Typology of incoherence due to the didactic transposition in Quebec textbooks introducing abstract algebra
Résumé
As shown in the Quebec Ministry of Education curriculum, the first notions of abstract algebra are presented in the linear algebra class, at CEGEP level (students of 17 to 19 years old). After a census of the 13 French CEGEP of Montreal region, which offer pre-university preparation for mathematics, we found out that four textbooks (regularly re-edited) are used by the majority of teachers as guidance for this class (Ouellet, 2002; Amyotte, 2009; Charron & Parent, 2005; Papillon, 1993, 2012). Unlike high schools, CEGEP are free to choose the didactic material they propose to their students; textbooks do not have to be approved by a Ministerial commission. However, for the sake of consistency, editors try to respect ministerial guidance and organise the textbooks following objectives given by the ministry. Notably, amongst those programme objectives (MELS, 2010, p. 5), we found that the most relevant to the class of linear algebra students were:
— identify a certain amount of ideas in link with the subject to compare, classify and evaluate them;
— link pertinent ideas in a logical order;
— building a coherent argument / reasoning / proof (loose translation).
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