Reasoning and proving in Algebra. Examples from 8th grade school mathematics textbooks in Italy

Abstract

Some research studies concerning the didactics of Algebra discuss how learning to solve problems using symbolic algebraic language can be hard for students (Bohlmann et al., 2014; Palm, 2009). Students, in fact, have often difficulty to learn the ways in which the sym- bols should be manipulated to argue or to prove an assertion in order to reach a problem solu- tions. Although many studies conducted by mathematics educators discussed important contri- butions to this subject (e.g. Arzarello, Robutti & Bazzini, 2005; Boero, 2001; Carraher, Schliemann, Brizuela & Earnest, 2006; Lins & Kaput, 2004; Ursini & Trigueros, 2001), not many analysis were conducted on the role of the School textbook in this complex teaching /learning context. The paper, focusing on this aspect, discuses some preliminary MaTeK (En- hancement of Research Excellence in Mathematics Teacher Knowledge) Horizon 2020 project results, related to the analysis of some algebraic reasoning and proving tasks, discussed in 8th grade school mathematics textbooks in Italy.