Teachers' Understanding of Learning Trajectories for Formative Assessment

• In Event: 31.075 - Promises and Challenges in Implementing Research-Based Formative Assessment in a Large Urban District: Mixed Methods Findings

Abstract

Purpose
This paper examines teachers’ understandings of learning trajectories and formative assessment through the lens of how teachers sorted, interpreted, and responded to their own student work after being trained to use a learning trajectory for formative assessment. Through specific examples we show how teachers attended to different aspects of the work as well as how their interpretations reveal distinct goals and underlying views of learning.

Perspectives
Recent research on mathematics teaching promotes a view of ambitious instruction that calls for teachers to regularly make sense of student thinking (Lampert et al, 2010; Sztajn et al, 2012). Formative assessment, one of the more promising educational interventions (Black & Wiliam, 1998), involves continually eliciting and interpreting evidence of student thinking in order to improve teaching and learning. While teacher noticing of student thinking has been a focus of much recent research on mathematics instruction (e.g., Schack, Fisher & Wilhelm, 2017), less attention has been paid to how teachers interpret and respond to student work. Existing studies point to a tendency to focus on what students do rather than what they understand (Authors 2013; 2015). This paper adds to this knowledge base to further explore how underlying views of learning interact with sensemaking of student work.

Methods
This study is part of a larger qualitative inquiry that explored how teachers took up and made sense of learning trajectory-oriented formative assessment in a range of school contexts. Data were collected from a purposeful sample of 32 grade K-5 teachers from 9 schools through a series of 3 semi-structured interviews. Before the second interview, teachers were asked to administer a formative assessment item. They were then asked to (1) explain how they sorted their student work (2) analyze representative examples and (3) formulate instructional responses for each example as well as for the class as a whole.

Analysis began by producing an analytical memo to document each teacher’s categorization of student work and then looking across these memos to develop initial categories of sorting strategies, analysis of student work, and instructional responses. We then used a constant comparative approach to apply and continually refine these categories. All interviews were double coded, and any disagreements were reconciled through discussion.

Results and Significance
The professional development focused on using a learning trajectory to sort, interpret and respond to student work in relation to a progression of understanding; however, when looking at and responding to their own student work, teachers exhibited a range of strategies that reflected different purposes and learning orientations (see Figure 1). Some teachers continued to focus on correct answers or the on the presence or absence of specific features in student solutions. Other teachers conceptualized student performance in a progression—i.e., how close students were to solving the problem successfully. In the paper we illustrate how these strategies reflect different underlying notions of how math is learned. Our results suggest that teachers take up the learning trajectory differently, based on views of learning that may be reinforced by other commonly accepted practices where learning is conceptualized as an outcome.

Authors

• Caroline Brayer Ebby, University of Pennsylvania

• Janine Remillard, University of Pennsylvania

• Jordan D'Olier, University of Pennsylvania

• Nicole Fletcher, Teachers College, Columbia University