1 Introduction 1.Motivation of research The process of active teaching-learning related to intellectual abilities, qualifications, professional qualities and personality attributes perceived to operate transformed into property for him. The theory asserted teaching-learning method is solving active learning tasks. The selection and use of appropriate teaching-learning methods are very important significance for the quality of teaching. In strategic reform of national education systems Laos, years 2006-2015 proposed "innovation objectives, new contents of educational "and "training teachers and innovative methods teaching- learning ". But in reality, teaching mathematics in secondary schools Lao PDR shows innovation is not significant and no research on the application of perspective in active teaching-learning in math. From the above reasons, the topic chosen is "Applying theory active learning to teaching-learning Arithmetic and Algebra in grade six at schools the Lao People's Democratic Republic." 2. Research objectives To find out ways on applying the theory active learning to teaching-learning Arithmetic and Algebra in grade six at schools Lao PDR 3. Research function • Survey requirements and the status of mathematics teaching methods in schools Lao PDR. • System view of theory active learning was operated teaching-learning in mathematics in secondary schools. • Apply perspective of active learning to teaching Arithmetic and Algebra in Grade 6 to improve the quality of learning for pupils. • Pedagogical experiments to evaluate results of the topic. 4. Sciences hypothetical If the math teacher is fostering operational perspective theoretical approach combines the practical point of view it may be used effectively in teaching practice, 2 contributing to innovative teaching methods because point operations are core elements of active teaching methods in the schools. 5. Research Methodology • Use research methods to solve reasoning tasks (2), (3), and a part of the mission (1) (requirements for teaching math in Laos) • Investigate and observe( the status of teaching methods in Laos) and part of the task (4) (experimentally observed when teachers) • Using empirical methods to solve pedagogical tasks (4) 6. Donation of the topic In terms of theory: To prove the correctness of the theory active has effectively quality to apply in a new condition and circumstances of teaching mathematics in schools country Laos. In terms of practical: - Improvement of the status positive way of students learning mathematics in schools Lao PDR by active teaching-learning methods. - The content of thesis can reference for mathematics teachers in secondary schools Lao PDR. 7. The structure of the thesis The thesis consists of an introduction, three chapters and concludes: Chapter 1. Based theory and real status; Chapter 2. Apply the theory active into teaching-learning methods to teach arithmetic and algebra in grade six schools Lao PDR; Chapter3. Pedagogy experimental Chapter 1: Based theory and real status 1.1 The theory active in teaching-learning math in schools Some contents of actives in the psychological The actively process and through active of activities, each person into their own themselves, creating and developing their own sense. In Thought ethics, C. Mac and PH. Angghen " when people developments material product and transformed his material has change of his real thinking and the products of their thinking." The actively goals/subject is really active engine. According thesis L.S. Vugotski and A.N. Leonchiev "actives is the essence of psychology" meaning, human activity is the birthplace of the human psyche. Consciousness is the product of 3 active and human middle line to influence the phenomena, psychological phenomena are truth actively. The relationship between psychology and actively is relationship between, one hand are conditions, the purpose and the engine and other one hand are methodology, actions and actives. 1.1.1.1 The concept of actives We understand the actives are works process interaction between people and around the world to create products to the world and to the human product. Humans have created products to the world, has created its own psychology, and human psychology to be revealed, to occur inactive and through the actives. According to Marxist psychology, human life is an actives stream, is the goal of human actives interchangeably. Nguyen Xuan Thuc said the actives are mode of human existence. The first is action process of humans as material of goal in the world (world materials), to create products which contain the psychological characteristics of the person who created it. The second is the process of humans transforming those contained in world into myself; get more experienced of the world, these attributes, the rules of the world the human can comprehension and understanding process. 1.1.1.2 The actives characteristics - Actives are always the object of actives available or appear during action process. Actives learning are aimed at knowledge, skills to know, understand, acquire and put into the experience itself, which is acquiring knowledge &skills. - Actives are always carried out by the goal/subject to action. The teacher is the subject of teaching-learning actives. Students are subject to academic actives. The subject is a person, sometimes some people. Both teachers and students are the subject of teaching-learning actives. - Actives action indirect of the principle or using tools. People using voice, writing, numbers and pictures of psychology as a tool for organizational psychology and control in every human spirit. - Actives are always certain purposes. In all the actives of human purpose is very clear. Learning to get knowledge, skills and perception preparing action into life. 4 1.1.1.3 Structure of actives Life is a series of human actives. Actives are always motivated; take action to achieve the goals and to solve a given task. The aim is regulated by the means and the specific conditions where the action takes place. Action by the manipulation of the city, the actives depend on the means and conditions to achieve specific goals. 1.1.1.4 Types of actives Human actives are divided into two categories: active labor and actives indirect. If individual development, are three types succession of actives such as fun actives, learning and working. In other addition, actives are divided into four categories such as change actives, cognitive actives, value-oriented actives and indirect actives. Active teaching and learning are a cognitive actives; that mean is a kind of mental active, do not change the real objects, real relationships, etc There for humans analyze, synthesize, generalize, and remember that image [42, p.54-55]. 1.1.2 The actives theory of teaching-learning math in schools 1.1.2.1 Content math in schools "The content of general education to ensure universal, fundamental, comprehensive, user-system to real life, in accordance with physiological age students, meet the goals education at each level , capacity development to meet the aspirations of students "[27]. Thus, the contents of mathematics consists mainly of arithmetic, algebra, calculus and geometry with the working methods, the idea all contents as a basis for teaching comprehensive education. • Arithmetic, algebra and calculus consists of content aggregation, transformation homogeneous equation and any equations, functions and graphs, the elements of calculus analysis and cluster random sampling. • Geometry is the concept of geometry, geometric quantity, relation of the geometry, and allows offsetting a uniform, vector coordinates. 1.1.2.2 Students of actives learning mathematics in schools Content math in school is closely associated with the actives such as active 5 recognition and expression, complex math, intelligence actives in mathematics, and general intellectual actives language actives. 1.1.2.3 The theory actives in teaching-learning mathematics in schools Compositions of the basic psychological actives are engine, manipulation, content and results [19, p.73]. View of actives teaching methods are shown in the following: a) Give students implement and training actives and action components compatible with the contents and teaching purposes. b) Recommendation engine and conduct learning actives. c) Transfer knowledge, especially knowledge as means of approach and results of actives. d) Divide sub-level actives which to base in teaching process control. 1.1.3 The student actives of grade 6 to learning math:Each learning content are related to certain activities. Contents mathematic grade 6 of teaching actives are concepts, rules and exercises. The principal activities of secondary school students in grades 6 Laos is: identify activities, express a concept, a principle, a method, complex math operations, intelligence operations and joint operations the lanquage. 1.1.4 The meaning of an active perspective in teaching math in school Active perspective reflects the basic components of psychological, elements basis of teaching-learning methods and prove the Marxist theory on human development. In teaching actives for students to conduct self-learning, actives, positive, effective and ensure overall development of the body. 1.2 Innovative of teaching-learning methods 1.2.1 The need for innovation teaching-learning methods The strengthening development of human resources needed to enhance teaching-learning methods by towards strengthening and training actives to foster level of knowledge, skills, autonomy regular school (self-learning, self-study) and lifelong learning and creativity, enabling students to make collective a favorable learning environment, 6 students interact and learn from each other emulation mutual learning and promote active learning process. 1.2.2 Orientation innovation of teaching-learning methods. If not the only once way, is to create opportunities for students learning by active, self-discipline, initiative and creativity. The needs to become oriented the innovation of teaching-learning methods and is call orientation actives [23]. Orientation innovation of teaching- learning methods that can be applied effectively and contribute to schools Lao PDR. 1.3 Contents of curriculum and textbooks in Mathematics grade 6 schools at Lao PDR Secondary program in Laos consists of 4 layers: 6, 7, 8 and 9. Grade 6 program of Laos equivalent of grade 6 in Vietnam. 6 th grade math texbook of Laos was compiled by education reform program and was released in 2010 to use. 6 th grade math texbook Laos consists of 2 parts: there are 21 articles on algebra, geometry and 10 posts of distribution is 143 lesson time period is 33 weeks, a semester teaching 17 week, 16-week semesters and two teaching teach 4 periods per week. 1.4Current status of teaching mathematics in school Lao PDR 1.4.1 Purpose, object status of survey The survey to understand and assess the status of teaching-learning for a basis condition to suggestions of using the theory active into teaching grade six math at the secondary school Vientiane, Lao PDR. The numbers are 100 teachers of 18 schools survey on mathematics subject in secondary schools and results of 3812 students learning objects. 1.4.2 The situation in general education Number of student dropout is morespecific in 2010, lower secondary school student dropout 12.6%, high secondary school students dropout 9.3%, graduation rate by volume is 68.9% lower secondary school and high secondary school is 75.3%. The teachers training not yet widespread and deep expertise, fostering teacher quality is low, fewer teachers use teaching methods to encourage student learning, teachers mostly use teaching methods by teacher lecture -student listening, recording and fellow teachers form and lack of 7 teacher explained. Number of students in overcrowded classrooms, low quality teaching, learning outcomes between cities and rural areas are different. 1.4.3 Results of the survey in the state of mathematics teaching some schools in years 2006-2010 1.4.3.1 Status of teachers a) Use of teaching-learning methods of teachers. b) The self-training and retraining of teachers on teaching-learning methods. c)The difficulties when applying active teaching-learning methods d) The interest of the manager 1.4.3.2 Status of students learning 1.4.3.3 Conclusions of the survey situation Mathematics teaching situation in the schools at Vientiane, for generally are poor quality study when compared to the requirements of science - society today. Poor academic results due to many causes which are related as follows: • The majority of teachers do not use many of positive teaching methods. They use teaching methods require less active students, teachers work mainly. The cause of this situation is by teacher limited retraining to innovation teaching methods. Although, some teachers have train themselves fostered by reading, but confusion in the application of the actual teaching. • Student motivated to learning weak, lazy thinking and lack of initiative. The cause of the students' learning not high because teacher to teach not create encouragement for students interested in learning is a significant of part. The survey was conducted in schools in Vientiane seen such poor quality that the schools in remote rural areas, many learning conditions is limited, such as the quality of learning will how? This is inevitable and urgent reform of teaching-learning methods to enhance the quality of student learning. Chapter 2: Applying active theory into teaching-learning arithmetic and algebra grade 6 at school Lao PDR In chapter 1 we was present an overview of the actives theory in teaching-learning, students actives learning mathematics in schools of grade 6 and innovative of teaching-learning methods. Orientation applied to 8 solve the problems above of teaching arithmetic and algebra in grade 6 schools Lao PDR are: Author directly applied to teaching specific contents; Applying through teachers by training of teachers. 2.1 Applying direct to teaching specific contents. 2.1.1 Active and components active Example 1: lesson "signs are divisible of 3, and 9"  The content of the lesson: Teach to students about the signs some of number divisible to 3, to 9  The purpose of the lesson: Helping students remind the signs are divisible to 3 and 9  Compatible between contents and teaching-learning purposes was mentioned above can give students practice actives and generalized language actives as follows: Teacher: Observe students 510.115 += ; 9)51(519.15)19.(1510.115 ++=++=++=+= ; 9)51(15 ++= 310.0100.2203 ++= ; 5)19(0)199.(2310.0100.2203 ++++=++= 99.2)302(30299.2 +++=+++= Let's analyze some numbers a similar following: ?378 = ; ?253 = Student: ??? Teacher: Each number of the above has a total of 2 analyze expression. Student: You have commented on each expression. Student: ??? Teacher: Please comments with the general contents. Student: ??? Teacher: Start from divisibility properties of an overall view, you explain why 378 can divisible to 9 and but 253 can not divisible to 9. Student: ??? Teacher: Let the conclusion of each case and the general conclusion? Student: + Conclusion 1: "The sum of the numbers is equal 9, is divide to 9" + Conclusion 2: "The sum of the numbers is not equal 9, is not divisible to 9" The general conclusion: "The total numbers is divisible to 9 and that's just the numbers divisible to 9" Teacher: Observe students 110.3100.01000.22031 +++= 9 1)19.(3)199.(0)1999.(2 ++++++= 139.302999.2 +++++= )9.3999.2()1302( +++++= )3111.2.(96 ++= )3111.2(3.36 ++= Let's analyze a similar the following 3414; Students: ??? Teacher: have you (students) a comment about the expression (1) and (2)? Student: - expression (1) is the sum of two expressions which are an expression is the sum of the numbers and is an expression of the number is divisible to 9 - Expression (2) is the sum of the two expressions is an expression which is the sum of the numbers and is an expression of the number is divisible to 3. Teacher: Start from the examples and comments, please explains some of the nature number divisible to 3. Student:??? Example 2: The lesson "The characteristic nature numbers of the addition with multiplication"  Lesson contents: The characteristic nature numbers of the addition with multiplication  The purpose of the lesson: to help student proficient use of the addition with multiplication. Specifically acabcba +=+ )(  The compatible with contents and teaching-learning purposes was mentioned above, students can practiced actives for expression, identifying the nature of the distribution of multiplication and subtraction algorithms act of thinking through the following exercise:Calculate the value of the following expression: 21 62103162 ×−× =A . We can guidance to student perform by following steps: Teacher: Please analysis. Student: )1031(6262103162 −=×−× Teacher: Let shortened 21 )1031(62 − =A . Student:??? Example 3: Train in the “Calculation of the brackets expression” in “the expression”  The content of the lesson: the calculation expression of the brackets 10  The purpose of the article: Helping students apply the rules proficient expression of the brackets.  Compatible with content and teaching purposes mentioned above can be practiced for student activities shown, therules recognize expressions of the brackets and algorithmic thinking activities through the following exercise: Calculate the value of the expression: ( ) [ ] ?99100210292913 =−−−= A Want to A be included B in this calculation ( ) [ ] 9910021029 −−= B . Want to B be included C in this calculation ( ) 991002102 −−=C . Want to C be included D in this calculation ( ) 991002 −=D . Want to D calculate the E: 99100 −= E So rigth from the start E then calculated D, and the C, and the B, and the A. Therefore, the calculation must be done in the following order: ABCDE →→→→ Example 4: The lesson "Calculation of integers"  The contents of the lesson: the integer calculation  The purpose of the lesson: to helping students apply versed in the rules of integer  Compatible between contents and teaching purposes mentioned above, we can be practiced students thinking actives through the exercise following. Please describe the process of calculating the value of the expression follow: 13 −a with .2;1;0;1;2 −−=a We can describe in two ways: Make a table or chart. Example 5: The lesson "greatest common divisor"  The content: the greatest common divisor  The purpose: to help student find skills the greatest common divisor.  Compatible between contents and teaching-learning purposes mentioned above, we can be practiced for student actives and generalized language actives as follows: [...]... Score (1-4) SL % Score (5 -6) SL % Score (7-8) SL % Score (9-10) SL % 20 2 ∑ TN 312 50 16, 02 188 60 ,25 57 18, 26 17 5,44 ĐC 1 303 98 32,34 165 54,45 36 11,88 4 1,32 TN ĐC 324 315 57 103 17,59 32 ,69 190 167 58 ,64 53,01 62 43 19,13 13 ,65 15 2 4 ,63 0 .63 TN ĐC 63 6 61 8 107 201 16, 82 32,52 378 332 59,43 53,72 119 79 18,71 12,78 32 6 5,03 0,97 Comparison Chart 2 times over the following 6 tests of two layers of... 0 7 3 3 7 6 13 4 7 15 7 16 5 31 25 32 29 6 30 25 35 25 7 16 12 13 10 8 8 5 10 4 TN 212 0 0 9 14 63 65 29 18 ∑ ĐC 2 06 2 16 20 31 54 50 22 9 Table saw on the percentage of poor, average, good and excellent No ĐC No Stu- 9 6 2 4 0 10 3 0 1 0 6, 07 5,11 5, 86 4,90 10 2 4 0 5, 96 5,01 Score (1-4) SL % Score (5 -6) SL % Score (7-8) SL % Score (9-10) SL % 2 ∑ TN 104 dent 10 9 ,61 61 58 ,65 24 23,07 9 8 ,65 ĐC 1 101... times the 6 tests No Class 2 TN ĐC TN ĐC No Stu312 303 324 315 1 1 6 0 9 2 7 22 7 22 exam score X i 3 4 5 18 24 104 28 42 93 23 27 103 33 39 95 6 84 72 87 72 7 35 28 38 30 8 22 8 24 13 9 13 4 11 2 10 4 0 4 0 5 ,69 4,93 5 ,63 4,91 TN 63 6 1 14 41 51 207 171 73 46 24 8 5 ,64 ∑ ĐC 61 8 15 44 61 81 188 144 58 21 6 0 4,92 Table saw on the percentage of poor, average, good and excellent over twice the 6 lesson... (5 -6) SL % Score (7-8) SL % Score (9-10) SL % 2 ∑ TN 104 dent 10 9 ,61 61 58 ,65 24 23,07 9 8 ,65 ĐC 1 101 32 31 ,68 50 49,50 17 16, 83 2 1,98 TN ĐC 108 105 13 37 12,03 35,23 67 54 62 ,03 51,42 23 14 21,29 13,33 5 0 4 ,62 0 TN ĐC 212 2 06 23 69 10,84 33,49 128 104 60 ,37 50,48 47 31 22, 16 15,04 14 2 6, 60 0,97 Comparison Chart 2 times through empirical examination of class after class experiment and control -... 3.3.5.1 Quantitative assessment Based on the results after two pedagogical experiments, showed that the quality of student learning and higher grades experiment students in class Address Teachinglearning methods in experiment class really better then address class, which is no coincidence Indeed, the tables have the following statistical parameters: Class TN ĐC No student 63 6 61 8 Test No 63 6 61 8 X 5 ,64 ... 0,05 To test the hypothesis H 0 we use the quantity random Z With Z= X TN − X ĐC 2 S12 S 2 , from the above statistical + N1 N 2 23 parameters: N1 = 63 6, N 2 = 61 8; X TN = 5 ,64 , X ĐC = 4,92; S12 = 2,44, 2 S 2 = 2 ,62 , we have: Z = 8,01 With α = 0,05 us find the limit value Z t : ϕ (Z t ) = 1 − 2α 1 − 2.0,05 = = 0,45 Look up table values are Laplace Z t = 1 ,65 2 2 Compare Z we have Z with Zt> Zt So... calculation: 1) (−12) × (+12) = ? ; 2) (+22) × ( 6) = ? ; 3) (−25) × 0 = ? Teacher: Fill in the blanks in the table: a b a ×b 5 -6 -13 20 Teacher: Perform calculations 5 × (−3) × 6 = ? -25 -20 - 260 -100 Teacher: Enter a comma ( =, ) in the appropriate box 1) (−32) × 8 0; 2) 15 × (−3) 15 ; 3) ( −9) × 2 −9 The active theory has been applied to the lesson as follows: 16 - The activity is compatible with the... control - The weakness of the class experiment is 10,84% lower than the 33,49% class control; - Experiment grade point average is 60 ,37% higher than the 50,48% class 22 control; - The class of experiment is quite higher than 22, 16% class control 15,04% The talent for experiment is 6, 60% higher layer than the 0.97% class control Average rate, quite well in class exeriment is always higher than control, the... the same base how? Students:??? Example 9: When training for students of the nature of such multiplication a + b = 11, c = 6 Calculate the value for the expression: M = a(b + c) − b(a − c) Students: M = a(b + c) − b(a − c) = ab + ac − ba + bc = ac + bc = c(a + b) M = 6. 11 = 66 Teacher: Ending suggest the following engine operating as follows: In the process of calculating an expression, sometimes... general activity of grade 6 students in learning mathematics ( see contents at page 12 to page 17, chapter 1 of the thesis) c) The principal activities of grade 6 students in learning Mathatics (see content and examples see page 26 to page 28 chapter 1 of the thesis) d) The activities of teaching mathematics in secondary schools (Internal text and examples see page 17 to page 26, chapter 1 and part 2 . 4 ,63 ĐC 315 103 32 ,69 167 53,01 43 13 ,65 2 0 .63 ∑ TN 63 6 107 16, 82 378 59,43 119 18,71 32 5,03 ĐC 61 8 201 32,52 332 53,72 79 12,78 6 0,97 Comparison Chart 2 times over the following 6 tests of two. Score (5 -6) Score (7-8) Score (9-10) SL % SL % SL % SL % 20 1 TN 312 50 16, 02 188 60 ,25 57 18, 26 17 5,44 ĐC 303 98 32,34 165 54,45 36 11,88 4 1,32 2 TN 324 57 17,59 190 58 ,64 62 19,13 15 4 ,63 ĐC. 13 2 0 4,91 ∑ TN 63 6 1 14 41 51 207 171 73 46 24 8 5 ,64 ĐC 61 8 15 44 61 81 188 144 58 21 6 0 4,92 Table saw on the percentage of poor, average, good and excellent over twice the 6 lesson of the