MINISTRY OF EDUCATION AND TRAINING
HANOI NATIONAL UNIVERSITY OF EDUCATION

DO THI PHUONG THAO

DEVELOP MATHS SELF-STUDY SKILLS FOR
PEDAGOGICAL PRIMARY EDUCATION UNIVERSITY
STUDENTS
Speciality: Mathematical theory and teaching methods
Code: 62.14.01.11
SCIENCE EDUCATION PhD THESIS SUMMARY
HÀ NỘI – 2013
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The Thesis was completed in: Mathematics and informatics
department,
Ha Noi national university of education
Advisors:
1. Junior Prof. Dr. Vũ Quốc Chung
2. Dr. Lê Tuấn Anh
Reviewers 1:
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Reviewers 2:
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Reviewers 3:
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The thesis will be defended at Hanoi national university of
education
Date :

and develop self-learning skills in maths, the training will gain double
effection. It not only improves training qualification but helps the students
to get skills of self-study and devote their whole lives for work. At the
same time, they are the people whose directly guide and have effect on the
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formation of soft skills for students at the age of building human
behaviour - elementary students. Education will get higher efficiency if
the training process is turned into self-training process. Although many
students initially had awareness of the meaning of the "self-study" but
have limitation in process due to the lack of a scientific guidance. The
survey results show that "self-study" - forming the active skills to
dominate the knowledge - must be guided by the method of scientific
guidance and real experience.
Starting from the above-mentioned reasons, we have chosen the
title: "Developing maths self-study skills for students in ETT in the
universities".
2. PURPOSES
Give some specific measures to develop maths self-study skills for
students in ETT in the universities, contributing to improvement of the
qualification of teachers in ETT.
3. OBJECTS AND SCOPES
3.1. Objects
Some measures in developing maths self-study skills for students in
ETT in univesities.
3.2. Scopes
Reserch on maths self-learning study skills (mainly base on some
modules: Introduction to statistical theory, Mathsematics 1, Mathsematics
2, Methods of teaching Mathsematics in Primary School) for students in
ETT.
4. HYPOTHESIS

been paid attention enough neither theory nor practice. The application of
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the measures to develop maths self-study skills for students will
contribute to the training content and method renewal of ETT students
following the orientation of turning training into self-study training.
9. STRUCTURE OF THE THESIS
Thesia includes: Introduction, Content and Conclusion. The content
of the thesis consists of three chapters: Chapter 1: Theoritical and practical
basis; chapter 2: The measures of development maths self-study skills for
ETT students; chapter 3: Pedagogical practice.
Chapter 1
THEORETICAL AND PRACTICAL BASIS
1.1. Historical overview
1.1.1. The researches in the world
1.1.2. The reseaches in Vietnam
1.1.3. Some conclusions
In general, the above authors have studied the problem in many
ways such as: Self-study is current requirement and necessity for all ages;
dialectical relationship between objective and subjective factors in self-
study progress. . . However, until now, according to the materials that we
accessed, the authors have not mentioned the profound issues such as:
developing specific criteria for self-study skills; practical and theoritical
maths self-study differences; dishtinguishing between promotion and non-
promotion ofmaths self-study skill teaching basis; assessing maths self-
study levels of ETT students; proposing measures to practice self-learning
and self-study of ETT students… Therefore, our research focuses on
objects of students on ETT faculty.
1.2. Scientific basis of self-study
1.2.1. Philosophical basis
1.2.2. Psychological basis

behaviour. . . to achieve the purpose or specified criteria, or how
successful standard or regulation "[40, tr.25-27].
1.5.2. Maths self-study skills system
According to the general understanding of the skills, refering to the
research, we divided the maths self-study skills into 35 components and
two groups of skills: Group of cognitive skills (7 component skills ) and
group of activites skills (28 skills).
1.6. Maths self-study skills assessment of ETT students.
1.6.1. Expression of the maths self-study of ETT students
1.6.1.1. Characteristics of ETT students
1.6.1.2. Mathsematics teaching program of ETT sector
1.6.1.3. Grouping expression of maths self-study of ETT students
By reseaching characteristics of maths self-study training in ETT
faculty and psychological characteristics of ETT students, we believe that
the concept of maths self-study skills for ETT students has similarities
with maths study skills in general, including the two main skills.
However, in group work skills have a number of separate skills to prepare
vocational skills for future primary school teachers. In particular, the first
group is the expression of awareness on maths self-study skills. The
second group is the expression of activities in the maths self-study skills.
To learn more about the issues, we researched students expression in
theoritical and practical math self-study of ETT students.
1.6.2. Criteria for assessemet on math self-study skills level
Based on 13 components symbol skills, we built the system of
criteria and indicators of the component skills of maths self-study skills to
form the initial basis for the assessment on ETT students skill levels.
Basing on the research, the system of criteria and indicators for
component skills, we built a questionnaire consisting of 50 questions,
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dividing into two categories to explore math self-study: Type 1- an

After that students take the
example of two collective sets and use Ven diagram to show the
relationship between the two sets.
Level 3: In the content and element set, students are able to study
and describe the contents of the lesson in many different ways. For
example, when expressing the elements of a set A which is the set of test
equation x (x - 5) = 0 defined on the real set, students can provide three
ways to determine as the following:
Option 1: A = {0, 5}
Option 2:
{ }
A x / x(x 5) 0= ∈ − =¡
Option 3:
Level 4: In the content of the set, students are able to make the
following questions:
? Content of the "collective" can be used in math training in the
elementary program? Give examples?
? In primary school, in a hidden way, how many ways to access
collective concept? Give examples?
In addition, students have the skills to detect and correct errors in
the given answers, in the example of the context of implicative relations:
Give the set A of quadrangulars, set B of squars, set C of rectangulars, set
D of parallelogram, set E of trapezoid. Determine the implicative
relationships between the sets above?
If the first answer is:
C B D E A⊂ ⊂ ⊂ ⊂
After checking, students will find themselves determined
incorrectly. They will realize that a square is a special case of a
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0 5

self-study; organizing activities for them to practice, build their own
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situations on maths self-study skills;focusing on group discussions
through seminars; compiling guidance book on maths self-study;
fostering mathsematics knowledge and methods of teaching ETT students
to meet the requirements of the current renewal in primary training.
Chapter 2
METHOD OF DEVELOPING MATHS SELD-STUDY
SKILLS FOR PEAGOGICAL PRIMARY EDUCATION
UNIVERSITY STUDENTS
2.1. Principles of building measures
To build pedagogical measures of training and developing Maths
self-studying skill for students trained as a teacher in primary school, we
propose the 7 principles
2.2. Proposed some measures aimed at developing Maths self-
studying skill for students trained as a teacher in primary school
2.2.1. The first method: Bring upself-studying motivation for
ETT
2.2.1.1. Scientific basis of this measure
The group of Maths self-studying skill for students trained as a
teacher in primary school includes skill of determination the purpose, skill
of creation Maths self-studying motivation. Two these skill are the most
important and essential in in the teaching process. The author Wilbert J.
Mckeachie said: "One of the most important tasks of teaching is how to
form the inner learning motivation for students being interested in
learning" [8, P.116] So, How do lecturers implement their teaching and
learning task to enhance awareness of self-studying, to identify the
purpose, motivation, proper attitude in studying for students?. “ Studying
is task of student, He was a student and he learned for himself. Teaching
methods and learning methods must be based on the student's

and motivation for students; public criteria for evaluating the results of
self-study is one of the criteria for evaluating faculty of teachers; Visit
some schools reached national standards and the others met a lot of
difficulties; organiza for students to learn Elementary Standard and
criterias evaluating Elementary teachers in the primary schools; organiza
seminars for lectures and students exchange professional experience with
the teachers in primary schools;
2) Development of skill creating self-studying motivation.
One of the important factors to decide the effect of skill creating
Maths self-study motivation. To have skill creating motivation in process
of Maths self-studying, the leaners need to implement tasks of Maths self-
studying by 8 principles.
To help the leaners to create Maths self-studying in teaching
process, lectures need to : Let students see the internal contradictions in
the lesson content; let them know that they must to study. Teachers must
create and realize of this need; Teaching methods of teachers have to
make the relationship between the student and learning objects so suitable
that it makes students to really want to study; Trainers can offer solutions
of situations or comments, the answers that are opposed to available
knowledge to stimulate rejection of students; teacher indicates the
progress of the students. Teacher need to pay special attention to bad
students groups by creating opportunities for them to finish successfully
small tasks; teachers need to incorporate teacher's teaching methods and
students' self-learning method; in the teaching process, teachers should
evaluate the results of their self-studing.
2.2.2.The second Measure : Organization of Maths self-studying
activities for ETT
2.2.2.1. Scientific basis of this measure
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According synthesis of research in the world and fact in Vietnam,

f) Training teamwork skills
g) Training self – evaluate Maths results.
2) Training the necessary skills to prepare for students to meet the
practical requirements of teaching in primary
a) Training skills to explain the solution of problem in Primary
School Mathematics
For example 10: Age of younger sister is more than effects of age
of younger sister and older sister is 17. Total age of them is smaller than
double age of older sister is 5. Now, how old are they?
The solution usually students in general could use a hidden place
as follows: Call Age of younger sister now is: x (age); age of older sister
is: y (years. According to the article, we have: x - (y - x) = 17 and x + y -
2y = 5. By solving the above equation, we will find out her age and your
age. But when we instruction for elementary school students, we have to
moving into the language of mathematics in primary school. There are
many ways we can refer to one of the following ways:
Method 1: Use the line diagramb) Training skills to organize
situations stimulate student to work in groups in Primary
Age old sister and I are now:
Twice her age is:
17 5 5
Looking at the diagram shows: Age of younger sister is: 17 +5 =
22 (years old). Age of older sister is: 22 +5 = 27 (years old).
Answer: 22-years old, 27 years old.
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c) The meaning of teaching and self-learning processes
With the teaching process, we have been helping students with
environmental practices, and develop self-study skills Math armed above.
2.3. Method 3: Develop and use Mathematics self-study
situations for Pedagogic Primary Education University students
2.2.3.1. Scientific basis of the measure
Teaching practical applications has shown that the quality of
teaching depended so much by the environment. Therefore, the research
of the interactions and relationships between teachers, school environment
is necessary and very important to practical significance. Author Guy
Brousseau, who studied the mutual relationship and interaction between
teaching (Teaching) - (Academic) - environmental knowledge in the
teaching process. He built "a situation - Didactic situation given by the
teacher, so that students can build or revise their knowledge, as is the
answer to the demands of the environment, not by the will of the teacher
satisfaction " [91, tr.37]. Taught in a situation - Didactic usually go
through three phases: Phase Transfer (Trust) a situation; Mixed personal
research; institutionalized. We researched and also considered the
environment in view of the situation. Especially when researching the
environment of self - study mathematics, we’ve considered in the
perspective of self-study Math situations.
2.2.3.2. Objective of the measure
Construction and application of self-study situations in the process
of teaching Mathematics in order to help students frequently practice
Maths self-study skills.
2.2.3.3. Content and how to organize
1) The concept of self-study Mathematics situations.
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A Mathematics self-study problems, assignments, questions,. . . .
has been developed to help people learn to use the knowledge, experience,

instruction. Besides, Nguyen Canh Toan stressed: Teachers should not
answer everything, they only suggest students the ways to study, and let
students do it themselves so that they can mobilize their knowledge.
Prime Minister Pham Van Dong also said: At university, we don’t teach
knowledge we only teach methods. According to research of
psychologist: Some mattered situatiosns can stimulate human thinking
[51]. Therefore, we build self-study guide for students to develop
Mathematics self-study skills for Pedagogical Prime Education
University students.
2.2.4.2. The purpose of method
Building guided self-study materials to help students practice Math
skills in the classroom and at home in order to develop self-study skills
Math for Pedagogical Prime Education University students. And help
students learn how to build self-guided math materials for primary school
students
2.2.4.3. Content and organizing
To build guided self-study materials according to self-study
situations in the process of teaching Mathematics.
1) Construct guided self-study materials for mathematics for
Pedagogical Prime Education University students.
a) Guided self-study materials for mathematics
b) The structure of guided self-study materials for mathematics
The structure of guided self-study document should be ensured
about the following: directions for use; objectives; program structure;
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guiding question for self-study modules; modular content; question test
results of self-test module; knowledge modules focus; applied exercises;
homework answers apply.
c) The process of using guided self-study materials for
mathematics

a | b,a | c
can we say a is a divisor of b + c? why?
3)
a,b,c
∀ ∈
¥
nếu
a | b
can we say a is bxc convention? why?
4)
a,b,c
∀ ∈
¥
nếu
a | b,b | c
can we say a is a divisor of c? why?
?From the results obtained above can you draw about the
divisibility properties of the set of nonnegative integer, statements of that
nature?
The next section we construct multiple-choice questions test results
of self-learning modules " the divisibility and division with remainder ".
In this section, we propose a document structure guided self- study
Math for Primary School students to create new knowledge for
themselves. This structure has five basic steps. He teaches design
exercises, students practice and applied the new rules found in the specific
case in order to turn into their own knowledge.
b) Develop guided self-study learning materials for Primary
students: "Dividing fractions"
We have designed the document consists of 16 situations for
students in grades 4 for guided self-study fraction division with five-step

tr.149] with the situation proposed by students under the conduction of
teachers
In this section we offer examples of organizations sermina in article
"Teaching and calculations" [16, tr.149] with five scenarios proposed by
students under the conduction of teachers.
2.2.5.4. Conditions of method
In this section we propose to ensure conditions for the
implementation of effective measures for the management, faculty and
students.
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2.3. The relationship between methods and conditions of
methods which developed Mathematics self-study skills for ETT
2.3.1. The relationship between 5 methods
2.3.2. The conditions of 5 methods
Chapter 3
EXPERIMENTAL PEDAGOGY
3.1. The purpose and task of experimental pedagogy
3.1.1. The purpose of Experimental Pedagogy
In order to test scientific hypotheses and consider the feasibility and
effectiveness of the pedagogic measures proposed in the thesis.
3.1.2. The task of experimental pedagogy
3.2. The content and procedure of experimental pedagogy
3.2.1. The contenr of experimental pedagogy
We choose the content of the Mathematics 1, Mathematics 2 and
Introduction to Probability and Mathematical Statistics theory.
3.2.2. The procedure of experimental pedagogy
3.2.2.1. State 1,2
In stage 1, 2 we conducted experimental pedagogy according to the
6-step procedure in the proportion of the content of the course during the
semester, especially in the organization of exams results, to ensure

layers in the third period has shown the significant improving of the level
of self-study skills Mathematics of Primary Education students in the
experimental class. The results of three states has prove the feasibility of
the measures proposed in the thesis.
3.4.2. The result of gained knowledge of the control class and the
experimental class
3.4.2.1. Qualitative analysis
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