MINISTRY OF EDUCATION AND TRAINING HANOI NATIONAL UNIVERSITY OF EDUCATION DONE SOUPHIDA DESIGN AND USE MODULAR MATERIALS IN TEACHING MATHEMATICS TEACHING METHODS FOR STUDENTSOF TEACHER TRAINING COLLEGES IN LAO PEOPLE'S DEMOCRATIC REPUBLIC Specialty: Theory and Method of Teaching Mathematics Code: 9.14.01.11 SUMMARY OF DOCTORAL DISSERTATION IN EDUCATIONAL SCIENCES HANOI, 2020 COMPLETED AT HANOI NATIONAL UNIVERSITY OF EDUCATION Supervisor: Assoc Prof Dr Tran Trung Dr Hoang Ngoc Anh Reviewer 1: Assoc Prof Dr Dao Thai Lai Reviewer 2: Assoc Prof Dr Tran Viet Cuong Reviewer 3: Assoc Prof Dr Nguyen Trieu Son The dissertation is protected in front of the School-level Dissertation Committee at: Hanoi National University of Education at hour .date .month year 2020 The thesis can be found at: National Library of Vietnam, Hanoi or Library of Hanoi National University of Education LIST OF PUBLISHED WORKS Pham Anh Giang, Done Souphida (2016), “Developing a syllabus on the Method of Teaching Mathematics in pedagogical schools in accordance with the approach of implementation capacity for pedagogical students”, Journal of Educational Sciences, The Vietnam National Institute of Educational Sciences, Issue of 01/2016 (pp 43-44) Tran Trung, Done Souphida (2019), "Designing modular materials for mathematics teaching method in pedagogical colleges in Lao People's Democratic Republic to develop the capacity of students", Journal of Education, Issue of 04/2019 (pp 322-327) Tran Trung, Done Souphida (2019), "Designing teaching modular materials for Secondary school mathematics in pedagogical colleges in Lao People's Democratic Republic", Journal of Education, Issue of 05/2019 (pp.150-154) Tran Trung, Done Souphida (2019), "Designing teaching modular materials for mathematics teaching methods for students studying Mathematics Pedagogy at pedagogical colleges in Lao People's Democratic Republic", Journal of Educational Sciences, The Vietnam National Institute of Educational Sciences, Issue of 7/2019 (Letter of publication acceptance dated 07/6/2019) Tran Trung, Done Souphida (2020), "Using materials by module in teaching maths - teaching methodology module for maths students at Lao teacher training colleges", Vietnam Journal of Education, Volume 4, Issue (p.25-29) OVERVIEW Rationale The philosophy of education in the 21st century shows the main idea is to take "lifelong learning" as a foundation, based on the general goals of learning: learning to know, learn to work, learn to live and learning to be human From the above orientation, Lao People's Democratic Republic has proposed training plan for human resources from 2006 to 2015 in four directions: (i) Strengthen the content of teaching in the general education program in the Lao People's Democratic Republic, general education lasts 12 years; (ii) Encourage and expand the opportunities of people with school attendance age, improve quality and educational connection; (iii) Organize strategy and action plan of educational sciences; (iv) Pay attention to expand technical schools and vocational training Lao's education and training system is increasingly improving the quality of human resource training To improve the quality of teaching, the problem should be fostering for teacher training students the necessary competencies right from the time they were still studying in universities Currently, one of the approaches that are drawing interest is modular teaching In education, the modular approach goes with the ideology of teaching technology, it is a modern way of structuring or organizing the teaching content so that the training program becomes more flexible For the above-mentioned reasons, we choose the following research topic for the dissertation: "Designing and using modular materials in teaching Mathematics Teaching Methods for students in the pedagogical colleges in Lao People's Democratic Republic" Aims of the study Designing a module-based document on Teaching Methods in secondary school Mathematics and to produce a methodology for using those modules in the teacher training process at the Teachers Training College in Lao PDR, to improve the quality of training and contribute to fostering self-study capacity for students of Mathematics Teacher training College Research Scopes Mathematics teaching method in Teacher Training College, Lao PDR mainly an outline of teaching methods in high schools, not deep skills on teaching methods of specific content While, the specific subjects of secondary school math lack the part of teaching method of this knowledge, which mainly teaches pure knowledge of secondary school mathematics and high school mathematics Therefore, Therefore, the topic design documents according to the Mathematics method of teaching module in Mathematics at secondary school Research subjects and objects 4.1 Research Objects: Modular documents on teaching methods of specific contents in Secondary school mathematics for students of Teacher Training Colleges in Lao People's Democratic Republic 4.2 Research subjects: The process of teaching Mathematics at secondary school for Maths teacher training students of at Teacher Training Colleges in Lao People's Democratic Republic Scientific hypothesis If you can design modular documents on Mathematics teaching methods and use them in Math teacher training at Teacher Training College, Lao PDR, it will contribute to improving the quality of teaching Mathematics methods in teacher training in Lao PDR, at the same time contributing to the development of self-study capacity for students Research mission 6.1 Research on the theoretical basis of the design and use of materials in modules in teaching mathematics teaching method for Teacher Training College students in Lao PDR 6.2 Surveying the status of design and using materials in modules in teaching secondary school mathematics for Teacher Training College students in Lao PDR 6.3 Design, compile modular documents in teaching secondary school mathematics for Teacher Training College students in Lao PDR 6.4 Organized teaching secondary school mathematics and using module-based on teaching methods in training for Teacher Training College students in Lao PDR 6.5 Pedagogical experiment to test the feasibility and effectiveness of the proposals in the thesis Research mathodology 7.1 Theoretical research methods: Research theoretical documents related to the design and use of modular documents in teaching general teaching method Study the content of curriculum using module materials in teaching teaching method in Lao PDR in particular 7.2 Methods of investigation and observation: Using questionnaires, discussing with experts to investigate the actual situation of teaching and learning with designing and using modular materials in teaching secondary school mathematics at Teacher Training College, Lao PDR 7.3 Method of Pedagogical experiment: Organize experiment of the content of and using modular materials in teaching secondary school teaching mathematics at Ban Keun Teacher Training College, SavannaKhet Teacher Training College, Lao PDR to assess the feasibility and effectiveness of the topic 7.4 Methods of mathematical statistics: The dissertation uses qualitative analysis methods, quantitative analysis to draw conclusions related to the contents considered Evaluate results by using mathematical statistical methods in educational science 7.5 Case study method: Monitoring, analyzing and evaluating self-study results of some students participating in pedagogical experiments to see the impact of pedagogical effects on weak students Average, capable and good Contributions of the dissertation 8.1 Systematize and clarify some theoretical bases on the design and use of modular materials in teaching of Teaching Training Colleges students, Lao PDR 8.2 The dissertation adds more modular materials on Mathematical Teaching Methods in "Secondary school mathematics" subject to help students self-study 8.3 Designed and proposed the method of using modular materials to improve the effectiveness of teaching on teaching methods in Secondary school mathematics at Teacher Traning Colleges, Lao PDR 8.4 Facilitate for Secondary school mathematics teachers (and other subjects) with reference materials to design and use modular materials in teaching at colleges The points are defending the thesis 9.1 The designing and using of materials according to the module on Mathematical teaching method in mathematics training teacher at Teacher Training College, Lao PDR is necessary 9.2 Materials according to the Mathematical Teaching module have been designed and how to apply them in Math teachers training in Teacher Training Colleges, Lao PDR is a feasible and effective self-study material, contributing to improve the efficiency of teacher training and develop self-learning capacity for students 10 The structure of the thesis In addition to the Introduction and Conclusion, the content of the thesis includes three chapters: Chapter Theoretical and practical basis Chapter Design and use of modular materials in teaching Mathematics teaching methods for Teacher Training College students, Lao PDR Chapter Pedagogical experiment The thesis includes references and attached Appendix Chapter THEORETICAL AND PRACTICAL BASIS 1.1 Overview of study history of the topic 1.1.1 Studies in foreign countries The first module appeared in the United States, in the early 20th century, it was appeared in the instant refresher training program in the automobile factories so that workers could learn by themselves or learn by themselves under the guidance of the engineers (typically the car maker General motor and Ford car) In France, courses with modular structures were held during the post-World War II era in coal mines But the difference is that American workers are trained to meet the demand of the production line In Sweden, the training program for logging workers is structured in accordance with the order and basic content through training modules The training system in Sweden has been put into use since the year 50 of the 20th century Modular training is not only limited to America and Europe but also developed in Australia, typically a model of model training widely developed in Australia The modular teaching organization is widely deployed all over the world, especially the International Labor Organization (ILO) The credit system comes from Harvard University, which was conducted by President Eliot in 1872 The rigid classical training program is replaced by a wide selection of programs Some Southeast Asian countries such as Thailand, Vietnam, and Singapore have deployed universal modular teaching that can be used for all subjects International Conference on "Deploying and applying modules in training" Southeast Asia countries such as Thailand, Singapore, have also acquired and applied modularized techniques of teaching content, and organized modular training The 21st century is the era of science, technology, information and communication, the rapid transformation of the market economy; this leads to the inevitable that the knowledge economy has been opened In conclusion, the program with a modular structure and modular training methods have been developed and widely applied in many countries around the world Building the modular program structure in each country, in each field 1.1.2 Studies in Vietnam The modular training program has been around since the 70s of the twentieth century in American programs in South Vietnam In the North of Vietnam, the modular training program was introduced a little later with new techniques and technologies mainly came from Eastern European countries Vietnam has been developing a modular training program since 1988 through the topic "Self-study candidate" of the Institute of Higher Education and Research in terms of capabilities and conditions for effective application of modular teaching Author Nguyen Minh Duong in the work "Module of practicing skills - approach and compilation" has given the theoretical basis of the teaching module Following Nguyen Minh Duong, author Do Huan has built up the structure of the technology training program according to the modular structure, the products of the thesis "Modular approach in building the structure of vocational training programs" systematized get the rationale for the apprenticeship program according to the module approach The author Dang Thi Oanh continues to develop her research direction, and has successfully defended the Ph.D thesis in Pedagogical Science - Psychology: “Using simulation situations to train technology design skills New document research papers for students of the Faculty of Chemistry, Pedagogical University " Also following this research direction, the author Pham Van Lam has done a doctoral thesis with the topic: “Improving the quality of practice in general physics at the Technical University by self-study with modular guidance "[29] On the basis of studying the theoretical basis of the module, teaching module, structure of the teaching module, the module-oriented self-study method, advantages and disadvantages of modular guided self-study methods In 2010, Duong Huy Can, in his doctoral dissertation on education with the topic: "Enhancing self-studying skills for students studying chemistry at pedagogical universities with modular guided self-study method" In 2010, in Doctoral Dissertation on Education of Nguyen Thi Nga with the topic: "Building and using modular guided self-study materials of general chemical knowledge - specialized chemical high school program learn to improve students' knowledge ”[32] In 2017, Tran Duc Khoan conducted his doctoral dissertation with the topic "Building and using modular guided self-study materials in general physics to foster the self-studying capacity for university students studying engineering" In conclusion, the study of teaching modules has been conducted by many Vietnamese scientists under different perspectives but they have a common direction when studying the module is to clarify the nature 1.1.3 Studies in Lao People's Democratic Republic To develop the country, the first thing to define is human resource development, in which education is the key factor determining the human resource of Lao PDR Training and developing human resources in Laos is especially important in the industrialization and modernization of the country The "Human resource development strategy up to 2020" by the Central Committee of the Lao People's Revolutionary Party (2002) [43] mentioned the topic quite comprehensively Right from 2006, the Resolution of the 8th Party Congress of Lao People's Revolutionary Party [48] affirmed that "The most important resource to implement industrialization and modernization is human resources" In order to improve teaching capacity for teachers, there are many project topics on renewing teaching methods in universities, colleges and high schools such as the book on "Materials for fostering Mathematics teachers at Secondary and High School" Study on innovation of teaching method in general and teaching method of Mathematics in particular in Lao PDR, there are a number of scientists interested in research such as the Doctor of Education Science thesis In general, the above scientific works have focused on studying the most basic and general problems of Mathematics teaching methods under Lao's Ministry of Education in order to develop human resources in general There has been no research on the construction of modular guided self-study materials in teaching for pedagogical students in Laos; No works have been fully and systematically presented the promotion of self-studying skills of students in using modular materials at pedagogical colleges in Lao PDR 1.1.4 Some comments In general, the authors studied modular materials for Mathematical teaching methods on many aspects such as: - Modular materials for Mathematical teaching methods is a requirement of teaching innovation and it affirms the importance and necessity of modular materials for teaching methods - The dialectical relationship between external factors and internal factors of document design during modular teaching - The actual situation of designing modular materials for teaching methods of some teachers and students is still limited Self-study activities are not frequent - Some authors have pointed out the manifestation of the capacity of teaching mathematics of students studying mathematics pedagogy in colleges - There is no set of tools for assessing the self-study skill level of students of pedagogical colleges in Lao PDR - Measures to develop self-study skills of pedagogical students in teaching curriculum have not been proposed - There are no documents and means to support pedagogical students in Lao PDR to self-study the Maths teaching methods Therefore, we focus on studying the above issues through students studying Mathematics Pedagogy of Lao PDR 1.2 Training program for students studying Mathematics Pedagogy in pedagogical colleges of Lao PDR 1.2.1 Output standard of the training program of Mathematics Pedagogy of Lao PDR The output standard of training program of maths pedagogy in colleges of Lao PDR is approved by the Ministry of Education and Training with five basic requirements: - Political, moral and lifestyle qualities: Patriotism, love of socialism, compliance with the Party's guidelines and policies, the State's policies and laws Has educational ethics, love for works, attachment to education - Has the ability to understand the subject and the educational environment: There is a method of regularly collecting and processing the information on the needs and characteristics of their subjects - Math learning capacity: Students studying Mathematics Pedagogy in colleges need to ensure subject knowledge, master knowledge, and ensure accurate subject content, system, - Educational capacity of the subject: Performing the task of educating ideologies, feelings and attitudes through education and integrating the contents in accordance with the built plan - Deployment skills: Skills of expression and interpretation make others understand their meaning, emotion, and attitude accurately and effectively In order for students to meet the professional standards, the future teachers themselves need to practice professional skills during the time of studying at the pedagogical colleges Therefore, the output standards of students will reflect the strengths - weaknesses in the current training program and find out the issues that need to be supplemented 1.2.2 Training program for Math teachers in Teacher Training Colleges of Lao PDR Education reform in Lao PDR is currently oriented towards capacity development for learners We also agreed to approach the competencies in the general education program of Vietnam to apply in teaching at the pedagogical colleges of Lao PDR From the academic year 2013-2014, the pedagogical colleges are assigned by the Lao's Ministry of Education and Sports to train teachers in the form of 12 + (4-year system) with the math modules in the training program as follows: 10 often considered a small module, or it can also be a sub-module containing learning materials A teaching module consists of three major constituent parts as follows: Input; Module body; Output These three parts are a unified whole [7] Input Module’s body Output Diagram 1.1 Structure of the teaching module (1) The input of teaching module includes: The name or title of the module; Introducing the role, importance and benefits of the module; (2) The module body contains a full range of teaching content, along with necessary instructions on ways to learn to help students gain content and form selfstudy methods The module body is a key part of the module (3) The Output includes: A general summary; A final exam; Instruction system to continue learning If all goals of the module are met, 1.3.2 The process of designing modular materials in teaching Mathematics teaching methods In this thesis, we study the design of documents according to the Mathematics module of Secondary School (1st semester) in Mathematics Teaching Program at Teacher Training College, Lao PDR Design module documents on Mathematics teaching method for students in Teacher Training Colleges, Lao PDR to improve the quality of teacher training - Ensure the science of document design according to implemented modules - Ensuring the pedagogical quality of modular document design content In order to elucidate students' cognitive levels - Ensure the feasibility of modular document design - Ensure practicality It is the content and presentation of modular document designs 1.3.3 The process of designing documents according to modules in teaching Mathematics teaching method The process of designing documents according to modules in teaching or teaching module for short is the process of modifying documents The materials after modularization have the same structural form as the structure of the teaching module (including Input System, Module Body and Module System) and carry the full integrity of the teaching module - Integrity of capacity development for students: Students will develop some competencies after doing research and self-study with teaching module materials to 11 help students acquire knowledge - Integrity in structure: Modulated self-study materials not only contain educational goals and contents, but also integrate in it both content and implementation process to achieve the goals 1.3.3.1 Prepare the script 1.3.3.2 Prepare learning materials for Secondary Mathematics For example, with the Mathematics subject at lower secondary school in the Math Teacher training program at the Lao PDR Vocational College, you can design modules on Mathematics teaching method according to each specific content in the training curriculum Submodule is a relatively independent part of a teaching module to perform the task of a knowledge content At the same time, teachers can compile into theoretical modules, exercise modules, and supplementary modules to support students' learning 1.3.4 The process of using modular materials in teaching at Lao PDR vocational schools Modular materials have the effect of improving the quality of teaching and learning, thereby contributing to improving the effectiveness of math teachers' training at Lao PDR vocational schools + Using modular material as a reference in teaching for teachers and students + When using the material, it is necessary to adjust the parts and the content of the sections to ensure it is suitable for learners + Teachers who use modular materials in class need to change traditional teaching methods 1.3.5 Modular Document Evaluation Method and Criteria As with other teaching materials, modular material is developed and used as a teaching material for students 1.3.5.1 Develop evaluation criteria for modular self-study materials The author uses the questionnaire evaluation criteria to consult experts according to the suitability or inappropriateness level in teaching at colleges with the 5-level Liket scale 1.3.5.2 Modular self-study document review method To evaluate modular self-study materials, the research topic uses the method of consulting experts on the proposed content 1.4 The situation of teaching about Mathematics teaching method in Teacher Training College, Lao PDR Before 1996, the yearly training program in the Teacher Training Colleges in Lao People’s Democratic Republic was issued and the textbook of the Lao People’s Democratic Republic was compiled and used 12 In order to investigate the status of teaching mathematics teaching method in the teacher training colleges, Lao PDR, we designed and distributed survey questionnaires for 35 teachers teaching Maths Teaching Methods in Colleges in Lao People’s Democratic Republic, including: Ban Keun Teacher Training College and Savannakhet Teacher Training College For the investigation on teachers using teaching methods for math students, the result is as follows: Usage level Teaching methods Presentation Oral method Discovering and solving problems Regularly Sometimes Not use 63% 70% 53% 35% 30% 44% 2% 0% 3% The survey results show that teachers have used many methods, in which the oral method is used the most which accounts for 70%, Less use accounts for 30% and Not apply accounts for 0%, Presentation method is similar to the oral method, teachers regularly using this method accounts for 63%, less using accounts for 35% and not using accounted for 2% To learn about the current status of teaching Mathematics teaching method in Secondary school mathematics for students in teaching training colleges, Lao People’s Democratic Republic Question In the module of Mathemetics Teaching Method, what content did you learn below? A) Theory and general tecahing method B) Specific content teaching methods in Mathematics C) Method of solving mathematics exercise Question In addition to the Mathemetics Teaching Method, did you learn about teaching methods in specific subjects in Math? A) No B) Yes but only a little C) Learned a lot Results: 100% of students answered the interview, Question For the Secondary school Mathematics module, did you study the knowledge of methods of teaching equations and geometry? A) No B) Yes but only a little C) Learned a lot Results: 100% of students answered the survey, interviews said that they learned the method of solving problems by topics 13 The content of Secondary Mathematics in Mathematics teaching methods program is done after students have studied and researched the module “Mathematics teaching method” Studying Secondary School Mathematics is organizing for students to apply the general knowledge they have learned to implement the mathematics lesson at the Pedagogical Schools We also studied and in-depth interview about the difficulties of secondary school teachers when applying the knowledge of Mathemetics teaching method, learned in Pedagogical Colleges of Lao People’s Democratic Republic Teachers not take pains to explore and improve teaching methods During teaching hours, many teachers are more serious about giving presentations than encouraging students to study Students are less involved in the development of lesson content, usually only mechanically recorded, etc 1.5 Conclusion of Chapter The thesis has synthesized and analyzed the achieved results of research works of domestic and foreign authors in the approach of modules in teaching On the basis of research on the training program of Mathematics in Pedagogical Colleges and the Output Standard of the Mathematical Pedagogical Curriculum, we study and teach in the direction of capacity development for students Pedagogical College of in Lao People’s Democratic Republic Although the general level of teachers and students in Lao People’s Democratic Republic is still relatively low, it is still possible to exploit and apply teaching perspectives and theories and some Maths teaching methods according to modules at pedagogical colleges CHAPTER DESIGN AND USE OF MODULAR MATERIALS IN TEACHING MATHEMATICS TEACHING METHOD FOR STUDENTS IN PEDAGOGICAL COLLEGES OF LAO PEOPLE’S DEMOCRATIC REPUBLIC 2.1.An overview of Secondary School Mathematics in the Mathematical teaching method program in Lao People’s Democratic Republic In the Secondary school Mathematics training and research program in pedagogical colleges in Lao People’s Democratic Republic, the module has objectives that students must achieve after studying to complete the lesson module, - In terms of knowledge: Students must master the concepts, properties, formulas, reasoning and seconday school mathematics - In terms of skills: Students must have the skills to acquire knowledge and observe and apply knowledge to the practice of teaching Math 14 - Regarding attitude: Students have a serious attitude in learning, well prepare the theory, exercises and collect, accumulate self-study The structure of the materials of Mathematics secondary school curriculum includes 13 chapters and the Lao College of Education is taught in students including: Chapter 1: Redundancy, equality, square root Chapter 2: Geometry in plane Chapter 3: Vector Chapter 4: Linear function, inequations Chapter 5: Trigonometry Chapter 6: Inscribed angle in circle Chapter 7: Area and volume Chapter 8: Indices and radical equations Chapter 9: Geometry transformations Chapter 10: Quadratic function Chapter 11: Linear equations Chapter 12: System of equations and inequations Chapter 13: Probability and Descriptive Statistics The time of Secondary school Mathematics has (1-4-0); credits = 65 lessons theory = 13 lessons; practices = 52 lessons; self-study So far in Laos, secondary school mathematics has not been generally differentiated in the output standards according to the training stages in the pedagogical college - Knowledge criteria: Understanding the teaching and learning principles of basic Mathematics teaching methods in the program such as Algebra, Geometry, Trigonometry, etc in the Secondary school Mathematics textbooks - Criteria of teaching skills: Ability to use various subjects of Mathematcis subjects in the program such as Algebra, Geometry, Trigonometry, Calculus etc Secondary school Mathematics textbooks - Criteria for assessing and commenting on the learning process: Having skills to use many basic assessment strategies of Secondary school Mathematics in the program such as Algebra, Geometry, Trigonometry, Calculus, Integral, etc in the secondary school textbooks 2.2 Designing modular materials for Secondary school Mathematics method in teacher training college Lao PDR 2.2.1 The structure module documents secondary school maths teaching mathod in Teacher Training College Lao PDR According to the framework program of the Ministry of Education and Training of Laos designed for math colleges students, Colleges put the Mathematics part of secondary school in the Math teaching method and there is a difference when 15 designing detailed outlines for This module To overcome the difficulties in teaching and learning Secondary Mathematics of teachers and students, we design materials according to modules based on the above principles In the subject of Mathematics at the lower secondary school, the research includes the following basic contents according to the training program of the Lao PDR Vocational School [50], [51], [52] Modular document design to help students self-study with guidance to suggest and guide students to study each problem The structure of modules on teaching method of mathematics in Secondary Mathematics is designed according to each chapter in the subject's curriculum and is supplemented to teaching and self-study, including: Chapter Redundancy, equality, square root Content 1.1 Solving exponential equations, equalities and the square root equations Module 1.2.Teaching methods for exponential, equality, the square root of Chapter Geometry in plane Content 2.1 Solving plane geometry questions Module 2.2 Teaching methods for plane geometry Chapter Vector Content 3.1 Solving vector equations Module 3.2 Teaching methods for vector Chapter Linear function, equation, inequation Content 4.1 Solving linear function, equality, inequality Module 4.2 Teaching methods for linear function Module 4.3 Teaching methods for equation Module 4.4 Teaching methods for inequation Chapter Trigonometry Content 5.1 Solving trigonometric equations Module 5.2 Teaching methods for trigonometry Chapter Inscribed angle in circle Content 6.1 Solving inscibed angle in circle exercises Module 6.2 Teaching methods for inscribed angle Chapter Area and volume Content 7.1 Solving area and volume exercises Module 7.2 Teaching methods for area and volume problems Chapter Indices and radical equations Content 8.1 Solving indices and radical equations Module 8.2 Teaching methods for indices and radical equations Chapter Geometry transformations 16 Content 9.1 Solving geomrtry transformation questions Module 9.2 Teaching methods for geometry transformations Chapter 10 Quadratic function Content 10.1 Solving quadratic function Module 10.2 Teaching methods for quadratic function Chapter 11 Linear equations Content 11.1 Solving linear equations Module 11.2 Teaching methods for linear equations Chapter 12 System of equations and inequations Content 12.1 Solving system of equations and system of inequations Module 12.2 Teaching methods for system of equation Module 12.3 Teaching methods for system of inequation Chapter 13 Probability and descriptive statistics Content 13.1 Solving probability and descriptive statistics ecxercises Module 13.2 Teaching methods for probability Module 13.3 Teaching methods for descriptive statistics - The first construction direction: Constructing documents according to the text form module of the Mathematical program at Lao College of Education with each module consisting of smaller modules - Second construction direction: Building materials according to digitalized modules Arithmetic modules include modules and smaller modules 2.2.2 Structure of modular materials for Secondary school Mathematics in teacher training colleges Lao PDR The following is an illustration of the modules: module on teaching method of algebraic content, module on teaching method of geometrical content used in teaching Mathematics at secondary schools in Lao PDR: 2.2.2.1 Modular illustration of teaching method of algebraic content MODULE 4.3 TEACHING METHOD FOR EQUATION module introduction In Lao’s common textbook, along with the number system extension is solving the equation in each corresponding set of numbers The concept of equations is formed from hidden to explicit Equation is a central, fundamental content in algebraic programs at secondary schools In the main curriculum as well as in advanced program, According to Bui Van Nghi (2012), there are some notes about the presentation: When changing equations, it is recommended to write in the form of propositional functions, for example: (x - 1) (x - 2) = � x - = or x - = The word "or" is used with the meaning “equivalent to” Target of using modules 17 * Knowledge - Definition of linear equation, quadratic equation  with an unknown member and solution formula - Equation form equals to linear equation, quadratic one with an unknown member and corresponding condition - Vieta's formulas and its applications - Knowledge of absolute value - Knowledge of domain of a function - The identities that need to remember - Calculation rules with algebraic expressions - Solving problems by setting up equations * Skills - Skills to make students aware of the dynamics of set of roots in the process of transformation - Skills of analyzing both semantic aspects and syntax aspects of equations - Skills to guide students to represent solutions on the number axis, on the coordinate plane, on the circle of units - Practical application of equations in practice: In math textbooks in Laos, there are not yet many practical problems - Skills to systematize forms and methods of solving equations (included in the program) for students * Attitude: Students have a sense of serious attitude in learning, selfassessment, good preparation of self-study contents Basic conditions to learn Module subject * Knowledge in Mathematics: Student learned Mathematics at Secondary School * Reference [1] Education Department (Laos), Textbook 8, grade, Educational publisher [2] Education Department (Laos), Department of training teachers Mathematics syllabus Secondary School, Education of publisher [3] Education Department (Laos), Textbook 8, grade, Educational publisher [4] Bui Van Nghi (2014) Teaching methods for detailed contents of Mathematics Publishing of Vietnam University of Education The unit should research knowledge Sub-module Teaching Superlative equations a hidden Sub-module Teaching Quadratic equations a hidden Sub-module Notes in teaching equations THE FIRST TEST B MODULE I Sub-module 1: Teaching Superlative equations containing a hidden THEORY 18 1.1 The equation containing one hidden 1.2 Two equivalent equation 1.3 Equation transformations 1.4 The first equation is a hidden and a solution Exercises II Sub-module 1.2: Teaching quadratic equations containing a hidden THEORY EXERCISES III Sub-module 1.3 Notes in teaching equations Teaching ways to solve equations is to solve Mathematics, therefore it should be noted some following activities: - Noting for students to understand the concept, from there, identify and classify with some types of basic equations - Noting practice for students have skills to solve the types of equations discovered and found - The most important noting for students to remember some of basic issue of equations such as, Experimental and experimental experience - Another note in teaching equations is semantics and syntax The semantics are abstract +) Syntax side, note for students how to use correctly symbols (such as symbols of equivalence “ ”symbols of inferred “ ”symbols - When teaching mathematics by making equations, the teacher should pay attention to the students to represent the elements of task - When summarizing at reviewing the content of equations, teachers need to ask or organize systematic common forms of equations and solutions for students C INSTRUCTIONS FOR REVIEWING D FINAL TEST 2.2.2.2 Illustration of module of teaching method of geometric content 19 MODULE 2.2 TEACHING METHODS OF THE GEOMETRY ON THE PLANE Introduction to module In teaching and learning geometry in secondary schools, there are different types of activities, such as drawing activities, The purpose of the module * Knowledge - Activities to prove geometry of the student’s Secondary School - Teaching and training activities geometric proof for secondary school students * Skills - Training geometry proofing activities - Exploiting, building the system or a number of a form exercises to train skills to prove geometry for students - Self-study skills, application of information technology in learning and research * Attitude: Positive and actively during both self-study and cooperation Conditions required for learning modules * Mathematical knowledge: Students learned Mathematics at Secondary school *Reference [1] Education Department (Laos), Textbook grade, Educational publisher [2] Education Department (Laos), Department of training teachers Textbook of Mathematics at Secondary School, Educational publisher [3] Education Department (Laos), Textbook 8, grade, Educational publisher [4] Dao Tam (2009) Teaching methods for the geometry at high school Publishing of University of Education [5] Pham Gia Duc, Pham Duc Quang (2011) Innovative textbook of the Mathematical teaching methods in secondary schools to establish and develop creative capacity for students Publishing of Vietnam University of Education The unit should research knowledge Module Some forms of mathematics prove geometry at Secondary school Module Activities to prove geometry at Secondary school A INITIAL TEST B CONTENT Module Some forms of Mathematics prove geometry at secondary school I Target * Knowledge - Students understand the concept of geometric knowledge, geometric form of activities and some geometric activities at Secondary Schools * Skills - Having capacity analysis some activities that is active geometry, identify, classify active form geometry 20 II Guide students to self study Request Students research on material geometric to define some basic geometric forms of Secondary School students Request Students exploit textbook materials, Teacher’s Geometry books at Secondary School III Contents Prove that the two triangles are equal (2) Proving that two straight lines are equal (3) Proving that the two angles are equal (4) Proving two parallel lines (5) Proving three points in line (6) Proving two perpendicular lines (7) Proving related to triangle (8) Identification signs related to quadrilateral 2.3 Using module materials on secondary school Mathematics at teacher training colleges Lao PDR 2.3.1 For the students Using module materials on secondary school Mathematics at teacher training colleges, Lao PDR can be in many forms: self-study completely, self-study under the guidance of teachers When studying with the Mathematics module of Secondary School Mathematics at the Lao PDR Vocational College, the teacher must carefully guide the students on the learning method to achieve the highest efficiency The principle of learning with modular materials must ensure contents: (i) Individualized learning; (ii) Improve students' learning motivation 2.3.2 For the lecturer In addition to the advantages, there are still many limitations in the modular Mathematics materials for Secondary School, such as the time teachers have to spend a lot of effort in collecting documents as well as choosing the knowledge part in the process of building modules Besides, the materials according to the Mathematics module of Secondary School have been built based on the characteristics of Mathematics students With this teaching method, the teacher can only teach some lessons in the classroom training program, the rest of the lessons, the teacher assigns students to go home for self-study and self-study in the form of assigning tasks to students The most important and decisive step in the teaching process is effective learning In order to learn effectively accordance with module materials, based on the practical process of students 'self-study as well as teachers' classroom teaching process 2.4 Conclusion of Chapter On the basis of theory and practicability presented in chapter 1, we have analyzed the position and content of Mathematics at secondary school Develop and give forms of 21 using modules according to modules to contribute to practical skills for students of Lao’s pedagogical colleges CHAPTER EDUCATIONAL EXPERIMENTS 3.1 Experiential target Educational experiment is conducted to test the feasibility and effectiveness of the materials according to the module developed in the dissertation and the materials in the teaching process in order to teach teaching methods of detailed content in Mathematics at Secondary for Laos Teacher training College students is more effective in self-study, Educational experiment is conducted via steps with responsible detail following: Educational experiment the first in order to test the effectiveness of the materials by modules for Laos Teacher training College students 3.2 Object, location and implementation time Educational experiment research contents of the dissertation were conducted during a year from the 2017-2018; 2018 - 2019 the academic school years with the following tasks and locations The first in 2017 - 2018: Experiment of exploring the teacher’s for comments and evaluations and students who are learners and study results on compiled documents The object is the junior students who have studied and are studying the part of the Mathematics at Secondary in Ban Keun Teacher Training College Classes organize experiences and competitions according to the actual year or the previous year of the school Experiment and Control Class No School years 2017 - 2018 2017 - 2018 School Ban Keun Teacher Training College Savannakhet Teacher Training College Class of experiment DC Class K5A1 K5A2 K3B1 K3B2 3.3 Contents of experiment To deploy experiments in two directions: - Using the materials accordance with modules under text form or digital form to help students learn by themselves - Use material accordance with modules to support teachers' teaching in the classroom Round organization teaches with modules including: equation and 22 Geometric in plane teaching methods; How to proceed as follows - For the experiment group: Students self-study Mathematics at Secondary through module materials and complete the tasks of learning in the form of using materials according to the module mentioned in Chapter - For the Control group: We organize for students study by themselves in the usual way such as, studying according to the notes, the teacher’s words, according to the curriculum and the materials reference Case studies content in the use of module materials: Tracking the self-study of the Mathematics at Secondary of typical students group 3.4 Experimental methods of education - Methods of investigation: Giving survey forms for selected the Mathematics Teachers and Students of Teachers training College to collect information around the exploitation and using of the module materials on Mathematics teaching methods in Mathematics for Secondary students Observation method: how students use materials by the module on teaching methods of detailed content of the Mathematics Secondary outside class hours Monitoring the process of self-studying Mathematics of secondary with materials according to modules of a group of students with different levels of awareness, belonging to the experimental group during the educational experiment to assess the progress of students on self-study - Based on the activities of students through the pedagogical lessons, analyzing the learning process of students in general, the self-study process in particular We evaluate the learning results by a scoring scale (a 10-grading scale) divided into levels as follows: + Very good : 9,0 – 10 + Good: 7,0 – 8,0 + Average : 5,0 – 6,0 + Weak: under 5,0 Through the survey results, we research, synthesize, analyze data and assess the feasibility and effectiveness of the using of the module material contribute to fostering teaching methods the specific contents Mathematics at Secondary for Students 3.5 Result of experiment 3.5.1 Result educational experiment round (semester 1, 2017 – 2018) - Content 1: Organizing for students self-study accordance with module materials to check the feasibility of documents + Experiment of group: Organizing for students self-study with module (Teaching methods equation; Geometric teaching methods on the plane) in two directions + Control group: Organizing for students to study in the usual way 23 + Average score: The average is the parameter specific to the concentration of data in which: the score; n is the number of students; is the frequency + Variance: S �n (X = X )2 i n- ni is the number of students gain X I score + Standard deviation: S = S The variance and standard deviation of parameters measure the dispersion of the data around the mean value, and the smaller S indicates that the data is less dispersed and highly concentrated + Wrong standard metrics: e = s n S 100% X To compare two different groups, groups with smaller groups v including more uniform quality + Variable coefficient: v = T = (X T N - X DC ) + Inspection quantity: S TN nT N - + S DC nDC - Degrees of freedom f = nTN + nDC - 3.5.2 Result of Educational experiment round (semester 1, 2018 – 2019) Content 1: Surveying and evaluation of the student’s self-study before and after learn by them-self with the module materials - Content 2: Simultaneous application of two forms of using the module according to the module as presented in Chapter 2, to contribute to supporting self-study of Mathematics teaching methods for students after adjusting from the results of educational experiment round - Content 3: Testing the feasibility of the module materials to help self-study teaching methods of the detailed content of the Mathematics Secondary for students who have edited from educational experiment results in the round The second Educational experiments were implemented in the schools as follows: Ban Keun Teacher Training College; Savannakhet Teacher Training College; the selection of experiment and control subjects is based on criteria such as experiments round 1: 3.6 The result of case research The opinion of sample selection: The selection of sample to monitor the student’s the progress in the process of using the module materials in self-studying teaching methods of detailed contents of Mathematics Secondary school Researching to select a research sample based on the results of exchanging with 24 teachers of mathematics in junior high school, simultaneously interviewing and observing attitudes and analyzing learning achievements of students The study analyzed and selected students 3.7 The results of consulting experts on documents according to module of teaching method of Mathematics in Secondary school After the pedagogical experiment, using the tools designed in section 1.3.5, we consulted experts who are math teachers from Teacher Training College(TTC) in Laos to assess the suitability level and the quality of the kit In addition, the topic has surveyed the opinion of 70 students participating in the experimental group using module materials on teaching secondary school mathematics method to evaluate the effectiveness of the materials in teaching math students at TTC, Lao PDR, the results are shown in Table 3.22 as follows: The survey results show that students appreciate materials of teaching method of mathematics in secondary schools that help students be more excited, improve their self-study ability and documents suitable for the learning program of students at TTC 3.8 Conclusion Chapter Pedagogical experiment results show that the content of the document according to the method of teaching method of Mathematics in secondary school is consistent with the program of training math pedagogical students of Lao PDR The topic can be developed in the development of modular materials for other parts of the training program at TTC Lao PDR CONCLUSION Pursuant to the purpose and tasks set out in the topic dissertation, we have studied the following issues: Having synthesized and analyzed the achieved results of the researches of domestic and foreign authors in the direction of the modular approach in teaching After analyzing the current status of Mathematical teaching methods for students at TTC in Lao PDR, the dissertation has proposed the principles, directions and procedures for developing materials according to the module, and at the same time building documents according to Module on teaching methods of detailed contents in Secondary School Mathematics Conducted pedagogical experiment with modular documents to evaluate the effectiveness and feasibility of the topic Pedagogical experiment results show that the content of the document according to the Mathematics module of Secondary School in accordance with the program of math teacher training students in Lao PDR Experimental results show that the topic is feasible, research purposes have been achieved and scientific hypotheses have been proven ... people with school attendance age, improve quality and educational connection; (iii) Organize strategy and action plan of educational sciences; (iv) Pay attention to expand technical schools and... secondary school mathematics and high school mathematics Therefore, Therefore, the topic design documents according to the Mathematics method of teaching module in Mathematics at secondary school... modules in the training program as follows: Credits Secondary school Mathematics: 2(0-4-0) High school mathematics : 3(0-4-3) High school mathematics 2: 3(0-4-3) History of mathematics: 2(2-0-0)