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

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.
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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

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,
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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

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 ++=++=++=+=

)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 −=×−×

. 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:
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number how to easily recognize the knowledge mentioned above.
Example 7: Unit “Ordering the set of integers”. To make students aware of the
significance of the object’s operations and activities teachers may suggest opening the
enginie as follows: In the set of natural numbers has a comparison, the same set of
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integers we have also carried out a comparison of the content that is today’s lesson.
Example 8: The lesson "exponentiation with natural exponent. Multiply the two
powers of the same number ". In order for the teaching objectives is a guide for
students to speak rules
nmnm
aaa
+
=.
, teachers can conduct intermediate suggests
the engine as follows: Teacher: Writing the product of two power after a power:
1)
23
2.2
, 2)
34
.aa
Students:???
Teacher intermediate to engine are as follows: Have students a comment about
the result the exponent of the power? Student:???
Through two examples above, please to know want the two powers have the
same base how? Students:???
Example 9: When training for students of the nature of such multiplication

,11=+ ba


+5+4
-2-3
+4
+3
+1
13
Teacher: Let's make a calculation
?)3()2(
=−+−

Teacher: Please observe at the illustration on the number line
From the above illustration we have
?)3()2(
=−+−
Students:

5)3()2(
−=−+−
Teacher: Based on the above calculation results, we can be presented in different
forms as follows:
5)3()2(
−=−+−

)32(
+−=
;
)32()3()2(
−+−−=−+−
;
Similarly do the following: 1)

.
Students:
523
22.2.2.2.2)2.2).(2.2.2(2.2 ===
;
734
) ).( (. aaaaaaaaaaaaaaaaa ===
;
Teacher: Do the same as above for the next power of two:
;2.2
200300

300400
.aa
.
Teacher: Observe and similar
23523
22)2.2).(2.2.2(2.2
+
===
;

34734
) ).( (.
+
=== aaaaaaaaaaa
;
?2)2 2.2.2).(2 2.2.2(2.2
500200300
===

=.
2.1.4 Divide to sub-activity
Example12. Helping students master multiplication distribution rules for addition and
multiplication on the subtraction distribution namely:
cabacba ).( +=+
and
cbcacba ).( −=−
with
)( ba ≥
.
Lesson 1(Lower): Miscalculated:
1)
13.100101.13
−
; and 2)
39.2561.25
+
Students:???
Lesson 2(Higher): Calculate the value of the following expression:
babaM
−++=
52014
with
100
=+
ba
. Students:???
Lesson 3(Higher): not the specific value, compare two expressions:
1034.43
−=

?)3()4(
=+×−
. Students:???
Teacher: According to the convention on the left "+" sign of the positive numbers in a
calculation, the calculation on how to be rewritten? Students:

3)4()3()4(
×−=+×−
Teacher: Please replace multiplication by addition
)3()4(
+×−
. Students:???
Teacher: You do the math there.
Students:

3)4()3()4(
×−=+×−
)4()4()4( −+−+−=
)444(
−+−+−−=

)34()444(
×−=++−=
12
−=
Teacher: Based on the above calculation results can be presented more
streamlined actives
)3()4(
+×−
as follows:


a
5 -13 -25

b
-6 20 -20

ba
×

-260 -100
Teacher: Perform calculations
?6)3(5
=×−×
Teacher: Enter a comma (
),,
><=
in the appropriate box.
1).
8)32(
×−
 0; 2).
)3(15
−×

15
; 3).
2)9(
×−


plans;
17
Phase 4: Teachers make lesson plans were designed in real classrooms.
Phase 5: Teachers talk about the lesson was done with the participation of the author.
2.2.4 Contents of training a) The content of teaching mathematics in secondary
schools (see contents chapter 1 page 11 to page 12 of the thesis). b) the 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 of the thesis 2.1 ). e) Lesson
plans samples.
2.2.5 Summary and evaluation: a) After training we will proceed please opinions of the
teachers involved in training content and training processes.b) Evaluate teachers were
trained in two contents: Assessment was developed through lesson plans and teachar
performance in the classroom project. c) Results of assessment (see pages 94, 95).
Chapter 3: Pedagogical experimental
3.1. Purpose/objective The organization of the pedagogical experiment was
carried out to implement the basic purposes: Illustrations, testing the feasibility and
effectiveness of the application of Perspective in teaching actives in accordance with
accounting practices education Democratic Republic of Lao People nowadays.
3.2. Experimental Organization We conduct controlled experiments, each lesson
experimental 2 periods, an experimental class and comparison with a control class.
Students experimental classes and control classes where the number of academic and
classified approximately the same. Experimental class by a teacher that we undertake
refresher class is taught by a teacher certified to teach others. All of the teacher are
vocational approximately and age the similar.Conclude the experiment, we examined
in experimental classes and control classes with the same title, the same as all marking
time and answers with the same scale.Content assessment is: check the level of
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3.3.2.1 Contents and process of training teachers
After training we were comments 20 teachers of participated in training course,
assessment teacher result of training processes 90% was very reasonable, 10% was
reasonable and 100% was very rewarding, useful and a breakthrough to enhance the
quality of teaching in Lao PDR.
3.3.2.2 The use level into teaching-learning of teacher’s experimental
The evaluation, we found that teachers participate in training course understand
and how to apply knowledge to design lesson plans. Through interviews and opinions
of the teachers observe in a lesson class: Teacher a little lecture, change to called
students on the board more than 4 times, oral (ask question, think and respond) more
than 4 times, teachers suggesting and help students solve problems more than 4 times,
teachers facilitate student discussions in small groups (2 to 4 people), student-self
exercise several times, and following attention the solution and lecture.
3.3.3 Analysis and evaluation of student learning through tests each
experimental lesson Summary of statistical results over 2 times the 6 tests
No Class No.
Stu-
exam score
i
X
1 2 3 4 5 6 7 8 9 10
TN 312 1 7 18 24 104 84 35 22 13 4 5,69
ĐC 303 6 22 28 42 93 72 28 8 4 0 4,93

2
TN 324 0 7 23 27 103 87 38 24 11 4 5,63
ĐC 315 9 22 33 39 95 72 30 13 2 0 4,91
∑
TN 636 1 14 41 51 207 171 73 46 24 8 5,64
ĐC 618 15 44 61 81 188 144 58 21 6 0 4,92

than the class control.
• Summary of results of statistical tests over 2 summarizes experimental plase
No Class No.
Stu-
exam score
i
X
21
1 2 3 4 5 6 7 8 9 10
TN 104 0 0 3 7 31 30 16 8 6 3 6,07
ĐC 101 1 9 7 15 25 25 12 5 2 0 5,11

2
TN 108 0 0 6 7 32 35 13 10 4 1 5,86
ĐC 105 1 7 13 16 29 25 10 4 0 0 4,90
∑
TN 212 0 0 9 14 63 65 29 18 10 4 5,96
ĐC 206 2 16 20 31 54 50 22 9 2 0 5,01
Table saw on the percentage of poor, average, good and excellent
No. ĐC No.
Stu-
dent
Score (1-4) Score (5-6) Score (7-8) Score (9-10)
SL % SL % SL % SL %
1
TN 104 10 9,61 61 58,65 24 23,07 9 8,65
ĐC 101 32 31,68 50 49,50 17 16,83 2 1,98
2
TN 108 13 12,03 67 62,03 23 21,29 5 4,62
ĐC 105 37 35,23 54 51,42 14 13,33 0 0

ii
∑
=
=
1
is the average, which
N
is the number of students,

i
X
the point (eg point 1,2,3 , 10),
i
n
the frequency that students gain points.
1
)(
1
2
2
−
−
=
∑
=
N
XXn
S
n
i

2
1
N
S
N
S
XX
Z
ĐCTN
+
−
=
, from the above statistical
23
parameters:

,636
1
=
N
;618
2
=N

,64,5
=
TN
X

;92,4

21
)(:
=
−
=
−
=
α
ϕ
tt
ZZ

Look up table values are Laplace
.65,1
=
t
Z

Compare Z we have Z with Zt> Zt.

So the level of significance
05,0
=
α
, the hypothesis
0
H
is rejected by the hypothesis
1
H

consistent with current practice in schools.
Some recommendations: Through research topics, to improve the quality of
Mathematics teaching at secondary schools in Lao PDR, we outlined a number of
recommendations follows: For teachers often need to improve. The educational
institutions and schools have considered the training and retraining of teachers is often
important task for improving the quality of teaching. Special attention should be given
training for teachers of modern teaching-learning methods which always make students
self-discipline, active and creative learning. At the same time training teachers to use
the equipment and modern techniques for teaching the subject. For students, set them
voluntarily, active in school by energetically speaking, answering questions posed by
the teacher. In addition to know how to set the learning at home. Strengthening the
provision of facilities and equipment, modern teaching techniques, reference materials
for teachers and students. Innovative programs, order lessons textbook for reasonable
and logical.
PROJECTS RELATED TO THE THESIS STATEMENT.
1. Outhay BANNAVONG (2012), "The situation reform math teaching methods in a
number of secondary schools Vientiane Laos', Journal of College Science Teachers
Hanoi. No 10, p 14-18.
2.Outhay BANNAVONG (2013), "Fostering secondary school teachers Laos applied
on an operational perspective on mathematics teaching methods ", Journal of
Management Education, No. 44, p 46-49 and p52.
3.Outhay BANNAVONG (2013), “Teaching aggregation operations on integers
(Algebra, Grade 6) organizations towards positive activities for high school students in
25
Laos ”, Juornal of Management professor education, Number 48, page 34, 35, 36.
4. Outhay BANNAVONG (2013), “The application of perspective in teaching math
activities in schools Lao PDR”, Journal of Education, No Especially in July,
page 92, 93.
5. Outhay BANNAVONG (2013), "Sub-level activities in teaching mathematics in
grades K-6 schools Lao People's Democratic Republic", Journal of Education, Special