The object of our research work is the study of duality in linear algebra. An institutional point of view is adopted. The anthropological theory of didactics has been chosen as main theoretical framework. It allows us to propose a description of the duality sector in the linear algebra domain, by decomposing it into five themes. An analysis of duality as a knowledge to be taught is realized at various levels, with among others the introduction and the definition of five purpose tools for this sector. Drawing on this presentation, a survey concerning duality was elaborated and submitted to students enrolled in first-year university mathematics or physics programs at the University of Namur (Belgium). We present the results by categorizing the difficulties met by the students. We show how we can speak of transition about duality, and how the identified difficulties can be interpreted as consequences of a change of institutional didactical contract. Finally, we formulate propositions for the introduction of duality in linear algebra. The statement of various perspectives concludes our work.
|Date of Award||30 Sep 2010|
|Supervisor||Suzanne THIRY (Supervisor), Valerie HENRY (President), Marc ROMAINVILLE (Jury), Ghislaine GUEUDET (Co-Supervisor), Jean-Luc DORIER (Jury) & Carl WINSLOW (Jury)|