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MINISTRY OF EDUCATION AND TRAINING
HANOI NATIONAL UNIVERSITY OF EDUCATION

NGUYEN THI TRUC MINH

CONTRIBUTING TO THE DEVELOPMENT OF THE
ARITHMETIC TEACHING COMPETENCE FOR
ELEMENTARY PEDAGOGY STUDENTS AT UNIVERSITIES

Major: Theory and Methodology of teaching Mathematics
Code: 9.14.01.11

A SUMMARY OF DOCTORAL THESIS
IN EDUCATIONAL SCIENCES

HANOI – 2019


THE WORK WAS COMPLETED IN HANOI
NATIONAL UNIVERSITY OF EDUCATION


Supervisors:
1. Dr. Le Tuan Anh
2. Assoc Prof. Dr. Tran Viet Cuong

Reviewer 1: Assoc Prof. Dr. Cao Thi Ha
Reviewer 2: Assoc Prof. Dr. Nguyen Trieu Son
Reviewer 3: Assoc Prof. Dr. Tran Dien Hien

The thesis will be defended before the university council at
Hanoi National University of Education, No 136 Xuan Thuy, Cau Giay, Hanoi.
At............................................ 2019

The thesis can be found at:
- National library of Vietnam
- The library of Hanoi National University of Education


LIST OF PUBLISHED PROJECTS OF
THE AUTHOR RELATED TO THE THESIS

1. Nguyen Thi Truc Minh, Training the skill in combining cooperative teaching

method with teaching method of detecting and solving problems in instructing
maths for students of elementary pedagogy, Journal of Education, volume
404, 2017.
2. Nguyen Thi Truc Minh, The reality of developing arithmetic teaching
competence for elementary pedagogy students, Journal of Education, volume
427, 2018.
3. Nguyen Thi Truc Minh, Arithmetic teaching competence’s elements

of

elementary pedagogy students, Journal of Education, volume 429, 2018.
4. Nguyen Thi Truc Minh, Le Tuan Anh, Developing preservice elementary
teacher students’ understanding of arithmetic contents and explaining
mathematical bases of arithmetic contents in elementary mathematics
textbooks through teaching mathematical subjects, HNUE Journal of Science,
volume 63, 2018.
5. Nguyen Thi Truc Minh, Training designing skill and organizing arithmetic
teaching activities for primary pedagogy students towards developing
students’ competence, Vietnam Journal of Education, volume 05, 2018.
6. Nguyen Thi Truc Minh, A number of measures to develop arithmetic
teaching competence for elementary pedagogy students, Journal of
Education, volume 450, 2019.


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INTRODUCTION
1. Reason for choosing the topic of the thesis
1.1. Our country's education is in the process of fundamental and comprehensive
innovation, transforming an education form imparting knowledge to developing both
learners' quality and competence. This has set up universities with many challenges to
improve the content and teaching methods in the training strategy human resources to
meet social needs. In particular, improving the content and methods of training skills
for students is a central and urgent task.
1.2. With the requirement of reforming the education of our country today,
teachers in general, elementary teachers in particular are facing difficulties and
challenges with changing educational goals, teaching methods are changing from the
type of teaching that focuses on the role of teachers and teaching activities focusing
on the role of students and learning activities. Newly graduated elementary teachers
have not yet met the requirements on teaching and mathematics teaching competence
is still limited. Some teachers have not mastered the basic knowledge of mathematics
in primary, even some teachers are not proficient in performing complex calculations
and solving typical problems in grades 4 and 5.
1.3. In primary school subjects, mathematics is very important, it takes up most
of the time in the teaching curriculum in primary school. The knowledge and skills of
elementary mathematics have many applications in life, which are essential for
workers and for other subjects in primary and secondary education. In the elementary
mathematics curriculum, arithmetic knowledge play the mainstream role, is the basis
for teaching the remaining knowledge circuits.
1.4.Through finding out the literature, we find that there is a number of
constructions focusing on studying of the training and developing of professional
competence for elementary teachers. However, these works focus on fostering and
developing the teaching competence of elementary teachers rather than focusing on
developing this competence for elementary pedagogy students in the training process.
In addition, there have been many works studying on training professional skills and
developing mathematics teaching competence for students at teacher training schools,
but most of them focus on developing teaching competence for mathematical
pedagogy students at junior and senior high schools. Until today, according to the
literature we have known, no work has studied on developing arithmetic teaching
competence for elementary pedagogy students. Therefore, the researched results are
not enough to meet the needs of society, the change of content and educational
programs.


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From the above reasons, we choose the problem: “Contributing to the
development of the arithmetic teaching competence for prospective elementary
teachers at universities” for our research topic.
2. Research target
Determining arithmetic teaching competence’s elements need to develop for
elementary pedagogy students and propose pedagogic measures to develop arithmetic
teaching competence for elementary pedagogy students at universities, contribute to
improve the quality of elementary teacher training.
3. Research task
- Researching the theory on issues related to developing mathematics teaching
competence and arithmetic teaching competence for elementary pedagogy students
at universities.
- Researching the reality of developing mathematics teaching competence and
arithmetic teaching competence for elementary pedagogy students at universities.
- Proposing measures to develop arithmetic teaching competence for elementary
pedagogy students in the formal training process at universities.
- Pedagogy experiment to test the feasibility and effectiveness of the proposed
measures.
4. Research subject and object
- Research objects: Theory and reality of arithmetic teaching competence, the
process of training teaching skills for students, the process of training elementary
pedagogy students at universities.
- Research subjects: The process of developing arithmetic teaching competence
for elementary pedagogy students at universities.
5. Scientific hypothesis
If we clearly determine arithmetic teaching competence’s elements need to
develop for elementary pedagogy students and propose, perform pedagogic measures
to develop those competences, arithmetic teaching competence of elementary
pedagogy students at universities will be developed.
6. Research method
In order to carry out the above research tasks of the thesis, we use the following
research methods:
- Theoretical research method.
- Methods of observation, investigation.
- Pedagogy experimental method.
- Case study method.


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7. The new contributions of thesis and scientific arguments will be presented
- Determining arithmetic teaching competence’s elements need to develop for
elementary pedagogy students at universities.
- Proposing pedagogy measures is feasible and effective in developing
arithmetic teaching competence for elementary pedagogy students at universities.
8. The structure of the thesis
Besides the introduction, conclusion, the thesis consists of three chapters:
Chapter 1. The theoretical and practical basis on developing arithmetic teaching
competence for elementary pedagogy students at universities.
Chapter 2. Pedagogy measures to develop arithmetic teaching competence for
elementary pedagogy students at universities.
Chapter 3. Pedagogy experiment
Chapter 1
THE THEORETICAL AND PRACTICAL BASIS ON DEVELOPING
ARITHMETIC TEACHING COMPETENCE FOR ELEMENTARY
PEDAGOGY STUDENTS AT UNIVERSITIES
1.1. Overview of Research Issues
1.1.1. Overseas research situation
In the world, the issues of teaching skills and teaching competence have been
studied for a long time.
Starting in the 20s of last century, in the Soviet Union and Eastern Europe
countries had many works researching on teaching skills for pedagogy students. By
the 1960s, this problem was deeply studied and became a solid theoretical system. By
the 1970s, educational researchers in the Soviet Union and Eastern Europe continued
to study on organizing scientific labor and optimizing the teaching process.
In the Western countries and other countries such as Canada, America, Australia
and so on education researchers are especially interested in organizing to train
teaching skills for students. They based on the achievements of behavioral
psychology and functional psychology to organize training for students these skills
with the time of practicing is distributed more than that of theory. For typical
example such as the opinion of authors: J. Watson (1926), A. Pojoux (1926), F.
Skinner (1963), “The process of learning” of J.B. Biggs and R. Telfer (1987),
“Beginning teaching” of K. Barry and L. King (1993) and so on.
In the United States, since the 1970s, Ohio National University had studies on


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constructing modules to train professional-technical teacher, the results had 600 skills
to train technical-professional teacher were suggested. At Stanford University, based
on the basic American educational background, the research team of Phidenta Kapkar
proposed five technical groups of teachers while teaching in the report "Science and
art of training the teachers".
Since the early 1930s, American educational researchers and managers have begun
to study about the necessary competences of teachers to succeed in teaching and
education with the work of authors such as O’Day, McDiarmid, Clevenger-Bright,
Shulman and so on. With the specificity of Mathematics, there were the knowledge
models of the authors such as the model of teaching mathematics of Ball; at
Cambridge University, researchers gave “The Knowledge Quartet”; Petrou and
Goulding with “The knowledge model of teaching mathematics ” and so on. In 2007,
National Council of Teachers of Mathematics proposed seven specific standards of
mathematics teachers.
In the Asia-Pacific countries, the role and task of forming pedagogy skills have
also been identified in the workshop about "Workshop on renovation of the training
and retraining of teachers of the Asia-Pacific countries" organized by APEID the in
Seoul (Korea). The reports of the workshop identified the importance of forming
knowledge and pedagogy skills for students in the training process. The scientists
confirmed that “Professional knowledge is the basis of pedagogical art but only
presents in the system of pedagogy skills”.
1.1.2. Domestics research situation
Before 1975, the basic research on profession training for teachers had not yet,
teachers' skills were only mentioned in psychology books and pedagogy books
written based on the textbooks of the former Soviet Union. Since 1975, improving
quality teacher training have been interested more and more, many works studying on
this issue have begun to appear.
From 1990s, research trends on teaching competence and teaching skills have
become a matter of great concerned in our country. There is a number of theses and
topics of the authors such as Le Thi Nhat, Nghiem Thi Phien, Nguyen Canh Toan
and so on.
At universities, studying on developing teaching competence and teaching skills
for students were reflected in ministerial-level topics and theses of the authors such as
Nguyen Huu Dung, Trinh Thi Quy, Tran Anh Tuan, Phan Thanh Long and so on.
These topics and theses relatively presented the system of related theoretical issues,
found out the reality of forming pedagogy skills and training of teaching skills for


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pedagogy students. From that they proposed, checked and took over measures and
process training teaching skills for students to improve the quality of the forming and
developing of suitable teaching skills for pedagogy students.
About Teaching Theory and Methodology of Mathematics, there were some
theses studying on developing some teaching skills and teaching competence for
students of authors such as Pham Van Trao, Nguyen Chien Thang, Tran Viet Cuong,
Do Thi Trinh and so on. The authors focused on to study theoretical and practical
issues in developing teaching skills, job skills, teaching competence, and mathematics
teaching competence for mathematics pedagogy students. From that they proposed
measures to develop teaching skills and teaching competence for those students
through organizing to teach a subject at university, contributing to improve the
quality of training high school mathematics teachers.
On training pedagogy profession and developing pedagogy competence for
elementary pedagogy students, there were theses of authors such as Nguyen Thi Chau
Giang, Pham Van Cuong, Do Thi Phuong Thao, Pham Thi Thanh Tu and so on. In
addition, there were many theses focused on studying to foster and develop teaching
competence for elementary teachers of authors such as Nguyen Van Tan, Truong Thi
Thu Yen, Hoang Cong Kien and so on. These theses studied fostering and training for
elementary teachers how and procedure to apply a new teaching method to teach at
primary school to improve elementary teachers' teaching competence to improve the
quality of teaching at primary school.
1.2. The content arithmetic in elementary mathematics
1.2.1. Generalizing history of the formation and development of natural
number set
1.2.2. Generalizing history of the formation and development of rational
number set
1.2.3. The algebraic structure of number sets
1.2.4. Characteristics of the arithmetic content in elementary mathematics
curriculum
- Arithmetic content is arranged expanding and developing in accordance with
number rounds, gradually increasing through each stage, knowledge in the former
class is a premise to help students learning knowledge in the latter class.
- Arithmetic content in textbooks is built in combination between history and science.
- Arithmetic is the foundation for teaching other knowledge circuits and opposite.
- Arithmetic in elementary mathematics is inextricably linked with reality, with
the development of elementary students' mathematics competence (mathematical


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thinking and arguments competence, mathematical modeling competence and so on).
1.2.5. The goal of teaching arithmetic in primary schools
1.3. Characteristics of mathematics teaching and learning in primary school
1.3.1. Cognitive characteristics of elementary students
1.3.2. Mathematics learning characteristics of elementary students
- Thinking still depend on acting on objects and external events.
- Elementary students have ability to be aware of the invariant things and form
preservation concept, can distinguish qualitatively and quantitatively.
- Elementary students of the later classes have progress in spatial awareness
compared to students of the former classes.
- Elementary students initially have the ability to analyze, synthesize, abstract,
generalize and simple forms of reasoning and judgment. However, the development
of these abilities is not evenly.
- Mathematical concepts are formed through abstraction, generalization but
cannot only be based on perception because mathematical concepts are also the result
of particular thinking manipulation.
- Elementary students often judge according to their own feelings so reasoning is
often absolute. In fact, it is difficult for them to accept assumption hypothesis.
1.3.3. Characterictics of mathematics teaching in primary school
- Elementary teachers need to master the development of students' thinking,
correctly appreciate the existing ability and potential ability of students to have
appropriate pedagogy measures.
- Although the psychological view is the mainstream view, it is necessary to
realize the role of the logical view and the mathematical view.
- Can not teach mathematics but do not master the characteristics of
Mathematics, do not master the basic and necessary mathematical knowledge related
to the knowledge needed to teach.
- Limit the use of mathematical terms and symbols. Abstract mathematical
knowledge is presented through visual images and expressed in the way of children,
not using mathematical terminology or symbols.
- Mathematical concepts are described by description and are not defined.
Mathematical properties are not proved rigorously and logically, are explained and
illustrated with examples and reasoning.
- The knowledge and skills are formed mainly by practicing and are regularly
reviewed, consolidated, developed and applied in daily life.
1.3.4. Mathematical compentence of elementary students


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1.4. Arithmetic teaching competence of elementary pedagogy students
1.4.1. Competence, pedagogy competence and teaching competence
- Competence is ability to perform a task successfully through mobilizing and
using all resources of an individual effectively.
- Pedagogy competence is ability to perform education and teaching activities
attaining high quality.
- Teaching competence is ability to mobilize and use all resources of an
individual effectively to perform teaching task successfully.
1.4.2. Arithmetic teaching competence of elementary pedagogy students
Arithmetic teaching competence of elementary pedagogy students includes the
following element competences:
(1) Competence to understand physiological mind characteristics and
mathematical thinking of elementary students
This competence of students expressed through the following criteria:
- Understanding the physiological mind characteristics and cognitive
characteristics of elementary students.
- Having ability to understand the mathematical thinking of elementary students
through their ideas and mathematical language;
- Understanding the level of elementary students' achievement of arithmetic
knowledge. Understanding elementary students know what, do what and use that
understanding to teach arithmetic content.
(2) Competence to understand issues related to arithmetic content in elementary
mathematics.
This competence of students expressed through the following criteria:
- Understanding about structure and content of the arithmetic in elementary
mathematics curriculum;
- Mastering the solving method and solving proficiently arithmetic problem
forms, knowing to study a problem thoroughly and creating new problems.
- Understanding the constructing opinion of the arithmetic circuit, meaning and
relationship between the arithmetic circuit and other knowledge circuits in the
elementary mathematics curriculum.
- Determining the mathematical basis of the arithmetic knowledge in textbook.
- Knowing the formation and development history of number sets in elementary
mathematics.
(3) Competence to apply methods, means and teaching forms to teach arithmetic.
This competence of students expressed through the following criteria:


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- Understanding the strengths, weaknesses and using principles of the teaching
methods and forms often use in elementary mathematics teaching;
- Operating correctly the techniques and pedagogical processes of the teaching
means;
- Knowing how to choose teaching means, available teaching tools or
improving, creating other teaching tools suitable to the objectives and contents of the
lesson to enhance the visualization in arithmetic teaching;
- Knowing how to combine teaching methods, teaching techniques in a lesson, a
teaching activity to express own teaching ideas;
(4) Competence to design and organize arithmetic content teaching activities
This competence of students expressed through the following criteria:
- Understanding the form of the lessons and the teaching activity structure of the
lesson;
- Designing teaching activities fit with the objects and contents of the lesson and
teaching methods;
- Handling pedagogy situations well, mastering class, creating a friendly
learning environment.
- Writing and speaking clearly and fluently.
(5) Competence to anticipate elementary students' difficulties in learning arithmetic
and find how to help them overcome
This competence of students expressed through the following criteria:
- Understanding how elementary students learn arithmetic topics, systematizing
basic difficulties that they often encounter when they study each topic;
- Systematizing elementary students' difficulties and mistakes while they solve
arithmetic problem forms;
- Analyzing and pointing out the reasons leading to elementary students'
mistakes, providing how to repair mistakes for them.
(6) Competence to assess the learning process and use the evaluation results in
teaching arithmetic
This competence of students expressed through the following criteria:
- Understanding the purpose, requirement and principle of the assessment at
primary school;
- Using the methods and techniques of the assessment at primary school
effectively;
- Knowing regular assessment by positive comments;
- Knowing how to use feedback information from elementary students to adjust
teaching activities.


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1.4.3. Evaluation criteria the arithmetic teaching competence of elementary
pedagogy students at universities (The criteria are used to assess elementary
pedagogy students' arithmetic teaching competence at universities)
On the basis of theory research on assessment, we proposed the criteria to
evaluate elementary pedagogy students' arithmetic teaching competence in
accordance with four increasing levels (level 1, level 2, level 3, level 4), the higher
level includes the lower levels.
1.5. The reality of the arithmetic teaching competence of elementary
pedagogy students at universities
1.5.1. The purpose of the survey
1.5.2. The subjects and time of the survey
1.5.3. The contents of the survey
- Finding out the reality of developing the mathematics teaching competence of
elementary pedagogy students in aspects related to the arithmetic teaching
competence.
- Finding out the assessment of lecturers and elementary teachers, elementary
pedagogy students self-assessment about arithmetic teaching competence that the
fourth-year elementary pedagogy students achieve.
1.5.4. The results of the survey
The results of the survey showed that universities are always interested in
developing mathematics teaching competence for elementary pedagogy students, but
most only training some basic teaching skills for students. The arithmetic teaching
competence of fourth-year elementary pedagogy students has not been highly
appreciated. The important reasons for this reality are lack of time and conditions for
students to practice, lack of the attention of lecturers, especially teachers who are not
belonged the part of the teaching method and learning awareness of students
themselves are not high.
THE CONCLUSION OF CHAPTER 1
Based on the research results of domestic and foreign authors, we analyzed and
clarified the concepts of competence, teaching competence and gave our opinions
about the structure of teaching competence, elementary teachers’ mathematics
teaching competence.
Approaching by the way of studying the components of competence, we gave
our opinions on the structure of elementary pedagogy students’ teaching competence
including six component competences. These components interlink and depend on


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each other. Each component competence is described through criteria and evaluated
in accordance with four levels from low to high.
The research results of theory and reality are an important premise to us to
propose pedagogy measures to contribute developing elementary pedagogy students’
arithmetic teaching competence and improving the quality of training elementary
teachers.
Chapter 2
MEASURES DEVELOPING ARITHMETIC TEACHING COMPETENCE
FOR ELEMENTARY PEDAGOGY STUDENTS AT UNIVERSITIES
2.1. Orientations to construct measures developing arithmetic teaching
competence for elementary pedagogy students
- Measures must be consistent with theory.
- Measures have to fit with reality and be feasible.
- Measures have to be in accordance with the requirements of the teacher career
standards, orient towards the renovation of the curriculum and textbooks.
- Measures have to be in accordance with the component competences of the
arithmetic teaching competence that thesis determined to develop for students.
2.2. Pedagogy measures to develop arithmetic teaching competence for
elementary pedagogy students
2.2.1. Measure group: Developing competence to understand issues related to
arithmetic content in elementary mathematics
2.2.1.1. Base to propose the measure group
2.2.1.2. The purpose of the measure group
2.2.1.3. Measure 1. Teaching the subject “Advanced Mathematics” orient
towards connecting with arithmetic content in elementary mathematics textbooks.
In teaching advanced mathematics, lecturers can clarify the relationship between
advanced mathematics content and arithmetic content in elementary mathematics
textbooks through the following ways:
- Indicating the representation of the concepts and properties of advanced
mathematics in arithmetic content.
- Using the concepts of advanced mathematics to explain the constructing view
and mathematics basis of arithmetic knowledge.
- Applying the knowledge of advanced mathematics to orient finding the answer
of arithmetic problems.
- Using the knowledge of advanced mathematics to create new problems.


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2.2.1.2. Measure 2. Organizing teaching the subject “Advanced Mathematics”
by seminars focusing on contacting with arithmetic content.
Lecturers can organize teaching Advanced Mathematics for students by seminars
according to the 4-step process as follows:
Step 1. Preparing
The lecturer and students perform the following tasks:
- Students self-divide into groups appropriately, then each group chooses a
leader and a secretary.
- The lecturer gives seminar topics.
- The lecturer arranges for students to select topics, discuss contents that will be
implemented (focus on establishing the relationship with arithmetic content in
elementary mathematics textbooks) and set the working principle of the group.
- The lecturer suggests content structure and presentation form, supplies
materials or guides students looking for materials.
- The lecturer gives evaluation criteria.
Step 2. Writing presentation.
Each group of students performs the proposed tasks such as assigning tasks,
making an outline, studying document, discussing, writing a presentation and so on
in accordance with the working principle of the group.
Step 3. Reporting, discussing.
The lecturer arranges for students reporting and discussing no more than 2
periods per topic.
- Each group sends a representative to report the research results of the group.
- When the student completes the report, the lecturer organizes for students
discussing and commenting.
- Finally, the lecturer comments the results, adds and expands as necessary,
summarizes the knowledge gained (the knowledge of advanced mathematics).
Step 4. Evaluating.
Students' regular test scores is assessed through students' activities during the
seminar about the aspects such as the research results of the group, the form of
presentation, handling situations, answering questions from teachers and other
groups, attitudes and so on.
2.2.1.3. Measure 3. Organizing small learning projects on the relationship
between the knowledge of advanced mathematics and that of elementary arithmetic
through teaching the subject “Advanced Mathematics”
Lecturers can integrate small learning projects into the teaching process of
advanced mathematics according to the following 3 basic stages:


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(1) Preparating stage: Preparation may take a week or more depending on the
condition of the lecturer and students and necessary knowledge that students must
have before the project starting. The lecturer performs the following tasks:
- Finding out students about aspects such as competence, attitude, learning
awareness and so on.
- Dividing group: The lecturer need to study how to divide group scientifically
and reasonably. Each group should have from 8 to 10 students. Then, the lecturer
instructs students dividing each member’ s task in the group in accordance with the
competence and forte of them.
- Analyzing the relationship between advanced mathematics and elementary
arithmetic to determine the topics of project and students' tasks.
- Anticipating facilities, materials, resources for learning.
- Building a plan to evaluate.
(2) The stage of planning and performing project. The lecturer selects
appropriate time, spend 2 periods, before the evaluating stage about 2 weeks. The
lecturer and students perform the following tasks:
- The lecturer arranges for the groups selecting topics, defining objectives and
content and planning to implement learning tasks.
- Students implement works in accordance with the plan in self-learning time.
(3) The stage of reporting product and evaluating project. The lecturer spends
from 2 to 4 periods before the end of advanced mathematics. The lecturer and
students perform the following tasks:
- The groups submit their products to the lecturer.
- The lecturer arranges for students reporting the research results of each group,
commenting, discussing and complementing each other.
- The lecturer comments the points need to be adjusted, revised, supplemented
and finalized, evaluates the achieved results against the defined objective.
2.2.1.4. The conclusion of the measure group
2.2.2. Measure group: Creating arithmetic teaching potential for students
2.2.2.1. Base to propose the measure group
2.2.2.2. The purpose of the measure group
2.2.2.3. Measure 4. Training calculation teaching skills for students through
teaching the subject “Mathematics Teaching Methods”
The lecturer can spend 6 periods in Mathematics Teaching Methods specific
subjects to implement the following contents:
(1) Training the teaching skills of mental calculation


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The lecturer can spend 2 periods to organize a seminar as follows:
 Preparing seminar: The lecturer asks students listing mental calculated forms
and corresponding calculated method in accordance with elementary students’
cognitive level in each stage.
 Performing seminar: The lecturer organizes students presenting the contents
prepared. With each type of mental calculation that students give, the lecturer
organizes students discussing and drawing out the best mental calculated method and
the best way to teach for elementary students.
(2) Training the teaching skills of calculated techniques
The lecturer can spend 2 periods to organize a seminar as follows:
 Preparing seminar:
- Students divide themselves into 4 groups appropriately, then each group elects
a group leader and a secretary.
- The lecturer introduces topics (addition, subtraction, multiplication and division in
elementary mathematics teaching). In each topic, the lecture requires students to perform
the following contents: presenting the decimal structure of natural numbers, the
mathematical basis of the operation, explaining how to build and presenting the
computational technique of the operation on natural numbers written in decimal system,
the forms of calculations that elementary students often have trouble learning
mathematics, selecting the lesson contains that forms to design teaching activities.
- The lecturer organizes a lottery for the group leaders choosing the topics.
- After selecting a topic, each group of students will discuss and perform tasks in
their self-study time.
 Performing seminar: The lecturer arranges the groups presenting the contents
prepared. For each topic, the lecturer organizes discussing and commenting on the
contents to draw out appropriate teaching methods for selected calculation forms.
2.2.2.2. Measure 5. Creating the teaching potential of solving arithmetic
mathematics for students through the subject “Solving elementary mathematics”
In this measure, the lecturer can spend 4 periods in the subject “Solving
elementary mathematics” to organize seminar the following contents:
(1) Systematizing the forms of arithmetic problem
 Preparing seminar: students perform the following tasks in their self-study time:
- Classifying problem forms: Students rely on arithmetic problems in textbooks
to identify, call the name of the problem form, and systematize problem forms.
- Describing the characteristic of problem forms: For each problem form,
students describe its characteristics (conditions and requirements) or its general


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problem, present how to solve it, present how to teach elementary students to solve it,
systematize the common mistakes of elementary students when they solve it.
 Performing seminar:
The lecturer arranges for students to present and discuss the contents prepared.
Then, the lecturer draws out the results of the problem forms (characteristics,
solution, the common mistakes of elementary students when solving).
(2) Arranging for students to find out the causes and correct the common
mistakes of elementary students when solving arithmetic problem
The lecturer arranges for students to find the causes and correct the common
mistakes of elementary students when solving arithmetic problem by giving specific
situations (or problems), asking students to discuss and find the causes and suggest
how to correct the mistake of elementary students.
Example 2.8. When performing the calculation 396 + 25, there was an
elementary student did as follows:


396
25
646

Finding the mistake and wrong cause of the elementary student and giving how
to correct the mistake.
Students’ answer:
- The elementary student placed the digits of the terms not in line and column
leading to the wrong result.
- The wrong cause: The elementary student did not know how to arrange and
perform calculations, did not understand number structure.
- Way to overcome:
+ Asking the elementary student to test the result of the calculation by
performing a reverse calculation, so that he knows that he calculated wrong.
+ Asking the elementary students to present the calculating rule of the addition.
The teacher can analyze (or ask him to analyze) the structure of numbers 396 and 25
to help him to understand number structure.
+ Asking the elementary student to say the way he did so that he recognizes the
cause of the mistake.
+ Asking the elementary student to do again the calculation in accordance with
the stated above rule carefully.
+ The teacher need attend to help elementary students having habit checking the
results after calculating.


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2.2.2.2. Measure 6. Arrange for students to design situations, questions,
exercises in elementary arithmetic teaching through the subject “Training
Pedagogic Professions”
Through the subjects “Training Pedagogic Professions”, the lecturers arrange
for students to practice the following contents:
(1)
Designing reality situations in arithmetic teaching
The lecturer arrange for students to design reality situations in arithmetic
teaching by giving specific contents and asking students to design reality situations to
teach that.
Example 2.15. Asking students to design motivational situations for elementary
students to learn the lesson “Reducing fractions”
The designed situation as follows: An and Binh have the following comments:
10
2
An: “fraction
and fraction are equal”.
15
3
10
2
Binh: “fraction
and fraction are not equal”.
15
3
Finding out who are right?
(2) Constructing and using questions in arithmetic teaching
Before students are trained to construct and use questions in arithmetic teaching,
students were equipped the knowledge of constructing and using questions in
teaching.
The lecturer can organize seminars for students including the following steps:
- Step 1. The lecturer gives a situation (a situation can be a lesson, an exercise
and so on), selects the type of question and asks students to design questions to teach
the situation.
- Step 2. Students design questions as required, the lecturer records the questions
on the board.
- Step 3. The lecturer and students comment and evaluate the above designed
questions to choose the most appropriate question.
(3) Designing reality problems in arithmetic teaching.
With the characteristics of arithmetic content in elementary mathematics
curriculum, we only train students to design reality problems to reinforce necessary
calculation skills in daily life for elementary students.
 Introducing to students the practical problem designing process:
- Step 1. Defining the designing goal: Whom are the problems designed for?
What knowledge or skills of elementary students will be reinforced?


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- Step 2. Selecting objects, context and data: The situation of the problem must
be close to elementary students' daily life and relate to their need, their family,
society, school and so on; the data must be consistent with reality.
- Step 3. Presenting the problem.
- Step 4. Solving the problem to check the result and adjust.
 Arranging for students to practice designing reality problems:
The lecturer gives specific requirements and asks students to rely on the above
process to design the problem.
Example 2.22. Designing a problem help elementary students to train adding
skill, (no remember) subtracting skill in the range of 100 and help them to understand
when addition and subtraction are used.
The implementing results of students:
- Step 1. Defining the designing goals: Designing a problem to help 1st grade
students to train adding skill, (no remember) subtracting skill in the range of 100,
help them to understand when addition and subtraction are used.
- Step 2. Object: candies. Data: numbers in the range of 100. Context: right in
the classroom.
- Step 3. Presenting the problem.
Lan has 23 candies, Hue has 56 candies. Ask:
a. How many candies do both of them have?
b. Who's more candies? How many are more?
- Step 4. The problem has data and context fit with the knowledge level of 1st
grade students.
2.2.2.4. The conclusion of measure group
2.2.3. Measures: Training students to apply the knowledge of teaching methods
2.2.3.1. Based on proposing group of measures
2.2.3.2. The purpose of the measure group
2.2.3.3. Measure 7. Training students to design, organize arithmetic teaching
activities through teaching the subjects of “Mathematics Teaching Methods”
In this measure, with 4 periods (2 periods in the subject Mathematics Teaching
Methods, 2 in the subject Training Pedagogic Professions), the lecturer can train
students to design and organize arithmetic teaching activities oriented towards the
development of learners’ competence as follows:
(1) Providing necessary knowledge for students
Before training, the lecturer provides materials for students to self-study and
clarify the following issues:
- Elementary Mathematics contributes to develop elementary students'


18

competence.
- The characteristics of designing lesson oriented towards the development of
learners’ competence.
- Teaching methods are suitable with teaching oriented towards forming and
developing learners' competence.
- The basic principles of mathematics teaching oriented towards the
development of elementary students' competence.
(2) Training for students to design, organize arithmetic teaching activities
oriented towards the development of elementary students’ competence
i) The training process
Step 1. Researching the curriculum and contents of lesson, learners
Students perform the following tasks:
- Researching the content of elementary mathematics curriculum carefully,
understanding the level of knowledge and skills of arithmetic content that elementary
students must attain.
- Researching the content of the lesson will be taught, finding out the relation
between its content and the content of the lesson before it and that of the lesson after
it in the same topic, determining the quantity of knowledge elementary students must
attain when they learn the lesson, determining the mathematical basis of teaching
content and the intent of textbooks.
- Identifying the ability to meet cognitive tasks of elementary students:
identifying their cognitive and psychological characteristics, identifying their
attitudes, knowledge and skills, anticipating their difficulties and advantages when
they learn the new knowledge.
Step 2. Determining the aim of the lesson
When defining the aim of the lesson to competence-developed teaching, the
lecturer requires students not only identifying knowledge and skill goals, but also
identifying competences which can be formed and developed for learners through the
content of the lesson.
Step 3. Selecting teaching methods, teaching means and teaching forms
The lecturer guides students based on the content and objectives of the lesson,
cognitive characteristics of elementary students, characteristics of teaching methods
to choose teaching methods, teaching means and teaching forms appropriately.
Step 4. Designing, organizing teaching activities
The lecturer guides students to do the following tasks:
- Determining the logical sequence of the lesson to have idea to construct
teaching activities.


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- Thinking how to form and develop the components of mathematical
competence for elementary students through teaching activities.
- Focusing on learners' activities, elementary students' knowledge and skills to
define necessary learning activities to get learning results as expected.
- Deploying specific teaching activities: Completing the design of small
activities, the operations of both teachers and elementary students in each major
teaching activity of the lesson.
Step 5. Evaluating and adjusting
- The lecturer arranges for students to present their research right in class. The
students of the class comment on the following criteria:
+ Accurateness, logicality, science, clarifying the main content of the lesson;
+ Compatibility between teachers' activities and elementary students' activities;
+ Elementary students have opportunity to experience in order to develop their
necessary skills and competences;
+ The effectiveness of teaching activities.
- The lecturer comments the points need to be adjusted and revised, evaluates
the results of teaching activities designed by students.
- Students revise their design based on the lecturer’s comments and other
students’ comments, and then return it to the lecturer.
ii) Organizing the training
The training is conducted after students have been learned the teaching method
of specific contents and supplemented with the necessary knowledge. The training is
performed as follows:
- Before students practicing, the lecturer guides students to design and organize
the competence-developed teaching activities of an arithmetic lesson as a sample.
- The class is divided into four groups, each of which selects an arithmetic
lesson to design and organize teaching activities of the lesson in accordance with the
four steps 1st, 2nd, 3rd and 4th of the above process.
- Arranging for students to present their design results, then commenting and
evaluating the results (the step 5th of the above process).
2.2.3.4. Measure 8. Training the skill in combining teaching methods for students
In the content of this thesis, we train the skill in combining the cooperative
teaching method with the teaching method of detecting and solving problems in
elementary arithmetic teaching for students.
The steps of combining the cooperative teaching method with the teaching
method of detecting and solving problems in teaching:
- Step 1. Organizing to form groups: The teacher divides learning groups (each


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group has from 3 to 6 learners) depending on the requirements of each group and the
teacher’ s pedagogical ideas, and elects the group leader of each group.
- Step 2. Creating problems: The teacher creates a problematic situation;
learners detect the problem that need to be solved, state the problem and set goals to
solve it.
- Step 3. Discussing in group, solving the problem: The teacher determines tasks
and guides how to work for each learning group. The groups discuss, analyze the
problem and unify solution to solve the problem. Learners independently solve the
problem in accordance with the solutions discussed and then converse together to
unify the overall working results of the group. The teacher observes and assists the
groups when necessary.
- Step 4. Conclusion: The groups report their result; the teacher evaluates and
comments the results and then makes a general conclusion.
In the process of training pedagogical skills for students, after all students are
trained teaching skills such as lesson preparing skills, lecture implementing skills and
so on, the lecturer can train the skill in combining the cooperative teaching method
with the teaching method of detecting and solving problems for students in
accordance with 3 stages as follows:
a) Stage 1. Preparing:
- Arranging for students to understand and master the concepts, teaching process
and related issues of the cooperative teaching method with the teaching method of
detecting and solving problems (the lecturer can also integrate this understanding in
the teaching process of the subject Mathematics Teaching Methods).
- The teaching evaluation card: the lecturer designs the card in 2 fields that are
teaching skills and the content of teaching.
b) Stage 2. Training additional skills
In order to combine the cooperative teaching method with the teaching method
of detecting and solving problems in teaching, students need have skills: forming
group skill, the skill in organizing group activities, and so on. At this stage, the
lecturer trains students to help them to achieve these skills.
c) Stage 3: Training the skill in combining the cooperative teaching method with
the teaching method of detecting and solving problems in teaching
After completing the above phases, the lecturer arranges to train the skill in
combining the cooperative teaching method with the teaching method of detecting
and solving problems for students in the following steps:
- Step 1. Planning teaching: Arranging for students to choose the appropriate
lesson through analyzing the content and requirements of each lesson and basing on


21

the characteristics of the teaching methods. After that, the lecturer arranges for
students to make teaching plans for the selected lessons in accordance with the steps
presented above.
- Step 2. Teaching: Students teach the lesson prepared. The teaching take place
with the participation of the lecture and other students, these students play a role both
as participants and learners.
- Step 3. Evaluating the results: The lecturer and other students analyze, discuss
and evaluate the advantages and disadvantages of the teaching-student in accordance
with the teaching evaluation card to draw out conclusion and appropriate behavior in
order to teach more effective. The lecturer need to guide the criteria for students
clearly so that students only focus on the suggested criteria when assessing.
2.2.3.5. Measure 9. Arranging for students to converse, discuss on regular
assessment situations in arithmetic teaching through the subject “Mathematics
Teaching Method”
The lecturer can spend 2 periods in the subject “Mathematics Teaching Method”
to perform the following contents:
(1) Introducing to students the process of regular assessment in teaching.
- Step 1. Determining the assessment content.
- Step 2. Selecting assessment method and evaluating.
- Step 3. Stating comments.
(2) Arranging for students to converse, discuss on regular assessment situations
The lecturer arranges for students to converse and discuss on assessment
situations as follows: asking students to identify the assessment content and anticipate
the assessment method of the specific lesson selected; then the lecturer gives students
to watch a video the teaching of the lesson and asks students to observe the progress
of the teaching, record the teacher's assessment; lastly, the lecturer arranges for
students to converse and analyze the teacher’s evaluating method to learn the
teacher's experience.
THE CONCLUSION OF CHAPTER 2
On the basis of theory and reality, in this chapter we clarified directions to
propose pedagogy measures. From that, we proposed 03 measures groups including 9
specific pedagogy measures to develop arithmetic teaching competence for students.
For the purpose of developing arithmetic teaching competence for students, the
proposed measures are closely linked and used in combination in the teaching process
of the subjects on Mathematics and Mathematics Teaching Methods. Each measure is
implemented through one or two subjects in accordance with the teaching plan of the
primary education program in universities.


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Chapter 3
PEDAGOGY EXPERIMENT
3.1. The purposes of pedagogy experiments
We organized the pedagogy experiments to aim the following basic purposes:
- Testing the scientific hypotheses of the thesis through the teaching reality.
- Testing and evaluating the feasibility and effectiveness of the pedagogy
measures were proposed.
3.2. The content of pedagogy experiments
We organized pedagogy experiments at Dong Thap University. Based on the
curriculum and content of the elementary pedagogy, we experimented the
following contents:
(1) Equipping the mathematics basis of the arithmetic content in elementary
mathematics textbook for elementary pedagogy students through teaching the
subjects “Basic Mathematics 1” and “Basic Mathematics 2”.
(2) Training students to systematize arithmetic problem forms and their solving
methods in elementary mathematics, find out causes and how to overcome the
difficulties and mistakes of elementary students in arithmetic learning.
(3) Training students to design, organize arithmetic teaching activities oriented
towards the development of learners’ competence.
(4) Training students to create situations, questions, reality problems in
elementary arithmetic teaching.
(5) Training students to evaluate the learning process of elementary students in
elementary arithmetic teaching.
3.3. Tools to evaluate the result of the pedagogy experiments
We evaluated qualitative and quantitative the results of each pedagogy
experiment as follows:
- Qualitative assessment: We relied on observations, interviewed lecturers,
elementary teachers and students and case-study to further clarify the research problem.
- Quantitative assessment: We used the T-Student test to evaluate the
effectiveness of pedagogy experiments.
3.4. The first experiment
3.4.1. Organizing experiment
- The purposes of the experiment: Testing the feasibility and effectiveness of the
measures 5th.
- The content of the experiment: the second content.
- The subject of the experiment: 70 second-year students (36 students in the
experimental class and 34 students in the control class).
- Organizing experiment: The experiment was performed on 12/2015.
3.4.2. The result of the experiment


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