Mathematics education in K-12 schools has focused increasingly on the development of standards for students' learning of mathematics for the past three decades. The Common Core State Standards for Mathematics (CCSSM) define a level of quality regarding what K-12 students should know and do in mathematics. In addition to Standards for Mathematical Content, the CCSSM explicitly delineate the Standards for Mathematical Practice (SMP) that mathematics teachers should nurture in all students (NGA & CCSSO, 2010a). In the midst of widespread recognition of and attention to the CCSSM, however, questions still exist relative to teachers' conceptions of the SMP.

Pennsylvania is one of the states that adopted the CCSSM and crafted its own versions of the standards (The PA Core State Standards). Pennsylvania teachers are expected to have a clear understanding of the PA Core Standards. It is timely and appropriate to study Pennsylvania teachers’ conceptions, as the Standards have been adopted and implemented for several years since the revision and enactment of the PA Core Standards (2014). This study examined how eight western Pennsylvania elementary school teachers displayed their understandings about the SMP.

To this end, I conducted an in-depth interview with each teacher. The in-depth interviews featured the degree of alignment of the teachers' conceptions of the eight SMPs. The participating teachers exhibited varying degrees of conceptions aligned with the SMP. Of particular interest, the teachers' interpretations of SMP 4 ("Model with mathematics") was markedly different from the descriptions provided by the Standard’s authors. The findings have implications for school teachers, mathematics educators, professional development providers, and standard writers.