VIETNAM JOURNAL OF EDUCATIONAL SCIENCES

THE VIETNAM NATIONAL INSTITUTE OF EDUCATIONAL SCIENCES

You are here

Home

GENERALIZATION AND ABSTRACTION IN ADVANCED MATHEMATICS

GENERALIZATION AND ABSTRACTION IN ADVANCED MATHEMATICS

NGUYEN CHIEN THANG ncthang2009@gmail.com Vinh University
LE THI NGOC THUY thuy76sp@gmail.com Nghe An College of Education
Summary: 
The article addresses the generalization and abstraction in advanced Maths. The author analyses: 1/ Processes of generalization and abstraction when forming knowledge and concepts in advanced Maths; 2/ Analysis of difficulties and how to overcome the difficulties when implementing the above mentioned processes; 3/ Approaches in classifying generalization and abstraction in terms of perception, and orientations for developing each types of generalization in teaching advanced Maths at universities. In author’s opinions, generalization and abstraction are the two most important actions in the process of forming advanced Maths concepts. They are closely connected and supplemented to each other in the process of intellectual development by learners, particularly by Maths pedagogical students at universities. It can be seen that generalization is the first stage and abstraction as the final stage in the way to the truth of an advanced Maths knowledge in general or an advanced Maths concept in particular.
View file
Keywords: 
Generalization
abstraction
advanced mathematics
student
university
Refers: 

[1] Nguyễn Bá Kim, (2015), Phương pháp dạy học môn Toán, NXB Đại học Sư phạm, Hà Nội.

[2] Hoàng Chúng, (1978), Phương pháp dạy học toán học, NXB Giáo dục, Hà Nội.

[3] N. Hashemi, M. S. Abu, H. Kashefi, K. Rahimi, (2013), Genelization in the Learning of Mathematics, 2nd International Seminar on Quality and Affordable Education.

[4] M. Mitchelmore, P. White, (2004), Abstraction in Mathematics and Mathematics Learning, Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, p. 329-336.

[5] . Nguyễn Phú Lộc, (2010), Dạy học hiệu quả môn Giải tích trong trường phổ thông, NXB Giáo dục Việt Nam.

[6] Phan Trọng Ngọ (chủ biên), Nguyễn Đức Hưởng, (2003), Các lí thuyết phát triển tâm lí người, NXB Đại học Sư phạm, Hà Nội.

[7] G. Harel, D. Tall, (1991), The General, the Abstract and the Generic in Advanced Mathematical Thinking, For the Learning of Mathematics, Vol. 11 Num. 1, p.38-42

[8] D. Tall , (2002), Advanced mathematical Thinking, Kluwer Academic Publishers.

[9] Nguyễn Hữu Việt Hưng, (2001), Đại số tuyến tính, NXB Đại học Quốc gia Hà Nội.

[10] Hoàng Xuân Sính, (2003), Đại số đại cương, NXB Giáo dục, Hà Nội.

Journal: 
No. 139, April 2017

Articles in Issue

CURRENT STATE OF THE TRAINING OF PRESCHOOL TEACHERS WHO TAKE CARE OF UNDER 36 - MONTH OLDS IN VIETNAM
08/04/2021
PROFESSIONAL STANDARDS OF TAIWANESE UPPER SECONDARY TEACHERS AND LESSONS LEARNED FOR VIETNAM
08/04/2021
RECEIVING AND DECIPHERING LITERARY TEXTS IN THE NEW PHILOLOGY CURRICULUM
08/04/2021
CORRELATION BETWEEN PERSONALITY CHARACTERISTICS AND LEARNING STYLES OF STUDENTS AT HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY
08/04/2021
INTERNATIONAL LITERATURE AT UPPER SECONDARY SCHOOLS IN DEMANDS OF VIETNAM’S EDUCATIONAL RENOVATION
08/04/2021
COMPETENCE-BASED PEDAGOGICAL PROFESSION TRAINING AND RENOVATION TREND IN SCHOOL TEACHER TRAINING INSTITUTIONS
08/04/2021
A REVIEW OF THE LITERATURE ON METACOGNITION
08/04/2021
ENHANCING BASIC MATHEMATICAL COGNITIVE SKILLS TO PREPARE HUMAN RESOURCES FOR THE KNOWLEDGE-BASED ECONOMY IN VIETNAM
08/04/2021
TRAINING BANKING HIGH QUALITY MAN POWER AT UNIVERSITIES IN THE CONTEXT OF VIETNAM’S INTEGRATION INTO ASEAN ECONOMIC COMMUNITY
08/04/2021
EDUCATION OF LAW IN SECONDARY SCHOOLS - SEVERAL ISSUES OF CONTENTS AND METHODOLOGY
08/04/2021
ENHANCING SCIENTIFIC RESEARCH COMPETENCE FOR LECTURERS AT PEDAGOGICAL UNIVERSITIES
08/04/2021
THE NATURE OF GLOBAL CITIZENSHIP EDUCATION IN EDUCATION SYSTEM
08/04/2021
THE CURRENT STATE OF MANAGING THE DEVELOPMENT OF SCHOOL CULTURE AT TEACHER TRAINING COLLEGES IN THE RED RIVER DELTA
08/04/2021
MATHS TEACHING AND THE CONNECTION BETWEEN MATHS AND REALITY IN TEACHING
08/04/2021
ROLE OF TESTING IN CAREER COONSELING FOR UPPER SECONDARY STUDENTS
08/04/2021
SOLUTIONS FOR DEVELOPING PROFESSORS AND ASSOCIATE PROFESSORS IN VIETNAM
08/04/2021
TRAINING AND DEVELOPING INTELLECTUAL CAPACITIES THROUGH TEACHING MATHEMATICS GRADE 11 IN THE LAO PEOPLE'S DEMOCRATIC REPUBLIC
08/04/2021
INTEGRATING ENVIRONMENTAL PROTECTION EDUCATION IN SOCIO –NATURAL STUDY SUBJECT AT GARDES 1,2,3 AT PRIMARY SCHOOLS
08/04/2021
DEVELOPING TEACHING COMPETENCE FOR STUDENTS OF MATHEMATICAL PEDAGOGY
08/04/2021
APPLYING TOPSIS FUZZY METHOD IN ASSESSING QUALITY OF LECTURERS
08/04/2021
INTRODUCTION OF CIVICS SUBJECT AND WAYS OF ASSESSING STUDENT ACADEMIC PERFORMANCE IN THE UK’S CURRICULUM
08/04/2021
PEDAGOGY AND TEACHER EDUCATION SCIENCE
08/04/2021
CURRENT STATE OF PRIMARY TEACHER MANAGEMENT IN DAK NONG PROVINCE IN DEMANDS OF THE CURRENT EDUCATION RENOVATION
08/04/2021
TRAINING OF PHILOLOGICAL COMPETENCE FOR STUDENTS BY DEVELOPING QUESTIONS AND EXERCISES IN TEACHING OF TEXT READING COMPREHENSION AT UPPER SECONDARY SCHOOLS
08/04/2021