Scientific Article
previous document  unige:16639  next document
add to browser collection
Title

On the teaching of the theory of vector spaces in first year of French science university

Author
Published in EduMath. 1998, vol. 6, p. 38-48
Abstract In the French tradition of Bourbaki, the theory of vector spaces is usually presented in a very formal setting, which causes severe difficulties to many students. The aim of this paper is to analyze the underlying reasons of these difficulties and to suggest some ways to make the first teaching of the theory of vector spaces less inefficient for many students. We do not reject the necessity for formalism. On the contrary, on the basis of a historical analysis we can explain the specific meaning it bas in the theory. From this mathematical analysis with a historical perspective, we analyze the teaching and the apprehension of vector space theory in a new approach. For instance, we will show that mistakes made by many students can be interpreted as a result of a lack of connection between the new formal concepts and their conceptions previously acquired in more restricted, but more intuitively based areas. Our conclusions will not plead for avoiding formalism but for a better positioning of the formal concepts with regard to previous knowledge of the students as well as special care to be given in making the role and the meaning of formalism in linear algebra explicit to the students.
Keywords Mathematics education researchhistory of mathematicslinear algebralinear independencerankEuler
Full text
Article (Published version) (2.8 MB) - public document Free access
Other version: http://www.hkame.org.hk
Citation
(ISO format)
DORIER, Jean-Luc. On the teaching of the theory of vector spaces in first year of French science university. In: EduMath, 1998, vol. 6, p. 38-48. https://archive-ouverte.unige.ch/unige:16639

201 hits

64 downloads

Update

Deposited on : 2011-07-15

Export document
Format :
Citation style :