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:

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2

An: “fraction

and fraction are equal”.

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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.

19

- 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.

22

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

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.

1

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.

2

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.

3

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

4

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

5

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

6

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

7

8

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:

9

- 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.

10

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

11

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.

12

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:

13

(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

14

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

15

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.

16

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?

17

- 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.

19

- 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

20

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.

22

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

## Phát triển năng lực độc lập sáng tạo cho sinh viên Đại học Kĩ thuật thông qua dạy học Hóa học hữu cơ

## góp phần phát triển năng lực giải quyết vấn đề cho học sinh trung học phổ thông trong dạy học toán

## Tóm tắt Luận án Tiến sĩ Khoa học Giáo dục: Phát triển năng lực độc lập sáng tạo cho sinh viên đại học kĩ thuật thông qua dạy Học hóa học hữu cơ

## phát triển năng lực suy luận thống kê cho sinh viên cao đẳng chuyên nghiệp bản tóm tắt tiếng anh

## phát triển năng lực độc lập sáng tạo cho sinh viên đại học kĩ thuật thông qua dạy học hóa học hữu cơ bản tóm tắt tiếng anh

## tóm tắt luận án bồi dưỡng năng lực chẩn đoán cho sinh viên ngành giáo dục tiểu học đáp ứng yêu cầu đổi mới dạy học toán

## góp phần phát triển năng lực giải quyết vấn đề cho học sinh trung học phổ thông trong dạy học toán

## Đề cương bài giảng : Toán cơ sở dành cho sinh viên ngành giáo dục mầm non trình độ đại học

## GÓP PHẦN PHÁT TRIỂN NĂNG LỰC DẠY HỌC CHO SINH VIÊN NGÀNH SƯ PHẠM TOÁN LÝ TRONG DẠY HỌC HỌC PHẦN QUANG HỌC Ở TRƯỜNG ĐẠI HỌC HÙNG VƯƠNG

## Luận án Góp phần phát triển năng lực toán học hóa tình huống thực tiễn cho học sinh Trung học phổ thông qua dạy học Đại số và Giải tích

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