Keywords

Introduction

In Schoenfeld’s concluding chapter of the seminal book by Sherin, Jacobs and Philipp (2011), Mathematics Teacher Noticing: Seeing Through Teachers’ Eyes, he wrote that “noticing matters” (2011, p. 223). The variety of scholarship contained in this volume suggests that teacher noticing continues to matter and is ascending in prominence on the landscape of educational research. As a means to coherently explore the directions of teacher noticing inquiries, the editors have organized this volume into broad thematic sections (e.g., Noticing in Various Grade Bands and Contexts, Exploring Teacher Noticing and Equitable Teaching, etc.). These sections form a useful structure for navigating current scholarship in this area, and provide the occasion to revisit Schoenfeld’s titular question, “Now what?” (p. 223). Toward this end, I will examine some lingering issues and emerging challenges. I will conclude with an unanswered question regarding the practical articulation of teacher noticing.

The Fundamental Nature of Teacher Noticing

Looking across the literature, Sherin et al. (2011) characterized teacher noticing as consisting of two primary processes, “attending to particular events in an instructional setting” and “making sense of events in an instructional setting” (p. 5). These two processes correspond with the interrelated, component skills of “attending,” and “interpreting” put forth by Jacobs, Lamb, and Philipp (2010); however, Jacobs et al. (2010), identified a third component skill, deciding, which described teachers’ responses that flowed from interpretations (derived from events and behaviors to which teachers had attended). As one might expect, there is much consensus regarding the enactment of teacher noticing across the chapters in this volume. Whether noticing is described as identifying “what is noteworthy about a particular situation … [and] making connections between specific events and broader principles of teaching and learning” (van Es & Sherin, 2002, pp. 573–574) or a fluid enactment of attending, interpreting, and deciding (Jacobs et al., 2010), the presented research reflects a relatively shared understanding of what it means to notice. However, there still seems to be some differences in perspectives regarding how one should notice. Specifically, is noticing more appropriately focused on capturing and interpreting as much of the instructional landscape as possible including individual movements and postures? Or, should noticing processes be used as a filter to identify only the most impactful moments of a particular block of instruction? Indeed, one finds each of these perspectives in this volume. The former perspective is typified by Wells’ chapter on noticing of gesture as well as prior research by Schack et al. (2013). The latter perspective is represented by the Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (MOST) analytic framework described in multiple chapters (see Stockero, Leatham, Van Zoest, & Peterson; Teuscher, Leatham, & Peterson; and Stockero & Rupnow). In her commentary for this volume, Sherin, describes teacher noticing as a “construct under development” and examines these differing perspectives regarding enactment.

Digging even more deeply, the research community continues to grapple with the essence of noticing itself and the manner in which such noticing is situated within the social landscape of teaching and learning. Specifically, is teacher noticing a practice? Practice within complex environments (such as classrooms) is described as involving “the orchestration of understanding, skill, relationship, and identity to accomplish particular activities with others … [and] practice can be understood in terms of its goals, its activities, and its historical tradition” (Grossman et al., 2009, p. 2059). Teacher noticing, for some, would seem to exist as a socially situated practice. Schoenfeld (2011) argued that, “teachers’ noticing is intimately tied to their orientations (including beliefs) and resources (including knowledge)” (p. 231). Similarly, when describing professional vision, Goodwin (1994) remarked, “the ability to see a meaningful event is not a transparent, psychological process but instead a socially situated activity accomplished through the deployment of a range of historically constituted discursive practices” (p. 606). In this volume, chapters from the section on equitable teaching (see Baldinger; Kalinec-Craig; van Es, Hand, & Mercado) characterize or operationalize noticing in such socially situated terms. Conversely, Spitzer and Phelps, in their examination of noticing in the context of learning goals, define such noticing as a “discrete teachable skill” (p. 304) suggesting a construct organized around learning and carrying out a specific task. Similarly, Sturmer and Seidel’s development of a standardized measure to assess teachers’ professional vision implies a perspective oriented more toward skill than a social practice while other chapters appear more agnostic on this front. Given these dissimilarities regarding the fundamental nature of teacher noticing, perhaps some further consideration is in order. Certainly, the manner in which noticing is theoretically constructed by the research community will necessarily influence how it is studied and enacted.

The Relationship Between Teacher Noticing Components

Returning to the notion of consensus regarding the enactment of teacher noticing, all of the chapters espouse a component perspective. That is, noticing is typically described as consisting of multiple processes or skills (e.g., attending, identifying, reasoning, interpreting, connecting, deciding, responding, etc.). Jacobs et al. (2010) referred to such components (i.e., attending, interpreting, and deciding) as “interrelated skills” that must be executed in “an integrated way” (p. 169, 192); however, some researchers tend to isolate particular components for examination. For example, Males focused primarily on the component process of attending in her examination of middle and secondary teachers’ noticing in video-based contexts. Similarly, Amador, Carter, Hudson, and Galindo also concentrated their analysis on specific components (attending, interpreting, and deciding) and as they tracked changes in component performance over time.

Conversely, others have adopted a more integrated view of noticing components. To evaluate teacher noticing in the context of equality-oriented tasks, van den Kieboom, Magiera, and Moyer developed a rubric that synthesized the components of attending and interpreting. This perspective furthers a central thesis put forth by Castro-Superfine, Fisher, and Bragelman—that the component processes of attending and interpreting are deeply and reflexively related. Spitzer and Phelps also echoed this notion of attending and interpreting being deeply related. Additionally, in their chapter on influencing preservice teacher noticing, Teuscher, Leatham, and Peterson state that noticing components are nested and should be considered in concert. Moreover, several chapters seem to functionally blur the component processes of noticing in their analysis and/or reporting of results (see chapters by Lee & Choy, Baldinger, Kalinec-Craig, for examples). In such instances, the researchers describe noticing in component terms; however, these components tend to recede or disappear as one delves more deeply into the study itself. Sherin, in her commentary for this volume, succinctly describes such competing perspectives and argues that, “there can be features of our models that occur together while still being treated as separate elements”; however, she acknowledges that empirical study could, possibly lead to theoretically construed concomitant noticing components (p. 404).

From my vantage, advancing our understanding of the relationship among the component processes of teacher noticing is key area of growth for the field. Can we isolate and examine individual components? Or, do the components of teacher noticing only have meaning when considered in concert with one another? As with the theoretical nature of teacher noticing, the manner in which the research community conceives the relationship between noticing components will necessarily influence the very nature of teacher noticing.

The Measurement of Teacher Noticing

To some extent, each of the chapters in this volume focused on the measurement or evaluation of noticing performance. Nickerson, Lamb, and LaRochelle, in their examination of noticing measurement in secondary contexts, identify three primary means through which noticing data has been collected: (1) “observations of classroom practices and inferring” what was noticed, (2) “retrospective reflections on teachers’ practice,” and (3) “responses to items in relation to video or student work from others’ practices” (p. 383). Building on these varied data collection methods, Stockero and Rupnow describe three approaches to the measurement of teacher noticing, (1) “measurement using categorization of instances”, (2) “measurement using point or ranking systems,” and (3) “measurement in relation to a standard” (pp. 283–284). While these organizational structures are quite useful for considering similarities and differences in measurement perspectives among studies, several tensions still exist within this aspect of teacher noticing inquiry.

First, there remains a vexing problem of generalizing the specific. Measures of teacher noticing are increasingly useful to the extent that they may be enacted across differing contexts and projects. Thus, the creation of more generalized measures of noticing performance would be a positive development. However, such generalized measures appear to be in some fundamental conflict with the highly situated nature of noticing enactment. That is, teacher noticing is, by its very nature, inseparable from a particular context, community, and time. This connection to context is highlighted in the chapter by Nickerson et al. as they entail measurement challenges that are specific to secondary settings, and this uniqueness of the secondary context is echoed in the chapter by Krupa, Huey, Lesseig, Casey, and Monson. Nevertheless, researchers have attempted to negotiate the challenge of generalizing the specific in various ways. Notable among these attempts is the MOST analytic framework described in several chapters. This framework provides researchers with a general perspective for considering the extent to which individuals identify and capitalize upon key mathematical opportunities. Like nearly all of the other studies detailed in this book, though, the evaluation of noticing performance rests upon some manner of inductive analyses (e.g., coding, thematic organization, etc.). Perhaps the only exception is Sturmer and Seidel’s standardized approach to measuring professional vision; however, participation in this measure is distant, to some extent, from the enactment of teacher noticing in the mathematics classroom. This is not to suggest that Sturmer and Seidel’s approach is not a viable proxy for the measurement of noticing; rather, simply that responding to video-anchored Likert-type prompts is dissimilar from enacting the practice of noticing within a classroom. Yet, as a measurement tool in research, the standardized approach may yield valuable understanding of the construct of professional vision.

This brings me to another measurement tension—the use of proximal instrumentation for the study of teacher noticing. Returning to the three methods for data collection put forth by Nickerson et al., each method is distinct from actual teacher noticing. Likely the closest in proximity, inferring noticing from observed instruction, relies on post hoc researcher interpretations of an instructional act, part of which (interpretation, reasoning, etc.) is inherently veiled to everyone but the actual teacher. Many other researchers rely on video-recordings to measure or evaluate noticing performances, which constitutes, arguably, an even more remote approach. In some cases, teachers view videos of their own practice, while other studies task participants with noticing aspects of another teacher. While both forms of video use are contextually removed from in-the-moment teacher noticing, this latter use of video gives rise to important questions regarding its proximal viability. For example, if teacher noticing is characterized as a socially situated practice organized around not just knowledge and skill, but also goals and identity, to what extent can teachers assume the role of another? Can teachers “step into the video” such that their interpretations and decisions reflect what would actually transpire in their own teaching? Can teachers ably superimpose their own knowledge, goals, and identity upon a video-recorded instance of strangers from another time and place? My own research reflects a belief that such proximal measures can be valuable indicators of noticing practice; however, investigations focused on the distance between measure and practice would be quite useful.

Development of Teacher Noticing

Schoenfeld (2011) and van Es (2011) explored possible developmental progressions for teacher noticing, and their work has been extended in this volume by several authors (see chapters by Beattie and Lee & Choy for examples). Moreover, new findings by other authors may further illuminate such developmental pathways. For example, Males noted a shift from teacher-focused to student-focused comments in her study of middle and secondary teachers’ noticing. Such empirical findings could be used to increase the authenticity of noticing developmental progressions. One caveat drawn from the chapter by Krupa et al., though, is that contextual affordances and constraints likely influence how teacher noticing is practiced which, in turn, would affect one’s progression towards more sophisticated enactment. One such developmental context likely worthy of examination is the asynchronous online or technology-mediated learning environment. Typically (but not always), researchers, teacher educators, and professional developers build and implement experiences organized around face-to-face interactions. Given the directions of many post-secondary institutions (and professional development designers), it may be wise to further explore noticing development in technology-centered contexts. Such explorations may yield potential pedagogical possibilities regarding the practice of noticing. It would seem that most researchers, including myself, primarily rely upon various types of video analyses, interviews, and examination of artifacts within structured and supportive settings often to positive effect. Nevertheless, studies of teacher noticing in asynchronous technological contexts could result in the creation of new pedagogical designs for the development of this practice.

An Unanswered Question—What Do Teachers Think About All of This?

Schoenfeld (2011) concluded that teachers are able to develop noticing capacities, and the research in this volume further strengthens that conclusion. Many of the presented inquiries demonstrate a substantive positive change in some aspect of participants’ noticing abilities, which, in turn, leads to more responsive instruction. Thus, mathematics education professionals seem primed to broaden the impact of teacher noticing among practitioners. In addition to structured contexts for development (e.g., mathematics methods classrooms, professional learning events, etc.), practitioner articles on this topic have been published for both elementary (Thomas et al., 2014) and middle grades teachers (Thomas et al., 2015). Moreover, at least one statewide mathematics professional develop center has incorporated teacher noticing into its professional learning frameworks (KCM, 2015). Given this deliberate and appropriate linking of research to practice, I find it quite interesting that limited inquiry has been conducted regarding practitioners’ enactment and perceptions of the practice of noticing. Certainly, we have learned a great deal about how teachers, in various contexts, come to develop noticing capacities; however, we seem to know very little about how the structures and processes of schools and school mathematics (Steffe & Wiegal, 1992) influence how teacher noticing is perceived and implemented by practitioners. On this front, an introductory paragraph from the chapter by Nickerson et al. sets the stage quite nicely for the consideration of some key questions.

Imagine a teacher in a secondary mathematics classroom circulating while her 35 students work in small groups to solve an algebraic-generalization task. Perhaps she makes note of whether all students in a group are engaged and monitors students’ affect. She may wish that a particular student’s reasoning was visible or more understandable. She may or may not be looking for and may or may not be able to describe connections among the diverse mathematical responses. She likely observes many approaches taken to the task and critiques their sophistication, as well as their alignment with expected mathematical goals and the normative language, notation, and representations of mathematics. She wonders what statements, representations, or questions would support her students’ thinking (Nickerson et al., p. 382).

With this in mind, do teachers perceive trajectory-oriented noticing focused on tailoring responses to individual students (Thomas et al., 2014) to be a viable practice in their classrooms? Might special education teachers and intervention specialists feel differently regarding such viability? Per suggestions by Thomas et al. (2015), do middle grades teachers feel comfortable interpreting mathematics and implementing teaching strategies aimed at learning goals well outside of their grade level—and would their school principal support such actions? Facing contextual or logistical constraints, how might teachers and other educational professionals adapt teacher noticing for their particular classroom? How do they claim ownership of this practice? The more I interact with teachers and witness the evolving structures of the contemporary classroom and school, the more convinced I become that exploration in this area is worthy and perhaps even necessary to facilitate stronger connections between this important research and our practitioner communities.

Concluding Remarks

As a researcher thoroughly enamored with teacher noticing, I find it thrilling to see a rising interest in this topic among members of the scholarly community. I feel there is something quite intuitive about the component structure (e.g., attending, interpreting, deciding) and find the inherent responsivity of teacher noticing desirable in a very fundamental way. My goal with this brief chapter is not to suggest that researchers must converge on a particular understanding of noticing, its components, or how noticing should be measured or developed among teachers. Rather, we in the research community might explore the impact of different ways that noticing is characterized or operationalized. For example, what are the differences (or similarities) in teachers’ developmental pathways when teacher noticing is treated as a socially situated practice or, alternately, an assemblage of skills? Indeed, my hope is that we might capitalize on this growing concentration of scholarly energy to further our understanding of teacher noticing on a variety of fronts. I look forward to learning more from my fellow travelers as we continue to cultivate this exciting research field.