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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.

Teacher noticing has become increasingly acknowledged as a fundamental aspect of teacher professional competence. Teacher education scholars have examined how the development of noticing might be supported both in initial teacher education and in professional development. In mathematics teacher education, several studies have explored the use of video as a supporting tool for teacher noticing. It remains unclear how this body of work builds on the various theoretical perspectives of noticing prevalent in the literature, thus broadening our understanding of noticing. Furthermore, the field has not examined systematically the extent to which research has leveraged the affordances of digital video technologies, and whether scholars have employed different research methods to answer questions that are critical to teacher educators. This survey paper reviews studies published in the last two decades on programs centered on mathematics teacher noticing that used video as a supporting tool for teacher learning. Thirty-five peer-reviewed papers written in English were identified and coded along three dimensions: (1) theoretical perspectives; (2) use of video technologies; and (3) research questions and methods. This review summarizes important findings and highlights several directions for future research. Most studies involved pre-service teachers, and only a few centered on in-service teachers. Developers of the large majority of programs took a cognitive psychological perspective and focused on the attending/perceiving and interpreting/reasoning facets of noticing. Few studies used video-based software and few studies used grouping, and even fewer used randomized grouping. Evidence of program effects on responding and decision making, and on instructional practice, is limited and should be extended in the future. [Author abstract]

Teacher noticing has been widely understood as a kind of seeing or way of making sense of classroom events and instructional details. Such notions of teacher noticing often construe noticing as a disembodied, purely mental form of seeing and position the teacher as separated or separable from the observing environment. They rely on intuitive models that adopt the usual divide between mind, body, and matter, and that fuel the dualism between the individual and the environment. In this paper, I attempt to work towards a more comprehensive model of teacher noticing that instead proposes an entanglement of the cultural-historical, embodied-ecological, and social-material. Teacher noticing, in such a proposal, includes culturally and historically constituted forms of framing classroom events, embodied ways of accessing and exploring the classroom world, and active shaping and interaction with the classroom setting's social and material structure. [Author abstract]

Research summary: Exploiting opportunities is critical to a firm's competitive advantage. Not surprisingly, there has been considerable interest in the processes by which top managers allocate attention to potential opportunities. Although such investigations have largely focused on top-down processes for allocating attention to the environment, some studies have explored bottom-up processes. In this article, we consider both top-down and bottom-up processing to develop a model by which top managers form opportunity beliefs for strategic action depending on the allocation of transient and sustained attention. Specifically, this attentional model provides insights into how a top manager's attention is allocated to identify potential opportunities from environmental change and explores how different modes of attentional engagement impact the likelihood of forming beliefs about radical and incremental opportunities requiring strategic action. Managerial summary: Managers are interested in noticing and exploiting opportunities because the exploitation of an opportunity represents an important strategic action. Noticing and exploiting opportunities depends on how and where top managers allocate their attention. Managers can focus attention based on their knowledge and experience or as a result of something in the environment capturing their attention. In this paper, we consider both knowledge-driven and environment-driven processes for allocating attention to form opportunity beliefs. This opportunity belief arises from a two stage process. The first stage explains how a top manager identifies environmental changes as potential opportunities. The second stage explains how the top manager forms a belief that these identified environmental changes represent a radical or incremental opportunity worthy of exploitation.

Aspects of noticing which are often overlooked are brought to the surface and illustrated by accounting-for three accounts-of specific phenomena, two of which readers are invited to experience for themselves. These are used as a springboard for both illustrating the Discipline of Noticing as a method of sensitising oneself to notice possibilities for action, and reporting insights achieved through its use. This includes augmenting the discourse of Dual Systems Theory to include S1.5 (emotion) and S3 (creative insight) and linking it to a six-fold structure of the human psyche (enaction, affect, cognition, attention, will and witness). The aim is to enrich the discourse in which to account-for incidents as experienced by teachers themselves, and incidents observed by teachers and other researchers. The paper ends by distinguishing between measurement-based research validation, and phenomenologically-based validation which is part of the discipline of noticing.

The last decade has witnessed increasing interest in the study of teacher noticing in mathematics education research; however, little is known about the growth of teacher noticing and how it is influenced by teaching practice. Departing from the expert-novice-paradigm, in this paper we address this research gap by a cross-sectional study that investigates how Chinese mathematics teachers' noticing is affected by their developmental stage, measured by the length of their teaching experience. The study included 152 pre-service teachers at the end of their initial teacher education, 162 early career teachers with one to five years' teaching experience, and 123 experienced mathematics teachers with more than 15 years' teaching experience, who participated in a video-based assessment of their noticing competency conceptualized by the sub-facets of perception, interpretation, and decision-making. Our findings indicate a nearly linear growth in teacher noticing among Chinese mathematics teachers, with significant differences identified between pre-service and experienced teachers and only small differences between pre-service and early career teachers. Analyses using the method of Differential Item Functioning (DIF) further suggest that pre-service and early career teachers demonstrated strengths in aspects more related to reform-oriented or Westernized approaches to mathematics teaching, such as working with open-ended tasks, identifying characteristics of cooperative learning, and mathematical modeling tasks. By contrast, experienced teachers demonstrated strengths in perceiving students' thinking, evaluating teachers' behavior, and analyzing students' mathematical thinking. Our findings further highlight that the three sub-facets of teacher noticing develop differently within the three participating groups of teachers. These findings suggest that teaching experience acts as one influential factor in the development of teacher noticing in the Chinese context. [Author abstract]

The evolution of blended instructional environments requires teachers to extend professional noticing to learning analytics data presentations. This research is situated in the context of dashboards generated by a clustering algorithm that analyzed the performance of over 300 high school physics students on a diagnostic questionnaire and clustered them into characteristic performance profiles, which the algorithm then projected on specific student cohorts. Teacher noticing was elicited using semi-structured interviews centered on three dashboards presenting students’ performance, and teachers were asked to characterize emerging problem-solving knowledge and suggest responses to identified issues. Analysis of interview data from a sample of 10 experienced physics teachers revealed that teacher noticing was sensitive to dashboard features. While teachers tended to focus on individual students during the characterization stage, they preferred to address groups or the whole class at the response stage and focused less on providing individual students with personalized support.

It is known that teacher noticing skills improve through different interventions such as video clubs, lesson study, and short-term professional development programs. However, it is not known whether this improvement is permanent and whether teachers can transfer their noticing skills into the classroom. It is extremely important to provide an enduring change in teacher noticing skills. Rather than short-term programs, implementing long-running professional development programs, which last almost 2 years, enables teachers to maintain their noticing skills. At this point, the current study aims to develop in-service middle school mathematics teachers’ professional noticing of students’ mathematical thinking on pattern generalization during their involvement in a 2-year online professional development program enriched with collaborative discussion. Accordingly, the study was built on the professional noticing of children’s mathematical thinking framework, including three noticing skills: attending, interpreting, and deciding how to respond. Participants comprised 31 in-service middle school mathematics teachers with up to 15 years of professional experience working in public schools in seven different provinces of Türkiye. The teachers participated in the online PDP, including scenarios involving student strategies of particular mathematics content. The analysis of the data gathered from the pre-test and post-test let us conclude that the three noticing skills of the in-service middle school teachers exhibited incredible progress through their involvement in collaborative discussion in a long-running online PDP. Based on this result, the characteristics of the online PDP are put forth to develop teachers’ noticing skills.

In this paper, we respond to the continued harm of deficit discourses in mathematics education, focusing on discourses that systematically devalue the knowledge and abilities of students of color in classrooms in the United States. We specifically aim to (1) develop a sociopolitical framework for conceptualizing mathematics teacher noticing and (2) conceptualize and illustrate the enactment of noticing that challenges deficit discourses about these students and their communities—anti-deficit noticing—through the lens of our framework. We address our first research aim by introducing the FAIR framework, which foregrounds the role of sociopolitical Framing as an essential component of noticing that shapes and is shaped by Attending, Interpreting, and Responding, processes that have frequently been discussed in studies of teacher noticing. We show how an analysis using FAIR can contribute to understanding deficit noticing. We then conceptualize and illustrate anti-deficit noticing using the case of Oscar, a college mathematics instructor who worked with many Black and Hispanic students and himself identified as Hispanic. We discuss the local context that supported Oscar’s anti-deficit noticing and conclude with implications for future research and practice.

The teacher noticing construct is widely recognized in teacher competence and education research, particularly in the field of mathematics education. This paper surveys recent research on mathematics teacher noticing published between July 2019 and 2022, following an earlier literature review on teacher noticing across different disciplines. The study presented here analyzed 118 English-language articles published in peer-reviewed journals, focusing on conceptualizations, research methods, and relationships with other constructs, including teacher knowledge and beliefs. The findings suggest that the cognitive-psychological perspective on noticing, which emphasizes a set of cognitive processes, remains the predominant conceptualization. Recent research on noticing is characterized by a high proportion of studies based on small samples and qualitative research methods. While several studies have demonstrated the interrelatedness of noticing and professional knowledge, the relationship between noticing and beliefs and between noticing and instructional quality has rarely been addressed. Based on these findings, we highlight noteworthy contributions and critical shortcomings, and suggest directions for future research.