Abstract
While recent research demonstrates that teacher noticing is a core construct of teaching, it also raises new questions about this construct. Here, we offer an expanded framework that addresses three key questions. Specifically, we suggest that attending involves not only selecting particular features of instruction to observe, but also disregarding aspects of classroom interactions that are less consequential. In addition, we propose that a stance of inquiry about observed phenomena is central to drawing inferences about observed phenomena. Finally, we extend the boundaries of teacher noticing to include shaping, the act of creating interactions that provide increased opportunities to attend to and interpret noteworthy mathematical interactions. In other words, teachers are not simply passive bystanders in the act of noticing, rather they shape interactions to gain access to additional information to allow for further observation and interpretation of student thinking.
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1 Introduction
What is teacher noticing? And how does it develop? For the past 20 years, we have been both consumers and producers of research on teacher noticing. Like others, we have argued that teacher noticing is a key component of teaching expertise—that what and how teachers notice matters for student learning and for students’ experiences in the classroom. At the same time, it has become clear that teacher noticing has taken on different meanings and as a result, both the focus of and approaches to research on teacher noticing differ. We do not believe these differences are inherently problematic. In contrast, the breadth of research on teacher noticing assures us that the construct has great value for understanding the nature of teaching. Nevertheless, current research has raised several questions about the ways we have, up until now, conceptualized teacher noticing.
The construct of teacher noticing is particularly relevant in mathematics education. Over two decades ago, research documented the influence of mathematics teachers’ attention to student reasoning and sensemaking on students’ ability to develop deep and flexible mathematical understanding. For example, in the United States, these findings led to the creation of national standards that advocated for discourse-rich mathematics classrooms that centered student conceptual understanding and mathematical reasoning (NCTM, 2000). Yet, enacting classroom practices grounded in student thinking is no simple matter (Franke et al., 2007). An extensive line of research has sought to identify and characterize teacher cognition and instructional practices for launching and facilitating productive mathematics discourse (e.g., Leinhardt and Steele, 2005). Blömeke et al. (2015) position teachers’ noticing in their model of teacher competence and argue that it is central to effective instructional practice. We concur with this research and contend that teacher noticing is at the crux of developing responsive interactions focused on students’ ideas—capturing the invisible, moment by moment attention and sensemaking teachers engage in as they develop classrooms organized around student thinking.
2 Research on teacher noticing
Research on teacher noticing in mathematics education has advanced the field’s understanding of teacher attention and sensemaking in a range of contexts, including in-the-moment interactions (Sherin et al., 2011), teacher professional learning (Jilk, 2016; Seidel and Stürmer, 2014; Shah and Coles, 2020; Sun and van Es, 2015), and lesson planning and assessment (Choy et al., 2017). Other research has examined the relationship between teachers’ knowledge and their noticing (Hoth et al., 2018; Kersting et al., 2012; König et al., 2015), as well as how to develop teacher noticing for particular content domains (e.g., Sánchez-Matamoros et al., 2015; Schack et al., 2013). Still other research has sought to identify the core dimensions of noticing and how they relate to each other (Barnhart and van Es, 2015; Scheiner, 2016); the cognitive, social, and cultural-historical mechanisms of noticing (Hand, 2012; Russ and Luna, 2013) and how these mechanisms are informed by the histories of teachers and learners and the goals of mathematics instruction and schooling more generally (Jackson et al., 2018; Louie, 2018). While such work has demonstrated that noticing is a powerful construct for teaching, it has, at the same time, raised several questions that call for further inquiry.
One question concerns the nature of teachers’ selective attention. It is widely assumed that noticing involves teachers identifying objects of attention during classroom activity (Sherin et al., 2011), yet research suggests that attending may be more complicated than simply selecting events. For example, research on perception suggests that individuals have limited attentional capacity that restricts how many events they can focus on at any given time (Kahneman, 1973; Rensink, 2009). In mathematics education, in particular, Stockero et al. (2017) propose that noticing entails discriminating between different instances of mathematical thinking to identify those that will lead to more generative learning opportunities for students. This research raises questions then about the nature of selective attention for teaching.
The second question concerns what drives shifts in teacher noticing. Research finds that teachers can become more attuned to aspects of classroom interactions that are consequential for student learning and can develop more robust and nuanced understandings of observed phenomena (Seidel and Stürmer, 2014; Stanhke et al., 2016). Yet, the literature raises questions about what prompts this shift in noticing. Some research suggests shifts in noticing are tied to the specificity with which teachers see a phenomenon and the nature and kind of evidence they use to make sense of observed events (e.g. van Es, 2011). Other research suggests that shifts in noticing are tied to how teachers frame the task of noticing (Jessup, 2018; Russ and Luna, 2013). That is, as teachers participate in activity systems that are organized to support teachers’ learning to see and understand particular aspects of classroom activity, they come to frame the work of teaching as centrally focused on those aspects of instruction. Another line of inquiry suggests that shifts in noticing occur as teachers develop awareness of their own histories, commitments, and dispositions that influences what they identify as noteworthy and how they understand what they see (Erickson, 2011). This literature suggests that the ways in which teachers shift their noticing is complex and multi-faceted.
The third question concerns the boundaries of teacher noticing, a topic that has recently been debated in the literature (e.g., Amador et al., 2017; Scheiner, 2016; Sherin, 2017). Some research proposes that noticing extends beyond classroom interactions and is active in other contexts of teaching, such as during curriculum planning (Amador et al., 2017) and while reflecting on a lesson (Choy et al., 2017). Other research raises questions about whether noticing extends beyond attending and interpreting. For example, some research identifies decision-making as a third dimension of teacher noticing (Blömeke et al., 2015; Jacobs et al, 2010), an idea that has been taken up widely to investigate teachers’ professional noticing. Similarly, Stockero et al. (2017) introduce an alternative dimension, “building”, that includes making students’ thinking the object of attention to engage the class in making sense of a student idea. A related issue concerns how the dimensions relate to each other. Some research proposes a sequential relationship, while others suggest a more dynamic process in which teachers’ observations and interpretations are simultaneously engaged (Barnhart and van Es, 2015; Sherin, 2007; Superfine et al., 2017).
These questions suggest to us that teacher noticing is more nuanced than we originally conceived. The goal of this paper, therefore, is to revisit an earlier set of analyses that we conducted in order to elaborate the construct of teacher noticing. In doing so, we introduce a revised framework that extends our earlier conceptualization of teacher noticing and responds to emerging questions in the field (Sherin and van Es, 2009; van Es and Sherin, 2002).
The data we draw from was collected almost 20 years ago. We return to it today not because of the data per se, but because we have found it instructive to revisit our analyses to probe for new insights into teacher noticing related to questions the field has raised. As such, in what follows we share illustrative examples that both informed our original framework and highlight changes in our thinking since that time (Sherin and Han, 2004; van Es and Sherin, 2008). We conclude by discussing the implications of this revised framework for studying noticing during instruction and for research on the relationship between noticing and teaching more broadly.
3 An expanded framework for learning to notice
In 2002, we presented what was at the time a novel framework to explore learning to notice among teachers. The claim that noticing is a part of expertise was not new (Lesgold et al., 1988). In fact, a number of researchers had already begun to characterize the nature of teacher noticing (Berliner, 1994; Erickson, 1986; Mason, 2002). Our framework involved three dimensions. First, we theorized that noticing involved identifying key events that take place in a classroom. Second, the framework delineated two additional aspects of the process through which teachers interpret noteworthy events. In particular, we argued that teachers reason about what they observe based on their existing knowledge and that they draw inferences about particular features of instruction based on broader principles of teaching and learning (see Table 1). Specifically, we proposed that teachers use what they know about mathematics, learners, learning, and teaching mathematics along with their prior experiences as teachers and learners of mathematics, and schooling more generally, to make sense of and interpret student thinking as an instance of a broader mathematical idea (e.g., “She’s thinking about multiplication as arrays”) or theory of teaching and learning (e.g., “This is about having high expectations”).
The expanded framework we propose continues to highlight that noticing involves the two interrelated dimensions of attending and interpreting. Further, as before, we maintain that noticing is an active process. We also acknowledge that noticing happens in context, with different objects of attention affording particular kinds of noticing (Santagata and Yeh, 2014). Thus, we take noticing to involve actively interacting with the environment in ways that enable further observation and interpretation (e.g. Neisser, 1976). With this in mind, we introduce our revised framework (Table 2) which expands on the first two dimensions of attending and interpreting and introduces a third, what we refer to as shaping.
Specifically, we claim that attending consists of two parts: identifying key features of instruction and disregarding selected features of classroom interactions. We introduce a second part to the dimension of interpreting, what we refer to as adopting a stance of inquiry to observed phenomena. Finally, we propose that noticing involves a third dimension, what we refer to as shaping, that involves constructing interactions and contexts to gain access to additional information. We elaborate on each of these dimensions below.
3.1 Attending: identifying and disregarding features of classroom interactions
To situate our discussion of the first dimension, we return to our question about the nature of teachers’ selective attention.
3.1.1 Attending as identifying noteworthy aspects of a phenomena
In our early conceptualization, the first dimension captured attending, that is, where do teachers direct their attention among the blooming, buzzing confusion (Sherin and Star, 2011) of classroom life? We described attending as the act of identifying noteworthy events, what others refer to as marking (Mason, 2002), highlighting (Goodwin, 1994), and having checkpoints (Leinhardt, 1989).Footnote 1 This is consistent with others who define attending as looking for particular types of information, events, and interactions (Gibson and Ross, 2016; Miller, 2011; Scheiner, 2016).
While research emphasized that what teachers see can be automatic or intentional, as well as conscious or unconscious (Mason, 2011; Miller, 2011), Mason (2009) claims that noticing is particularly powerful when it involves an awareness on the part of the observer. He explains that some individuals can experience a situation but have little awareness of what is occurring around them, while others intentionally take note of particular features, events, and interactions. Like Mason, we propose that teacher noticing often involves a degree of intentionality concerning the features of classroom interactions that become the objects of teachers’ attention.
In prior research, we illustrated the nature of learning to attend by documenting shifts in what teachers highlighted when they discussed video excerpts of mathematics classrooms during meetings with peers, what we refer to as a “video club” and in pre- and post-interviews with researchers (Sherin and van Es, 2009). Across multiple video clubs, teachers increased their attention to students’ mathematical thinking (Table 3). For example, in the Nile video club that consisted of seven meetings with four middle school mathematics teachers over a school year, participants brought up issues related to the mathematics in the videos they viewed almost three times as much in their final video club meeting (86%), as compared with their first meeting (29%) (Sherin and Han, 2004). This was also the case for teachers who participated in the Mapleton video club in which seven elementary teachers met ten times over the course of one school year to view and discuss video excerpts from their math lessons. Participants in the Mapleton video club highlighted the mathematics in 27% of the teacher-initiated conversations in the first meeting, compared to 61% of teacher-initiated conversations in the last meeting (van Es and Sherin, 2008).
Other studies reported similar findings—that both prospective and in-service teachers can learn to shift their attention to the substance of student thinking and to the mathematics in the context of video-based learning contexts (Gaudin and Chaliès, 2015; van Es et al., 2017). One of the important findings from this line of work is that teachers’ attention is selective—teachers process simultaneous sources of information differentially (Johnston and Dark, 1986; Sherin, 2007). Further, while teachers cannot focus on all aspects of classroom interactions at the same time, they can and do come to attend to specific aspects of classroom activity when they become aware that those dimensions are worthy of attention.
3.1.2 Attending as disregarding selected features of classroom interactions
As we have worked to help teachers develop their noticing of student thinking, we have come to understand that paying attention to noteworthy features of classroom interactions is only one part of attending. Teachers must also focus their attention away from other features of classroom interactions. Thus, attending involves not only looking closely at some features of the classroom environment, but also disregarding other aspects of that environment. As Miller (2011) explains, “experts are often distinguished as much by what they do not notice as by what they do [notice]” (p. 52). Similarly, Erickson (2011) claims that teacher noticing involves “attending to some phenomena and disattending to others” (p.20). Miller (2011) describes this process as “cognitive tunneling” (Dirkin, 1983), stating that experts focus their attention on a subset of the information available to the exclusion of information outside of these specific areas. This method can be quite effective, for example, as in the case of hockey goalies who attend to the position and movement of the stick and puck but not to movement of the shooter (Panchuk and Vickers, 2006).
Though we did not previously highlight teachers’ attention away from particular aspects of classroom interactions (Sherin and van Es, 2009), when we review the data, we find evidence that such shifts occurred. Specifically, as teachers’ attention to student thinking increased, teachers paid less attention to other aspects of the interactions they had previously highlighted. For example, teachers in the Nile video club shifted their attention from initially raising issues related to teacher pedagogy in 57% of the discussion segments in the first meeting to 14% in the final meeting. Similarly, their focus on issues of classroom climate decreased from 14% in the initial meeting to 0% in the final meeting (Sherin and Han, 2004).
Interviews with teachers in the Mapleton video club provide further evidence that teachers disregarded some features of instruction as they learned to notice (van Es and Sherin, 2008). In both the pre- and post-interviews, teachers viewed the same four video excerpts and responded to the prompt, “What do you notice?” Teachers were asked this question repeatedly until they had no additional comments. What is particularly striking is that teachers did not simply mention all of the same phenomena in the pre- and post-interviews and then, in addition, highlight new issues related to students’ mathematical thinking in the post-interviews. Instead, in the post-interviews, teachers no longer mentioned many of the issues that stood out to them in the pre-interview. Interestingly, along with the increased focus on students’ mathematical thinking came an explicit focus away from issues that were not related to the substance of students’ thinking. Table 4 provides evidence from a subset of the Mapleton teachers’ interviews to illustrate this shift. We claim that learning to notice involved both selecting a new focus of their attention (i.e., student thinking), as well as shifting attention away from other issues related to teaching and learning, such as pedagogy and classroom climate.
Our point is that teachers do not simply add a new focus onto their existing tendencies, but in fact re-prioritize the objects of their attention in classroom interactions.
3.2 Interpreting: using knowledge and experience and adopting a stance of inquiry
To address our second question of what prompts shifts in teachers’ noticing, we returned to the second dimension of our framework, interpreting.
3.2.1 Interpreting as using one’s knowledge and experience to make sense of observed events
In our original framework, we proposed that interpreting involves using knowledge of one’s context to reason about a situation and furthermore, that as one gains expertise, one is able to reason about a situation in more sophisticated ways. This perspective is consistent with research that documents that individuals who are more expert within a domain are able to more effectively reason about that domain (e.g., Lesgold et al., 1988). Teachers have a wealth of resources they draw on to make sense of classroom interactions—their understanding of the discipline, content knowledge for teaching, knowledge of learners and learning, understanding of learners, and more. Along these lines, Erickson (2011) argues that teachers’ interpretations are profoundly influenced by their prior experiences and pedagogical commitments and thus vary from teacher to teacher.
We also emphasized that noticing entails making connections between specific events and broader principles of teaching and learning. This is similar to Goodwin’s (1994) notion of coding. When individuals are apprenticed into a practice, they develop knowledge that helps them characterize what they observe and organize their observations in a systematic way. While we continue to view this as important, we regard this phenomenon to be part of how teachers use their knowledge and experience to interpret what they notice and thus do not list it as a separate part of interpreting in our revised framework.
As we sought to elucidate how teachers used their knowledge and experience to make sense of classroom interactions, we focused in particular on how teachers made sense of students’ mathematical thinking (van Es, 2011). In doing so, we identified three general stances that teachers used to interpret what they noticed—descriptive, evaluative, and interpretive.Footnote 2 Some teachers primarily described what they observed by making statements such as, “The girl with the red shirt gave the first answer” or “I think what he said was ‘It should be a curve’”. Similar to Miller and Zhou’s (2007) findings, other teachers tended to evaluate what they noticed, pointing out what was correct or incorrect, or what went well or poorly, making comments such as, “I like how he added there” or “She wasn’t solving it correctly”. We also identified instances when teachers’ comments consisted of interpretations. In such cases, teachers made inferences about students’ thinking and understanding, often based on evidence in the video, making statements such as, “I think what he’s saying is because half of 100 is 50, it works the same way for 30 and 15” or “He’s thinking about multiplication as adding the same thing over and over again”.
In looking across these approaches, we characterized the interpretive stance as the most sophisticated of the three because it captured a way of examining classroom phenomena that was consistent with more expert sense making, which is often described as relying on a deep and substantive knowledge of the context (Berliner, 1994; Kersting et al., 2012). In fact, over time, teachers in both the Nile and Mapleton video clubs moved from primarily describing and evaluating what they noticed to consistently interpreting observations, an indication of their developing noticing expertise. This shift was evident in the stance that teachers in the Mapleton Video Club adopted from the second to the final video club meetings (see Table 5), with the teachers enacting an interpretive stance in greater than half of their comments in the final meeting compared to their comments in the second video club meeting.
3.2.2 Interpreting as adopting a stance of inquiry
While we continue to view one’s knowledge and experience as central to interpreting what is noticed, we propose that there is more that drives teachers’ developing expertise in this area. In particular, we claim that a shift in interpreting entails adopting a stance of inquiry. That is, interpreting is not only about trying to make sense of a phenomena but also involves seeing observed phenomena as something worth trying to figure out.
Adopting a stance of inquiry has been raised in the noticing literature previously. For example, Mason (2009) describes the discipline of noticing as developing an awareness of others to understand what someone is thinking and who the person is becoming in any given moment of instruction. Mason (2011) also explains that noticing entails “holding on to an observation and seeking multiple, preferably, conflicting possibilities” (p. 40) of their meaning. He contends that this approach enables teachers to more likely treat future events as novel interactions that can be acted on in the moment and not out of habit. These are key aspects of what we believe takes place when teachers adopt a stance of inquiry.
Our claim that the act of interpreting is driven by a stance of inquiry resembles research that asserts that a teacher’s epistemological framing influences how they understand the events taking place in their classrooms (Russ and Luna, 2013). That is, when teachers take on a stance of inquiry they are, in essence, taking on a new epistemological frame to the work of noticing, one that involves trying to figure out what students mean. While we understand there to be an important and dynamic relationship between framing and noticing, our emphasis here is on the central nature of an inquiry stance in supporting a teacher’s ability to notice.
When we reviewed the video club data, this inquiry stance was apparent both in the nature of the teachers’ comments in the later video clubs and the roles that they took on in conversations with their peers over time. Consider, for example, a discussion that took place during the ninth meeting of the Mapleton Video Club. The group viewed a segment featuring fifth grade students discussing the area of a rectangle. Students were asked to determine the height of a rectangle given a base of 12 feet and area of 360 feet2 (see Fig. 1).
What is the height of a rectangle with base 12 ft and area 360 ft2?
Students discussed several methods for finding the area, including dividing 360 by 12. One student, Maria, seemed to be trying to use the dimensions of the 2 × 5 rectangle to determine the height stating, ‘‘Since there’s five going down, you can just put one… and do it twice…” After viewing the clip, one teacher, Yvette initiated the discussion by stating, “I didn’t understand when [Maria] said, ‘Since there’s five going down…’” This question launched the group into a lengthy discussion of Maria’s approach. Frances suggested that Maria was counting the number of squares in a column but not considering that each square might have a height different than one. Elena connected Maria’s approach to what another student had done on the previous problem. This student determined the area of each column, and then divided by the given height to find the base of a single column. Wanda then drew a picture to illustrate what she thought Maria might have been trying to communicate. Overall, the teachers recognized the value of Maria’s approach but believed that Maria was not accounting for each of two columns having a base of 6 feet in this case.
Previously, we attributed teachers’ engaging in in-depth discussions of this sort primarily to teachers having developed sophisticated strategies for interpreting students’ thinking (Sherin and van Es, 2009). We propose here, however, that key to engaging in this work was developing and sustaining a stance of inquiry. That is, the teachers not only worked together to make sense of Maria’s approach, but they continually asked themselves, and each other, what Maria was trying to express. As noted above, Yvette first asked about Maria’s comment and said, “I didn’t understand when Maria said, ‘Since there’s five going down…” As the discussion continued, the teachers continued to ask questions of the group that we believe reflected a stance of inquiry: “Was she trying to count the boxes?” “Does she know that each side is worth six?” “Is that similar to what Tracey was thinking?” Our point is that it is because Maria’s comment remained an object of inquiry that the teachers were able to productively use evidence in the video to make sense of what she said.
The ability to sustain a stance of inquiry is also present when we re-examined the roles that teachers played as they participated in video clubs. In particular, van Es (2009) documented the ways that teachers participated in the Mapleton video club by elaborating ten different roles teachers adopted during the discussions. As we revisited the analysis, we identified two roles that, by definition, involved taking on an inquiry stance, the Prompter and Proposer. In the role of Prompter, teachers offered specific ideas and issues for the group to examine. Comments from the Prompter included questions like, “What does he mean when he says, ‘I looked at it sideways?’” and “How did she make that connection?” Van Es’s (2009) analysis documented that teachers took up this role more frequently from the first to the final video club meeting as a way to focus the group’s attention on students’ mathematical thinking. More specifically, in the first two meetings, teachers adopted the role of Prompter in 22% of the 44 distinct discussions that took place in these meetings.Footnote 3 However, in the final two meetings, the teachers took on this role in 56% of the 46 distinct discussions. Additionally, in the first two meetings, only two teachers prompted the group to discuss ideas they found noteworthy; whereas, in the final two meetings, all but one of the seven teachers took on this role, initiating noteworthy events for the group to discuss.
The role of Proposer also provides evidence of teachers adopting an inquiry stance. Van Es (2009) characterized the Proposer as offering explanations about events under discussion. Analysis found that the qualitative nature of teachers’ participation in this role shifted over time. In the first two meetings, the teachers were more definitive in their explanations and offered judgments about how a student should approach a problem (e.g., “He should really be thinking…”). In the final two meetings, however, teachers were more tentative in their explanations and expressed uncertainty about what a student might mean, remarking that they “weren’t sure” or “didn’t know”, even after offering a plausible explanation. We interpret such comments as reflecting an inquiry stance because they invite further exploration—either from themselves or from others in the group—of what a written or verbal explanation might reveal about student thinking. In sum, looking at the ways teachers participated in the roles of Prompter and Proposer over time suggests that teachers adopted a stance of inquiry as they tried to figure out and understand the details of student thinking.
3.3 Shaping
We now turn to address the third question that emerged in the literature concerning the boundaries of teacher noticing. Recent research suggests that noticing is more expansive than we previously conceived. In particular, a number of researchers take up the idea that there is more to noticing than attending and interpreting (Blömeke et al, 2015; Jacobs et al., 2011; Reisman et al., 2020). An important contribution to this perspective comes from Blömeke et al (2015) and Jacobs et al. (2010) who introduce decision making as a third dimension of noticing. This dimension captures the integrated relationship between the information teachers gather from their observation and sense-making of students’ thinking and their plans to respond in the moment. This idea has been taken up productively in a range of mathematics education research (Amador et al., 2019; Stahnke et al., 2016; Sanchez-Motomoros et al., 2019; Ulusoy, 2020) and has been used to document that as teachers attend to the details of student thinking and develop more robust interpretations of these ideas, they can provide more detailed and mathematically relevant instructional responses (Santagata and Yeh, 2014; Ulusoy, 2020).
We have also come to the conclusion that restricting noticing exclusively to attending and interpreting does not fully embrace what teacher noticing involves. As we considered this issue, we turned to the literature to inform our thinking. As a result, we propose an alternative third dimension, what we refer to as shaping. Shaping involves teachers constructing interactions, in the midst of noticing, to gain access to additional information that further supports their noticing. This dimension is based on literature that suggests noticing involves actively interacting with one’s environment. For example, Jazby (2016) explains that “making sense of complex situations is accomplished through information gathering” where individuals locate information in their environments to guide behavior. Similarly, Mason’s (2009) model of teaching as disciplined inquiry asserts that teachers are able to “exercise will, through which they can direct and guide both movements of their attention and engagement of their energies” (p. 220). Moreover, Hoth et al. (2016) identify teachers’ diagnostic competence as an ongoing process that takes place during classroom interactions that enables them to engage cycles of observation and interpretation to inform their decision-making. The idea that noticing is an active, rather than a passive, process is something that we have discussed previously, particularly in making the claim that a teacher’s attention is drawn to specific features of the environment, rather than simply attending equally to all that is taking place (Sherin, 2007). Here, we aim to make a different point—that noticing is active in that it involves constructing interactions that enable further attention to and sensemaking of student thinking. Thus, part of a teacher’s noticing may involve asking a student a question or looking more closely at what a student has written to access further information for the teacher to notice.
To be clear, shaping differs both in form and purpose from how researchers describe decision-making as a part of noticing. Jacobs et al. (2011), for example, explain that “deciding how to respond” involves teachers reasoning about a potential response to what they come to understand about student thinking. In contrast, “shaping” involves teachers and students engaging in an interaction with each other in the moment. Furthermore, “deciding how to respond” appears to serve as a mechanism for teachers to determine their next instructional move to, presumably, advance a student’s thinking (Jacobs et al, 2010; Smith and Sherin, 2019). This is consistent with Blömeke et al.’s (2015) model of noticing, that positions teachers’ decision-making as informed by teachers’ perception and interpretation of classroom interactions. “Shaping”, on the other hand, involves the creation of interactions for the purpose of gaining access to additional information, in this case about student thinking, which can then become the object of further attending and interpreting.
We recognize that the inclusion of shaping may appear to blur the lines between noticing and what we typically think of as “just plain good teaching” (Gardner et al., 1989, p. 72). Isn’t asking questions central to the work of teaching? Certainly, every question from a teacher or interaction between a teacher and student does not constitute shaping. By shaping, we mean to refer to those questions and interactions that have as their purpose to advance a teacher’s noticing. Smith and Sherin (2019) discuss the difference between assessing and advancing questions, with assessing questions intended to further reveal a student’s thinking and advancing questions intended to move a student’s thinking forward. Assessing questions, then, to us, would be part of the work of shaping, providing additional information for teachers to notice to make sense of a student’s idea. Advancing questions, in contrast, would not.
To be clear, we acknowledge that in introducing shaping, there continue to be questions about the boundaries of noticing. Shaping does in fact highlight the integrated nature of noticing and teaching. We would not expect to be able to clearly distinguish the two, since key to the work of teaching is continued noticing on the part of the teacher.
We have situated our discussion of shaping in the context of classroom interactions between teachers and students. Our review of the video club data suggests that teachers also shaped discussions as they sought to understand student thinking in this context. In fact, we identified two primary ways that teachers engaged in shaping as they learned to notice student mathematical thinking. First, teachers occasionally asked to access more information about a student’s ideas by further review of video. Across both the Nile and Mapleton video clubs, teachers asked if they could view a video segment a second or third time: “Can we see the clip again? I want to think about what they were talking about with angles” or “I need to hear it again…” Similarly, at times, teachers suggested the group look at a different part of a video than they had viewed already. For example, after watching a video from his class in which a student was describing an innovative approach to working with decimals, Daniel suggested the group look at a moment from earlier in the lesson, in which a different student described a similar approach. Of particular interest is that these instances of seeking out additional information in the videos increased over time. For example, in the Nile Video Club, this kind of conversation first came up in the third meeting, and by the seventh meeting, a request was made by participating teachers four times. This suggests that teachers worked to actively increase and shape their access to information about a student’s idea through evidence in the video and furthermore, that teachers did so as part of developing their noticing expertise.
Furthermore, in our earlier analyses, we identified conversations in the video club as being video-based or non-video based (see van Es and Sherin, 2008). That is, we distinguished discussions in the video club that explicitly focused on events in the video from discussions in which teachers discussed issues external to what was captured in the video, such as the district’s newly adopted curriculum or ideas they had about students’ understanding of a previous lesson. As we consider the notion of shaping, however, we now understand that some of these non-video based conversations were in fact acts of “shaping” that provided access to additional information to make sense of student thinking in the video.
For example, in discussing Maria’s approach to finding the height of the rectangle, at one point, Yvette raised a concern about how the curriculum intended to support students’ exploring area and perimeter through the use of arrays. The conversation shifted gears as several teachers took up this topic. The teachers discussed how the curriculum organized work with arrays beginning with numerous problems in which the area of each unit in an array was one, only to shift later to units in an array having variable measures. One teacher then drew a rectangle on the board, labeling it 12 × and the teachers discussed how the problem would change if the lines of the array were removed. In our coding of this segment, we characterized this discussion as non-video based because the teachers were not talking about the student thinking in the video but rather were discussing the curricular representation of the task. Returning to this interaction, we see, however, that this discussion provided teachers with additional information to make sense of Maria’s thinking, specifically it opened up the idea that Maria might be seeing each unit square as meaning one foot rather than six feet.
To further investigate this, we selected three Mapleton video club meetings—one from the beginning, middle, and end of the series of meetings—and reviewed those segments of conversations coded asnon-video based.Footnote 4 Our analysis showed that in over one-third of these conversations, teachers gathered information from outside of the clip to make sense of what they observed inside the clip. In some cases, this entailed highlighting an instance of student thinking that was not captured in video but nevertheless helped the group to explore the student thinking in the video. In other cases, as in the example with Maria above, the teachers sought out additional information from the curriculum materials (e.g., the kinds of representations used in prior lessons; the language used in a word problem) to understand what the source of a student confusion might be or why a student may have expressed an idea in a particular way. These findings support our claim that in the midst of noticing, teachers may shape the interaction in order to gather additional information to help them understand the situation under consideration.
4 Implications for noticing in classroom interactions
Over the past 2 decades, the idea that teacher noticing is a key component of teaching expertise has been embraced by research on teaching. Research has elaborated key dimensions of teacher noticing, how noticing operates during instruction, and what is involved as teachers learn to notice. Researchers have also applied innovative methodologies to the study of teacher noticing, attempting to capture teacher noticing “in-the-moment”, as well as identifying the relationship between teacher noticing and teachers’ instructional practices. As contributors to this research, it is not surprising that our own ideas about this construct are not the same as they were nearly 20 years ago when we published our original Learning to Notice framework (van Es and Sherin, 2002). While we continue to believe that attending and interpreting are key dimensions of teacher noticing, our understanding of these dimensions has developed to account for the ways teachers both focus on particular objects of attention and disregard others, to include adopting an inquiry stance to support the work of interpreting, and to capture that teachers’ actively construct—or shape—interactions to gain access to information to enable further noticing.
In sharing examples to support our revised framework, we have drawn on data from our research on teacher noticing in video clubs. Yet, we believe that our revised framework also applies to teacher noticing in the context of classroom interactions. Following the conclusion of the Nile and Mapleton video clubs, each teacher participated in an exit interview where they discussed whether the video clubs influenced their instruction in any way. In addition, we observed teachers from Mapleton video club in their classrooms several times over the course of the school year.
We have previously presented our analyses of the classroom observations, documenting that the teachers increased their attention to student thinking both in the context of the video clubs, as well as during instruction (Sherin and van Es, 2009; van Es and Sherin, 2010). While these analyses did not investigate whether the increased attention to student thinking came at the same time as decreased attention to other topics or interactions, several teachers mentioned this idea in their exit interviews. Ron, who participated in the Nile Video Club, summed it up this way, “I’m just looking at things differently, focusing much more on classroom discourse… and students’ questions and not on … who’s sitting next to who and if … students [think] the lesson is fun”. Similarly, Linda, a member of the Mapleton Video Club shared that her attention during instruction had also been “refocused… [away] from what I’m doing up there, it’s about what the kids are doing”. These quotes suggest that just as in the video club, the teachers not only came to pay more attention to student thinking during instruction, but that their attention also shifted away from other aspects of classroom interactions.
With respect to adopting a stance of inquiry, analyses of the classroom observations found that this practice increased significantly over the course of the school year (van Es and Sherin, 2010). Previously, we documented that teachers “positioned themselves as learners in the classroom” (p. 171) with respect to students’ ideas as they learned to notice. That is, teachers more consistently treated students’ ideas as objects of inquiry making comments such as, “That’s interesting” and “I’d like to know what you mean”. In fact, in this earlier work, we characterized these moves as teachers learning while teaching, which reflects adopting a stance of inquiry around students’ ideas.
Finally, as we reviewed the classroom observations, we found many instances of “shaping” in which teachers seemed to recognize that a student had an interesting question and wanted to know more about what the student was thinking, and thus constructed interactions to gather more information. We interpret teachers’ subsequent questions—“What do you think the value is?”, “Where is that question coming from?” or “How might you figure it out?”—as attempts to shape the interaction in order to extend the teachers’ noticing of the student’s idea.
As we consider the implications of a revised framework for learning to notice, we recognize that we have focused our research on noticing student thinking, one of many aspects of classroom interactions. Yet, we conjecture that this revised model is also relevant when considering teacher noticing for other aspects of classroom interactions, such as discourse, equity and access, and classroom climate. An important direction for future research entails understanding in what contexts and under what conditions this revised model of noticing applies. We propose that additional research in this direction will offer deeper insight into the construct of teacher noticing and have implications for how to support teachers developing their noticing to improve mathematics instruction.
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05 April 2024
A Correction to this paper has been published: https://doi.org/10.1007/s11858-024-01570-2
Notes
We acknowledge Sherin and Star’s (2011) critique of this dimension as not specifying what counts as the noticed thing and that, in fact, what a teacher highlights as being important already carries with it some interpretation because it is valued as worth highlighting.
It is not lost on us that we have, for years, discussed different approaches to interpreting using the term “interpretive” to describe one of the three approaches (Sherin and van Es, 2009).
Idea units consisted of segments of conversation defined by shifts in the topic of conversation (see van Es, 2009, pp. 108–109 for detailed description of segmenting meeting conversations).
Of the 90 idea units across these three meetings, 25 (28%) were previously coded as non-video based (van Es and Sherin, 2008).
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Acknowledgements
This research was supported by the National Science Foundation (Grant No. REC-0133900) and the Spencer Foundation. We want to thank the teachers who opened up their classrooms and who took the time to participate in the video club meetings.
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van Es, E.A., Sherin, M.G. Expanding on prior conceptualizations of teacher noticing. ZDM Mathematics Education 53, 17–27 (2021). https://doi.org/10.1007/s11858-020-01211-4
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DOI: https://doi.org/10.1007/s11858-020-01211-4