VIETNAM JOURNAL OF EDUCATIONAL SCIENCES

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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.
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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.

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[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.

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[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.

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Journal: 
No. 139, April 2017

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