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 PEDA
Trang 1MINISTRY 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
Trang 2NATIONAL UNIVERSITY OF EDUCATION
Supervisors:
1 Dr Le Tuan Anh
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
Trang 3THE 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
Trang 4INTRODUCTION
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
Trang 5From 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
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
- Theoretical research method
- Methods of observation, investigation
- Pedagogy experimental method
- Case study method
Trang 67 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
Trang 7constructing 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
Trang 8pedagogy 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
Trang 9thinking 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
Trang 111.4 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:
Trang 12- 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
Trang 131.4.3 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
Trang 14each 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