Learning Through Teaching: An Exploration of Teachers' Use of Feedback in Support of Responsive Teaching in Mathematics

• In Event: Promising Scholarship in Education: Dissertation Fellows and Their Research

Abstract

Purpose of study
Although large numbers of educational reforms and innovations have been developed, there has been relatively little change in the instruction that happens in classrooms (Rowan, 2002). This phenomena has led to reframing educational change as a process of implementation, not just the development and testing of reforms (Penuel, Fishman, Cheng, & Sabelli, 2011). A key point of leverage in the implementation of reforms and innovations is the process of teacher change, or how teachers change what they do in the classroom. Using the Measures of Effective Teaching (MET) Longitudinal Dataset, I study growth towards responsive teaching, or teaching that is attentive and responsive to the substance of student thinking, by documenting common growth trajectories for teachers adopting responsive teaching practices. The primary goal of this work is to provide stronger generalizable evidence for the different trajectories of change toward responsive teaching practices in middle school mathematics, and a more detailed understanding of what responsive teaching looks like in those classrooms. Therefore, this study aims to answer the following research questions:
1. How can responsive teaching be characterized by teachers’ engagement with student mathematical thinking?
2. What are the different trajectories of development of teachers’ classroom practices toward responsive teaching in mathematics?

Study design and methods
This project relies on in-depth qualitative analysis of classroom video data collected over the two years with grades 6-9 math teachers in the MET study. The work will take place in three main phases: (1) identifying the subset of teachers developing or with stable responsive teaching practices, (2) in-depth analysis of teachers’ engagement with student mathematical thinking, and (3) characterizing trajectories of growth toward responsive teaching.

To identify the subsample of teachers relevant to this study, the final video in year 2 for each teacher is rated in terms of the ways that students are engaged in the lesson and how the teacher engages with students’ thinking. Two-minute segments are rated in each of the following categories for different teacher actions: (a) Making Space for Student Thinking (Borko, Jacobs, Eiteljorg, & Pittman, 2008; van Es & Sherin, 2010), (b) Probing Student Thinking (van Es & Sherin, 2010), and (c) Advancing Student Thinking (Hammer, Goldberg, & Fargason, 2012; Pierson, 2008). Teachers that engage with student thinking mainly through finding student errors and correcting them are eliminated from further analysis as these teachers would have little room for growth during the study. The first video of the remaining teachers is characterized in the same way and compared with the final video to look for changes. Teachers that show differences will make up the developing expert subsample. Teachers with a sustained focus on students’ mathematical reasoning at both time points will make up the accomplished expert subsample (i.e. responsive teachers).

In the second phase of analysis, all of the videos from the developing and accomplished expert teachers will be coded in terms of the way that teachers engage with student thinking. Each classroom lesson will be transcribed, and units of teacher actions (with associated antecedent and resultant student thinking) will be identified. Each teacher action will be characterized as one of the three teacher actions presented earlier, along with one additional category: Interpreting or synthesizing student thinking (Colestock & Sherin, 2009; Levin, Hammer, & Coffey, 2009). Each instance is then coded for the focus of engagement, including: (1) Evaluation-focused (Sherin & van Es, 2009), (2) Error-focused (Pierson, 2008), (3) Conception-focused (Pierson, 2008), (4) Strategy-focused (Fennema et al., 1996; Smith & Stein, 2011), (5) Inquiry-focused (Sherin & van Es, 2009), and (6) Reasoning-focused (Hammer, Elby, Scherr, & Redish, 2005; Levin, Grant, & Hammer, 2012). From this coding, each teacher’s trajectory towards, or stability of, responsive teaching practices will be characterized based on patterns observed in the coded data.

Findings and Policy Implications
Preliminary findings indicate that teachers with stable responsive teaching practices rely heavily on making space for and drawing out student thinking in comparison to advancing student thinking. Additionally, these teachers’ actions show a variety of different focuses encompassing the entire analysis framework. In sequences of interactions with students, the focus often develops progressively to more substantive focuses. These findings highlight how teachers using responsive teaching practices are not exclusively focused on student mathematical reasoning, but may instead change their focus strategically to support student learning. Additionally, this suggests that developing responsive teaching practices may be explained by adopting a wider variety of focuses rather than abandoning of some focuses and adopting others.

Author

• Elizabeth B. Dyer, Northwestern University