Updating Perspectives on Lesson Structure in U.S. Classrooms

• In Event: 32.073 - Studying the Alignment Among the Common Core State Standards for Mathematics, Teachers' Perceptions, Lesson Design, and the Enacted Curriculum

Abstract

Objectives:
We explore at the structure of 54 CCSSM-aligned lessons, comparing them to prior lesson scripts documented in the U.S. We explored patterns in lesson structure across different types of curriculum materials to better understand how cultural teaching scripts are situated in an era of standards and in contexts where the NSF-funded curricula were in use.

Perspectives:
Mathematics teaching in the standards era offers the potential to shift from the cultural script in US middle school classrooms found by Stigler and Hiebert (1999): a) reviewing previous material; b) demonstrating how to solve problems for the day; c) practicing; and d) correcting seatwork and assigning homework. The widespread use of NSF-funded curricula at the middle school level and the adoption of the CCSSM offer the possibility of other teaching scripts. The CCSSM promised rigorous mathematics instruction that was lacking in previous US mathematics standards (CCSSI, 2010; Porter et al, 2011).

Methods:
We video-recorded the lessons of 54 teachers in seven states, involving 11 different curriculum programs. We transcribed the whole class portions of the lessons and group work as the audio quality permitted and parsed the transcripts of each lesson into roughly two-to-four minute chunks of lesson segments delineated by activity types. We coded and analyzed each lesson segment with six dimensions of activity types: timing in relation to students’ independent work, the focus of the activity, the function of the activity, teachers’ role and students’ role in the activity. We then looked at sequences of these activity types to identify patterns in the lesson structure.

Results:
We observed a number of lesson structures, some associated with the lesson script identified by Stigler and Hiebert (1999) and some that substantially diverged from that script. The two lesson structures most closely aligned with the traditional script were Introduction – Teacher led practice, which focused exclusively on teacher explanation, modeling, and guided practice. The second traditional structure was Demonstrating – Independent seatwork – Correcting seatwork. A second type of lesson structure emerged from our data, a lesson structure associated with TD materials. The general lesson structure pattern followed a sequence of Introducing students to the task and mathematics – Student group exploration on a problem or related set of problems set in context – Whole class discussion of student solutions. A notable variation within that pattern demonstrated a difference between CMP3 (Lappan et al., 2014) and CPM (Kysh et al., 2013). The CPM lessons had a fourth activity at the end of the sequence, which was Applying concepts to new problems, which was related to the ways the lessons in CPM were organized.

Significance:
Two findings stand out. First, the use of DM materials was strongly associated with the traditional lesson script found by Stigler and Hiebert (1999), despite the implementation of the CCSSM, with its intended rigor. Second, a different lesson script emerged in the classrooms where TD materials were in use. This finding suggests that curriculum materials written from principles that differ substantively from those in conventional materials have the potential to disrupt cultural teaching scripts.

Authors

• Demeke Gesesse Yeneayhu, University of Rochester

• Jeffrey M. Choppin, University of Rochester