Results From Lesson Observations Using a Common Core State Standards for Mathematics–Aligned Observation Tool

• In Event: 49.078 - Exploring Middle School Teachers' Use of Curriculum Materials in the Context of the Common Core

Abstract

Purpose
This paper describes analysis of classroom observations using a tool adapted to capture instruction emphasized in the CCSSM, especially the mathematical practices (MPs).

Methods
To examine teachers’ enactments of CCSSM, we used the Observations Scale developed for the University of Wisconsin-Madison Longitudinal Study of Mathematics and then adapted by the Middle School Mathematics Study at the University of Missouri. The first part of the observation tool documented the structure and mathematical content of the lesson, instructional materials, and the extent to which these materials influenced classroom lesson enactments. The second part was centered on classroom events: This part will be the focus of this proposal.
Classroom events were analyzed using a total of fifteen specific items clustered in four major themes:
1. Instructional focus based on a continuum ranging from procedural to conceptual.
2. Forms of connections made during the lesson.
3. Presence and influence of student explanations during classroom instructional events.
4. Mathematical practices evident in classroom events.

We observed 63 middle school teachers’ lessons with the purpose of understanding what materials teachers are using and how they are enacting lessons with a focus on CCSSM’s Mathematical Practices. Our analysis involved parsing the transcripts of video-recorded lessons into topically related sets (TRSs) (Mehan, 1979) and coding the TRSs according to the fifteen specific items comprising the themes.

Results
We found that the majority of the lessons (86.7%) focused on procedures, such as explaining computational steps used to solve a routine mathematical problem. This approach is typical of historical practices in US middle schools (Stigler & Hiebert, 1999). The conceptually-oriented teachers tended to use CMP materials and the procedurally-oriented teachers tended to use materials such as DIGITS, Glencoe and Holt. We conducted further analysis of classrooms where we perceived the focus to be more conceptual and aligned with the goals of the CCSSM (e.g., the classrooms in which the CMP materials were used) and found that the organization, interaction, and questioning patterns in the lesson facilitated greater integration of the Mathematical Practices. Students in a conceptually-oriented classroom were consistently asked to justify the reasonableness of their solution strategies, whereas procedurally-oriented teachers focused on the required steps to solve a problem for a correct answer. Teachers also made explicit the connections between mathematical concepts and provided students with cues which underscored the connections.

 
Conclusion
These results suggest that the design of curriculum materials is associated with teachers’ orientations toward and enactment of the CCSSM, particularly the emphasis on the mathematical practices (MPs). The teachers using the CMP materials had more robust views and enactments of the MPs, in contrast to the non-CMP materials, for whom the MPs were treated in more superficial and isolated ways.

Authors

• Demeke Yeneayhu, University of Rochester

• Cathleen Daniels Cerosaletti, University of Rochester