The analytical nature of student reasoning at the beginning of secondary school: What about when solving problems aimed at developing algebraic thinking?
This article presents the results of a research study seeking to document the analytical nature of the reasoning used by students ages 12 to 14 in the first cycle of school secondary (secondary 1 and 2) in Quebec in order to solve comparison problems aimed at the development of algebraic thinking. Analysis was performed to determine the analytical nature of this reasoning and the registers of representation employed by students. This analysis highlighted three main categories of reasoning: synthetic, analytical-leaning and analytical, as well as three main categories of registers of representation: purely numerical, intermediate and algebraic. The categories and types of reasoning are presented first, followed by a comparison between secondary 1 and secondary 2 and finally a look at the importance of immersing students very early on in rich, relevant mathematical activities that contribute to developing algebraic thinking.