Irish Teachers’ Perceptions of Reasoning-and-Proving Amidst a National Educational Reform

The syllabi driving the secondary mathematics education reform in Ireland expect students to engage in two components of reasoning-and-proving (RP) (Stylianides in For Learn Math 28:9–16, 2008): making mathematical generalizations (pattern identification and conjecturing) and providing support to mathematical claims (providing a proof/non-proof argument). This study examines the perceptions of pattern identification, conjecturing, and proof by 22 Irish teachers with varying levels of teaching experience via semi-structured interviews. These teachers perceived pattern identification and conjecturing as disconnected from proof construction. Indeed, teachers struggled to define conjecturing and proof. There also appeared to be a bifurcation in students’ classroom experiences with RP processes. Teachers stated that the experiences with proof of students with perceived lower ability levels ended at pattern identification while higher-level students rarely engaged in pattern identification and focused on memorizing proofs due to the influence of high stakes assessments. The implications of these results are discussed.