Jon D. Davis

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Related Assessment and Teacher Evaluation Systems

In this study, U.S. middle school teachers’ perceptions of Common Core State Standards for Mathematics (CCSSM), CCSSM-related assessments, teacher evaluation processes, and resources for implementing CCSSM were investigated. Using a mixed methods design, a national sample of 366 teachers was surveyed, and 24 teachers were interviewed. Findings indicated that teachers viewed CCSSM as including new content for their grade level. Teachers also reported using multiple curriculum resources to align with CCSSM and indicated that new assessments would serve as a proxy for CCSSM. Implications for rapidly changing policy, curriculum, assessment, instruction, and professional development related to CCSSM are discussed.

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.