +) Group 3: Teaching objectives: The teaching determines the interface of a pyramid cut by a plane through some simple cases (the plane is defined by three points, one point and one line) Major teaching and learning activities: Timing Teacher’s activities Students’ activities Activity Determine the interface of the pyramid Teacher: Organize students to Students: Work individually, or solve the solve exercises in the whole class: problem in groups Exercise: Given the pyramid S A BCD with the A BCD parallelogram at the bottom Call M , N the midpoints of the sides 18 Timing Teacher’s activities A B , A D , respectively and P is a point at side SC as shown Determine the area of the pyramid interface cut by the plane Teacher: Guide and support students to identify intersections, and call a student to the board to explain about the solutions Students’ activities S P D C N B Activity Teaching rules to define the interface by original lines of intersection Teacher: Ask students to comment on his solution Ask some open-ended questions: +) Which plane can be defined immediately? +) From those lines of intersection, can you identify the intersections with other planes? How? +) So, which intersection with the plane should be determined first next time? Teacher: In conclusion, the line of intersection with the bottom plane in the above problem is called the original line of intersection, since it can help to determine the lines of intersection with other planes of the pyramid This method is called the original lines of intersection method So, can you describe the steps of proving? Activity Practice Teacher: Assign homework to students M A Students: Comment and answer some questions of the teacher: +) Determine the lines intersection with the front side plane +) It is possible, to lengthen MN, which will cut the sides of the parallelogram at the bottom, thereby determining the lines of intersection with other sides +) With the front side plane Students: Memorizing, writing the name of the original lines of intersection method Students: Step Determine the original lines of intersection (the intersection with the bottom of the pyramid) Step Identify the lines of intersection with the remaining sides Step Connect the intersection points on the sides of the pyramid we get the necessary interface Students: Solving exercises, from simple to complex according to teachers' requirements +) Group 4: Teaching objectives: Teaching process of determining the interface of pyramid cut by a plane through a number of simple cases Major teaching and learning activities: Activity Doing exercise Teacher: Ask the whole class to solve two problems as follows: 19 Lesson Let the pyramid with the bottom A BCD not a trapezoid and P be a point of the SA edge as shown Determine the area of the pyramid cut by the plane S S P P A D A D B C B C Lesson Let the pyramid S A BCD with the bottom A BCD not trapezoid and P be a point of the SA edge as shown Determine the area of the pyramid cut by the plane Activity Develop a process for defining a profile Teacher: Call the two students to the board and draw in the A0 size paper (printed with the above figure) and then present the solution in the form of tables: Solution of exercise Solution of exercise Figure of exercise Figure of exercise Answer: Answer: Student: Go to the board Teacher: Call one or more to comment on the similarities and differences between the two solutions above, thereby determining the steps (which students have done) Student: Comment, draw out three steps: +) Step Determine the original lines of intersection (the intersection with the bottom of the pyramid); +) Step Identify the intersections with the sides of the pyramid; +) Step Connect the intersection points on the sides of the pyramid we get the interface we are looking for Activity Applying to solve exercise Teacher: Assigning students to solve some exercises in the textbook Some notices in the teaching process: Teachers should draw the pictures on A0 paper in advance to save time in class Classes should be divided into groups in order to have cooperation and competition among groups during the process of solving exercises Step Teaching: Teachers organize students to teach a lesson based on the lesson plan, not more than 30 minutes for a group The lesson takes place with the 20 participation of students and is recorded In class, students will analyze the video to evaluate the results of teaching and teaching skills of students Step Evaluation - Feedback: We received feedback from students and teachers as follows: Feedback from the first lesson: +) Students can visualize the "progressing to 0" of the sequence but still misunderstand it For example, students may not understand that the number of elements a sequence of numbers has +) Some ( −1) it is = n contents are not accurate: for example, in the first sequence, un n impossible to conclude that with the larger n, the un becomes smaller, and approaching but we can only draw the conclusions that are un gradually approaches +) It is difficult for students to determine the number N0 if the teacher does not give some examples, or ε should be given as a specific number, then it will be easier for students in finding N0, and understand the problem +) If possible, it is better to help students find the absolute value of the sequence in a natural way than to require students to it Feedback from the second lesson: +) This lesson is quite good, the questions are quite appropriate, with smooth gradation However, it should be corrected in Activity 1, because there are two sequences of which one has a limit of 1, the other has no limits, furthermore, showing a sequence with a limit other than and a sequence of infinite limits (or no limit) at the current level of students is a difficult job! +) There should still be given an example of ε that is a specific number, it will be easier for students in the process of finding N0, understanding the problem and some such numbers should be given, which get smaller to help to find out the N0 variations in each case +) If possible, it should be represented by a graph or a certain image of the "advance to 0" of the sequence! Feedback from the third lesson: +) The problem should be, if possible, modified, and the class should be divided into groups, given four similar problems, with only changing point P: corresponding to each group, position P will be the midpoint of SC (or SB, SA, SD, respectively) Thus, students can use a drawing or each group draw different shapes, but generally it does not affect the process of defining the interface, of which the degree of difficulty is equal After that, the teacher may also have suggestions about drawing pictures in the space in such a way that it is easy to see and imagine +) It can be shortened from three steps into two steps defining the interface for the sake of brevity +) There should be more specific questions (smoother gradation) suitable for each group Feedback from the fourth lesson: +) The lesson plan is quite good, detailed and positive, to motivate students' learning activities +) Teachers are not yet learn the lesson plan carefully, they not follow the lesson plans properly +) The the lesson plan needs to give more details in Activity 2, especially the expectations or situations, the possible answers that the author can anticipate during the lesson, to make appropriate adjustments +) Considering if defining the interface should include two steps or three steps +) The focus on the teaching process is good, but 21 the content needs to be more complete, more attention should be paid to the learning practice of students Some general remarks about the teaching on videos: +) Students’ ability to organize the board in general is not good, it should be paid more attention to in presenting, it is necessary to divide the table into columns to record and save important information the teacher wants to convey to students +) The ability to follow the lesson plan of the students is not good, some are too dependent on the lesson plan, leading to a lack of natural and flexible lesson +) The role of students in the teaching process is not good, not practical, the reason is that the students had perceived the knowledge beforehand so it was difficult to pretend as if they had not known +) The teaching objective section is generally good, but it needs to be more specific, on the other hand, it needs to be developed in the direction of competency development, it must show that after the lesson, what students can do, such as: be able to solve similar problems Step Reconstructing lesson plans Step Re-teach Step Re-evaluation 2.2.4 Situation 4: Guiding students to develop specific topics for teaching mathematics in high school In the context of educational innovation nowadays, teaching by topic, by building teaching topics will be an important requirement for teachers The objective is: Teachers build up and develop the teaching programs, in order to meet the requirements of integration in teaching, associating math with real life, etc in order to be suitable for students (in differentiated instruction) The basic idea is, teachers organize group activities for students to design teaching topics as an activity to develop learning programs, contributing to the development of the school program This is a complicated activity that requires the cooperation of students and the support of teachers to have good results This situation is aimed at developing competency in developing curriculum and differentiated instruction capacity for students 2.3 Using teaching situations in teaching method modules for students base on competency approach at universities 2.3.1 The general process of using situations in the teaching method module: The process of using a teaching situation is as follows: Stage 1: Modeling; Stage 2: students perform under the guidance of the teacher; Stage 3: Students perform by themselves, lecturers evaluate and feedback 2.3.2 Simultaneously using situations in Math Teaching Method modules of to develop implementation capacity of Math students The author proposes the process of synchronous use of situations in teaching modules of Math Teaching Methods to develop the implementation capacity of Math teacher students as shown in the following diagram: 22 Teachers select one to two units belonging to a chapter of high school math textbook related to the content of the Math teaching method module (algebra, mathematical analysis, geometry, etc.) Analyzing then lesson content, determining teaching objectives and developing teaching plans for selected units Not obainting teaching skills Observing and analyzing teaching hours of selected units Developing lesson plans of selected units Teaching in groups, practising the prepared lesson plans Obtaining teaching skills Developing teaching topics related to the Maths textbook contents in the selected high school CHAPTER PEDAGOGICAL EXPERIMENT 3.1 Purpose of pedagogical experiment: Results of pedagogical experiment through teaching to collect and analyze data on teaching capacity of students qualitatively and quantitatively to answer the following two questions: - How does students’ ability to analyze curriculum and design learning materials develop? - How the teaching situations affect the teaching skills of students? 3.2 Process of pedagogical experiment: The pedagogical experiment process was carried out through the following steps: Developing criteria for evaluating pedagogical experiment results; choosing pedagogical experiment method; determining content of experiments, collecting and evaluating results of experiments 3.3 Method of evaluating pedagogical experimental results 3.3.1 Qualitative evaluation criteria 3.3.2 Quantitative evaluation criteria 3.4 The content of pedagogical experiment 3.4.1 Pedagogical experiment documents: In order to implement the pedagogical experiment, we prepared the following documents: The frame of performance competency for university students in Mathematics major; teaching situations; teaching plans of some Math teaching method modules; some sample teaching 23 videos; a set of criteria for evaluating the performance competency of university students in the field of Mathematics (standardized); questionnaires for lecturers and, students etc 3.4.2 The procedure of pedagogical experiment 3.4.2.1 Phase 1: Initially experimenting the research results 3.4.2.2 Stage 2: Experiment on students at universities training Math teacher students 3.5 Pedagogical experiment process and obtained results 3.5.1 Experiment phase 3.5.2 Experiment phase 3.5.2.1 Time, location, sample selection for phase Consulting 19 experts, including scientists working at universities, research institutes and lecturers in specialized fields of Theory and Teaching Methodology, who are teaching at universities which train math teacher students 3.5.2.2 Results from consulting experts After analyzing the comments of experts, we put them altogether to standardize the criteria to evaluate the elements of skills in Math teacher students’ performance competency at some points: Adding a quantitative evaluation index in some criteria for easier evaluation, in which: adding content levels which "fully describe the objectives of knowledge, skills and attitudes" in skill 1; adding a quantitative description of skill from level onwards: Combining at least or more active teaching techniques in one teaching period At the same time, modifying contents in situations of micro teaching in activity 1, instead of "Organizing for groups of students to design some typical teaching situations (in common sense) in Teaching Maths and implementing teaching in groups, then asking students to record and submit them to the teacher ", it is changed into" Organizing and instructing groups of students to design some typical teaching situations (in common sense) in Teaching math and teaching in groups, then asking students to record and submit videos to the teacher" 3.5.2.3 The result of pedagogical experiment phase on students The results of experimental data analysis phase are as follows: a) Experimental results through qualitative data analysis Before organizing the pedagogical experiment, through the survey, we collected information that the majority of students did not have elemental skills of performance competency for Math teacher students or some students initially knew how to design teaching plans; how to organize teaching activities but mainly at low levels Regarding theoretical knowledge, students have basically gained knowledge of program analysis and teaching objectives; active teaching methods; the way young students perceive maths etc but when asking students to design products, most of them are confused and their skills are at a low level We integrated teaching situations in the lessons of teaching methods and the former were used mainly in practical lessons The situations were taught in different sessions (3 hours each), In session we applied integration in theoretical lessons to instruct students basic skills, for the remaining three sessions we organized practicing activities for students, the sessions could be separated by 2-7 days depending on the program of the school to help students have time to study by themselves and study at home: In periods of the first session, The author 24 organized for students to discuss basic skills of mathematical competence, and assigned specific tasks to train those skills in the next sessions Specifically, in situation 1, when we instructed students to analyze the objectives and teaching plan of specific lessons based on the analysis of the subject curriculum at high schools; based on the Ministry of Education and Training's output standards; Based on the references, students were very excited to discuss The groups worked enthusiastically, showed motivation and drew out system of goals in the sample lessons However, at the 2nd session (the next hours), the author asked students to determine teaching objectives and formulate teaching plans in lessons and on "The linear equation in the plane" (Geometry 10 - section 1.2), just over 30% of students were excited to participate in the required lectures, the rest stayed indifferent or did personal work when teachers did not observe Next, the author asked students to report on the prepared lesson objectives and the proposed teaching plans; organizing for students to discuss, showing the right and wrong in their work In the last lesson (3 hours of teaching), when the instructor asked students to continue to define teaching objectives and plan the lesson "cosine theorem", the number of students participating and interested in implementing the task increased, students in the group discussed enthusiastically and organized the task, however, we observed that there were still students who almost did not participate in the task, through analysis and interview, among students, there were students whose study reports were at average and under average level, their ability to cooperate was not good; There are 03 Laotian so their language competence was limited and it was difficult to join the groupwork activities The author directly discussed with the group leaders of the above students, asking them to organize extracurricular group learning after school, re-teaching the under average and average level students to ensure that they could grasp the program analysis skills.; determining teaching objectives and developing teaching plans To the final practice session, the lecturers asked students to discuss to build up teaching objectives and plan teaching lessons of "Interchange, Arrangement and Combination", then 25 out of 26 students were interested in participating and completing the task, and student was more active in doing of the task, and still submitted the product but still kept the indifferent attitude When carrying out situations 2,3,4, we drew out experience from teaching situation 1, we distributed the documents in advance and asked groups of students to self-study and read the materials themselves beforehand so when analyzing videos, more students participated, most students actively took part in the discussion, only Laotian students had difficulty due to language barrier, but when analyzing the last lesson video lesson "Interchange, Arrangement and Combination", these students basically analyzed better and reached the average level In the process of implementing situation on micro teaching , the groups had been familiar with the skills, so they were quite active, coordinating and helping each other in the process of practicing teaching skills However, through observation, the number of students who achieved skill in handling wrong 25 situations of school students did not achieve very high results There were some students who still depended on the lesson plans, and still were not creative yet In case of situation 4, when we asked students to discuss teaching topics related to the above lessons, 100% students were active, enthusiastic in the discussion process and each student submitted their complete assignment according to the teacher's request in a responsible way Thus, by observing the learning process of students, it is shown that they are very active and interested in teaching situations organized by lecturers; enthusiastically participating and elemental skills of math teaching skills of students are developed b) Experimental results through quantitative data analysis Table 3.7 Results of performance competency of the experimental group before and after the pedagogical experiment Skills The levels students obtained before The levels students obtained after the experiment the experiment Level Level Level Level Level Level Level Level Level Level 5 Skills Skills Skills Skills Skills Skills Skills Skills Skills 19 0 0 15 0 12 0 0 13 0 10 5 0 14 4 0 22 1 0 0 14 2 0 17 4 2 0 16 0 0 0 21 0 The table shows that the skills of students have developed to a higher level after the pedagogical experiment process, especially in skills 1, and 3, it is shown that the number of students achieving a high level is quite large: - The author initially affirmed that after the pedagogical experiment process, the skills of "program analysis and preparation of learning materials (especially defining teaching objectives)"; the skills of "designing teaching plans"; the skills of "Presenting lessons effectively" and that of "Helping students understand the relationship between new knowledge and previous knowledge and their application" were well-developed, before the pedagogical experiment students were at level but after the pedagogical experiment they reached level 2, and especially, there are some students reaching level (accounting for about 5-10%) - Skills 5, 6, 7, of the experimental students are developed from level 1, to level and 4, however, the rate is not high, the number of students reaching level 26 decreases and the skills of students have developed to the level 2.3 The number of students reaching level is very small These skills of students develop slower than skills 1,2,3,4 due to the situation of 2.3.4 students were practiced not much compared to the requirements set Unorganized students have many self-study activities which are mainly implemented at the request of the lecturers But the results give us confidence that teaching situations have helped students to develop skills 5,6,7,8 which are basic skills of self-studying skills of math students For skill No 9, because the situations did not focus completely on training skills to peer assessment, they mainly integrated assessment activities of students through comments and evaluation of others’ lessons; self-analysis, feedback and assessment of activities through video analysis and comments, evaluation of microteaching of the group members As the results showed that, before the pedagogical experiment, the students did not have the skills to evaluate, after the pedagogical experiment, the evaluation skills of the students reached the basic level (accounting for 80.1%), only 02 students reached level (accounting for 7.6%), and students still did not meet the assessment criteria c) Results from the analysis of students' performance through a case study Results of analyzing the development of students’ implementation skills in the case study Through the analysis of students’ self-assessment of skills before the experiment and assessing skills of implementation competency through the work of students submitted after the pedagogical experiment, including: teaching plan; video observation and analysis sheet; micro-teaching practice videos; teaching topics We analyzed in detail the implementation skills of students From the result of a case study, we can see that the students representing the average, good and distinction groups all developed implementation skills well after the pedagogical experiment Thus, the application of teaching situations designed in Chapter can help develop the skills of Mathematics majors at universities CONCLUSIONS AND RECOMMENDATIONS Conclusion Through the research, the dissertation has obtained the following results: 1.1 The dissertation has contributed to clarifying some theoretical issues about the implementation capacity in general and the performance of math teachers in the process of training teachers at universities, in order to develop their teaching capacity in order to develop teaching competency, to our understanding, that is to say the implementation or performance capacity for Math teacher students 1.2 Building a competency framework and criteria for evaluating the performance of university Math teacher students skills: Program analysis, in which particularly focusing on defining teaching objectives; content arrangement and appropriate teaching (Skills to design teaching plans); conducting lessons effectively; helping students understand the relationship between new knowledge and previous knowledge as well as their application; specifying the objectives, programs (plans) of each topic (subjects, chapters, lessons, etc.) for students; choose appropriate teaching strategies to help students understand mathematical concepts; organizing provoked activities for students; explaining mistakes and difficulties of students properly; evaluating learning outcomes to make timely 27 adjustments to suit students' abilities 1.3 Build the structure of each teaching situation with parts: Introduction; development; evaluation; pointing out common characteristics of a specific teaching situation to develop performance capacity for students; At the same time, the thesis also proposed principles to ensure the consistency of teaching situations: The teaching situations need to have a consistent structure, clarifying the main activities of lecturers and students in which students play the role of subject; teaching situations must be organized during or after the teaching of Math theory and teaching methods; teaching situations will take place in the classroom, in high school and maybe in other locations etc., ; the knowledge that students have learned, including knowledge of skills, teaching capacity, must be discovered, found out, debated and self-taught by students; teaching skills must be trained and formed through teaching situations; Each teaching situation must include selfassessment and peer assessment and evaluation of teachers The above principles are an important basis for successfully building math teaching situations in accordance with implementation capacity approach 1.4 The dissertation designed and implemented situations in teaching the mathematics teaching method modules to develop implementation capacity for Math teacher students, they are: Program analysis and designing teaching plan; analyzing the videos of high school Math teachers’ lessons; organizing students to practice micro-teaching some contents of math subject; guiding students to develop special topics for teaching mathematics in high school The situations built by the author based on theory and practice are highly feasible 1.5 The dissertation has built up a procedure of organizing teaching situations in the Math teaching method modules for teacher The process goes through stages: Teacher models for students; students perform under the guidance of teachers; Students it by themselves, the teacher evaluates and feedback 1.6 The results of pedagogical experiment show that, the framework of implementation capacity suggested by the author is appropriate; The construction criteria for evaluating the implementation capacity of Math teacher students are standardized and completely consistent with the framework of the implementation competency framework; The teaching situations developed by the author helped develop the skills of the math students and are feasible to implement and apply in teaching the math teaching method modules at universities The dissertation has achieved the research objectives The scientific hypothesis is acceptable, the project is completely feasible, capable of deploying in training math students at universities Recommendations 2.1 Spending more time on the modules of Math teaching methods or the modules related to training teaching skills in the Math teacher student curriculum at universities; 2.2 Equipping classrooms with adequate teaching equipment (projectors, computers, sound systems, etc.) to improve the effectiveness of the above situations in the teaching of Math teaching method modules 28 LIST OF THE AUTHOR’S ARTICLES RELATED TO THE DISSERTATION Tran Trung, Pham Anh Giang (2014), "Training math teacher students in competency development approach", Journal of Education, 328: 49-51 Pham Anh Giang (2014), "Training students to discover, practice rules of algorithm in teaching algebra 10", Journal of Science, Hong Duc University , No 17/2014: 53-62 Tram Phuong Thuy Nguyen, Tuyen Thanh Thi Nguyen, Thong Do Duc, Giang Anh Pham and Son Hoang Nguyen (2015), "Study Skill-Students Bad at Math in High Schools in Vietnam", International Journal of Learning, Teaching and Educational Research, Vol 14, N02: 53-67 Pham Anh Giang, Phan Anh Hung and Done Souphida (2016), "Developing the syllabus for the Math teaching method in accordance with the implementation capacity approach for pedagogical students", Education Journal, Vietnam Academy of Educational Sciences, special issue January 2016: 43-44 Hau Huu Nguyen, Tuong Anh Hoa and Giang Pham Anh (2017), "A study on capacity development of Mathematical pedagogy students", Uniwersytet Zielonogorski, nr 4/2017: 177-190 Pham Anh Giang (2018), "Designing micro-teaching situations to form and train teaching skills for Math teacher students", Science Journal of Hanoi University of Education, No 63 (5) : 105-114 Pham Anh Giang (2019), "Study and propose the structure of implementation capacity of Math teachers", Journal of Education, No 446: 38-45 Pham Anh Giang (2019), "Some situations in teaching math teaching method modules at universities in accordance with implementation capacity approach", Journal of Education, Special issue of May 2019: 138-143 ... 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... 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... 53-62 Tram Phuong Thuy Nguyen, Tuyen Thanh Thi Nguyen, Thong Do Duc, Giang Anh Pham and Son Hoang Nguyen (2015), "Study Skill-Students Bad at Math in High Schools in Vietnam", International Journal