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 ineffective 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 has 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.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
