Pre-Service Teachers' Understandings and Interpretations of the Common Core State Standards for Mathematical Practice

Abstract

For at least the past 40 years, the mathematics education community has attempted to characterize important learning goals for students that are not captured completely in specifications of mathematical content objectives. Mathematical processes such as problem solving, reasoning and representation have been prominent in these attempts. The most recent characterization of these learning goals is the Common Core Standards for Mathematical Practice (SMPs). If these important learning goals for students are to be accomplished, it is imperative that teachers understand what is intended to be learned and how their instruction might be tuned to promoting these outcomes. In this dissertation study, I investigated how pre-service teachers (PSTs) interpret and understand the SMPs. In particular, 17 PSTs, enrolled or recently graduated from an undergraduate or postgraduate elementary teacher education program, completed three tasks that were intended to be approximations of key phases of actual teaching practice: planning for instruction, enacting a lesson, and assessing students. Within each task the PSTs were asked to identify (a) instances during lesson planning where students would be likely to have the opportunity to use or learn to use specific SMPs, (b) instances in a video of a lesson where students engaged in using or learning to use specific SMPs, and (c) instances in assessment items where students had an opportunity to demonstrate their proficiency in using specific SMPs. The PSTs’ designations were compared to those of the authors of the curriculum materials. PSTs were also assessed on measures of their mathematical knowledge for teaching and mathematical beliefs. Overall, PSTs and the curriculum authors had low levels of agreement in their assignment of SMPs. A close examination of PST responses suggests that they tended to use different criteria to decide when to assign some of the SMPs to mathematical tasks or lessons. For instance, PSTs tended to assign the SMP, “make sense of problems and persevere in solving them,” whenever an instructional element involved a mathematics problem. On the other hand, curriculum authors tended to assign this SMP less frequently and appeared to demand more evidence of both sense making and perseverance. There were also features of the materials that prompted PSTs to assign particular SMPs. For instance, PSTs tended to assign the SMP “construct arguments and critique the reasoning of others” whenever an assessment item asked for students to write or show their work regardless of what was actually being asked of the students. This finding suggests that the SMPs may be underspecified as learning goals that can be enacted by teachers and students at this time. The sample of PSTs in this study had high levels of mathematical knowledge for teaching and similar mathematical beliefs, and the lack of variance across the sample did not allow detection of the influence these factors might have had on PSTs’ interpretations of SMPs. Results from this dissertation study help to inform the mathematics teacher educator community of patterns in PSTs’ understandings and interpretations of mathematical practices that could help to inform the way beginning teachers are prepared. More broadly, this study suggests that the mathematics education community needs to address the lack of clarity in the SMPs as they are outlined in the Common Core State Standards so that teachers, especially beginning teachers, can consistently implement the SMPs in the everyday work of teaching.