Using the Look-For Rubric to Examine Elementary Teachers' Instruction

• In Event: 14.043 - Roundtable Session 1
  In Roundtable Session: 14.043-14 - Analyzing the Common Core Standards for Mathematical Practice

Abstract

This presentation focuses on a methodological approach employed to examine teachers’ instructional changes, specific to Standard for Mathematical Practice (SMP) 1, making sense of problems and persevering, and SMP4, modeling with mathematics (NGAC & CCSSO, 2010). SMP1 and SMP4 have clear connections (Kanold & Larson, 2012). Problems are rich tasks such that it is (a) unclear whether a solution exists, (b) uncertain how to reach the solution, and (c) unknown to the problem solver how many solution pathways are viable (Schoenfeld, 2011). Tasks promoting modeling with mathematics include these features and add aspects of real-life to the task (Fennell, Kobett, & Wray, 2013). A posteriori coding (e.g, grounded theory, Charmaz, 2006) to analyze teachers’ instruction for elements of SMP1 and SMP4 appeared daunting. Thus, we employed a look-for rubric (Fennell et al., 2013) that enabled us to focus our qualitative analysis using an a priori approach.

Method

Teachers participated in a yearlong PD program that had multiple aims including making sense of the SMPs and implementing classroom-based tasks addressing the Standards for Mathematics Content. We hypothesized that teachers would show growth in their promotion of SMPs 1 and 4 after the PD.

Table 1. Participants’ demographic information.

Six K-5 teachers were randomly selected from the greater participant pool for this study, one from each grade level (Table 1). Teachers videotaped one day of instruction pre- and post-PD. Each video was analyzed in the following fashion. First, a team of three mathematics educators watched the entire video. Next, the team reviewed it again using the rubric. Teachers’ evidence of promoting these SMPs was tallied and notes were made for further reflection. The team shared findings with one another and discussed any coding discrepancies. Differences were resolved through discussions or re-watching the video.

Results and Significance

Results supported our hypothesis: teachers showed growth in SMPs 1 and 4 (Figure 1). The look-for rubric framed our analysis in a consistent and coherent fashion (Nilson & Ryve, 2010) enabling us to identify instructional moves related to the SMPs. This rubric also presented challenges. It was not exhaustive in observable behaviors or necessarily clear about terminology, which led to many discussions. One discussion explored how to determine whether and to what degree a task “encourage(s) them [students] to persevere” (Fennell et al., 2013, p. 1). Judging encouragement for perseverance proved challenging. Another discussion focused on what constitutes a “mathematical model appropriate for the focus of the lesson”, a descriptor for SMP4 in the rubric, instead of a mathematical representation appropriate for the focus of the lesson.

Figure 1. Overall findings of teachers’ promotion of SMPs 1 and 4.

Considering these challenges, the look-for rubric was a useful qualitative analytic tool for exploring K-5 teachers’ promotion of the SMPs. We continue to employ it and support its refinement in two ways: (1) refinement as an analytical tool for researchers, and (2) development of resources to help other researchers use this tool, such as definitions of terms and examples of descriptors seen in video analysis.

Authors

• Jonathan David Bostic, Bowling Green State University

• Gabriel Matney, Bowling Green State University