• East Asian mathematical journal
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• v.37 no.4
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• pp.461-480
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• 2021

There have been gradually a few studies on Noticing in the domestic and international area. For the purpose of increasing the concern on teacher noticing and pursuing the affluent studies on the noticing, this study tried to explore and understand the background, the meaning, and the properties of the teacher noticing while summing up the views of the various researchers. As a result, the teacher noticing could be defined as a cognitive process which is focused on mathematical objects, students' mathematical thinking, students' emotions, teaching strategies, classroom environment and interprets them to determine how to react. From this, noticing might be cognitive process which is a combined form of the objects and cognitive behavior, while the objects whom teachers notice covers up the mathematical objects and the teaching objects. Eventually, this study expects to serve as a basis to foster the in-depth understanding of teacher noticing and to derive the follow-up studies.

• School Mathematics
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• v.18 no.4
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• pp.773-791
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• 2016

Teacher noticing ability has been considered as one of important elements influencing a quality of teaching. Noticing is closely related to teachers' in the moment decision making in a class, and teachers notice things as they create and interact with their classroom setting. Mathematics teachers as an expert should notice students' mathematics learning during a class. The aim of this study was to analyze how mathematics teacher's pre-noticing activity that the teacher anticipated students' typical strategies and difficulties in learning targeted mathematics knowledge and prepared appropriate responses worked in practice. As a result, the teacher conducted three types of noticing in her classes: noticing shaping students' understanding by using students' misconceptions or errors; noticing creating students' learning opportunities based on their prior knowledge; noticing improving students' informal reasoning. This study concluded with discussion about the positive effect of teacher's pre-noticing activity on her actual noticing in practice, as well as implications for teacher education.

• School Mathematics
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• v.19 no.4
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• pp.795-817
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• 2017

Whereas noticing with relation to teacher expertise has been steadily studied in international contexts, there have been very few studies in Korea in this area. Given this, this paper reviewed the meanings of noticing based on Sherin and van Es as well as Jacobs et al. who provided foundational work and then analyzed recent studies on teacher noticing. A review of literature showed that recent international studies on noticing tend to elaborate the theoretical framework of noticing, diversify the methods of research on noticing, and extend to the range of noticing. This paper also included an analysis of domestic studies dealing with noticing either explicitly or implicitly. This paper is expected to serve as a basis to foster conceptual understanding of teacher noticing and to derive follow-up studies in Korea.

• Research in Mathematical Education
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• v.26 no.4
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• pp.311-331
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• 2023

This article explores how mathematics teacher educators (MTEs) engaged in collaborative inquiry into the microteaching experiences of preservice teachers (PSTs), ultimately developing a noticing framework through collective MTE inquiry. We delve into the specifics of what MTEs notice focusing on three emerging categories of noticing on PST's microteaching videos-lesson structure, task quality, and teaching practices. Each category, along with MTEs' noticing within these components, is elaborated through vignettes. This approach positions MTEs' noticing as a crucial element in the overarching vision to enhance the teaching practices of PSTs.

• Journal of the Korean School Mathematics Society
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• v.21 no.2
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• pp.183-206
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• 2018

It arises that teachers' professional competence should be considered not only with a cognitive perspective but also with a situative perspective. In this study, we considered mathematics teacher noticing as situational professional competencies of a mathematics teacher, and explored how mathematics teachers noticing on children's development of reasoning about variability in a video club has changed with the situative perspective. Findings illustrate that the 'interpreting' component among the three components of noticing-attending, interpreting, and deciding how to respond-was critically decisive for the change of the participant teachers' noticing. We also discussed how the video club intervention(the framework of children's development of reasoning about variability) can support the development of teacher noticing as a professional competence. This study has implications on the design of a video club to improve mathematics teacher noticing.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.377-411
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• 2021

This study aims to explore central and peripheral beliefs of mathematics teachers in the context of teaching and learning. For this purpose, this study analyzed teacher noticing of 8 mathematics teachers who are in-service in terms of mathematical beliefs using video-clips of math lessons. When the teachers in the video-clips seemed to have a teaching and learning problem, teachers who adopt noticing critized the classroom situation by reflecting his or her own mathematical beliefs and suggested alternatives. In addition, through noticing analysis, teachers' mathematical beliefs reflected in specific topics such as student participation in teaching and learning were compared to reveal their individual central and peripheral beliefs. Through these research results, this study proposed a model that extracts the central and peripheral beliefs of math teachers from the constraints of the teaching and learning context using noticing analysis. Additionally, it was possible to observe the teacher decision-making and expertise of mathematics teachers.

• East Asian mathematical journal
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• v.38 no.4
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• pp.397-414
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• 2022

This study tried to explore and understand the meaning, and the properties of noticing. The result of this study were first, the difference in mathematical noticing is distinguished in either the object which is paid attention is different or the object is same but differently interpreted or react. The cause of each difference could be described as mathematical objects such as conceptual objects and perceptual features. Second, teachers' teaching strategies, which narrow the gap in attention and play a key role in the formation of mathematical meaning, appeared in various places. This teaching strategy was implemented to distract students' attention. This study confirmed that the mathematical attention of teachers and students in math classes will differ depending on the object to which they pay attention, and that difference will be narrowed through teacher's discourse practice and teaching strategies through communication strategies.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.127-150
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• 2021

Recently, in the field of mathematics education, mathematical noticing has been considered as an important element of teacher expertise. The meaning of mathematical noticing is the ability of teachers to notice and interpret significant events among various events that occur in mathematics class. This study attempts to analyze the differences of pre-service secondary teachers' mathematical noticing and confirm the factors that cause the differences between them. To accomplish this, the items on class critiques were established to identify pre-service secondary school teachers' mathematical noticing, and each of 18 pre-service secondary mathematics teachers were required to write a class critique by watching a video in which their micro-teaching was recorded. It was that the teachers' mathematical noticing can be identified by analyzing their critiques in three dimensions such as actor, topic, and stance. As a result, there were differences in mathematical noticing between pre-service secondary mathematical teachers in terms of topic and stance dimensions. The result suggests that teachers' mathematicl noticing can be differentiated by subject matter knowledge, pedagogical content knowledge, curricular knowledge, beliefs, experiences, goals, and practical knowledge.

• The Mathematical Education
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• v.56 no.3
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• pp.341-363
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• 2017

This case study contributes to the efforts on identifying the essential features of responsive teaching practice where students' mathematical thinking is central in instructional interactions. We firstly conceptualize responsive teaching as a type of teachers' instructional decisions based on noticing literature, and agree on the claim which teachers' responsive decisions should be accounted in classroom interactional contexts where teacher, students and content are actively interacting with each other. Building on this responsive teaching model, we analyze classroom observation data of a 7th grade teacher who implemented a lesson package specifically designed to respond to students' mathematical thinking, called Formative Assessment Lessons. Our findings suggest the characteristics of responsive teaching practice and identify the relationship between noticing and responsive teaching as: (a) noticing on students' current status of mathematical thinking by eliciting and anticipating, (b) noticing on students' potential conceptual development with follow-up questions, and (c) noticing for all students' conceptual development by orchestrating productive discussions. This study sheds light on the actual teachable moments in the practice of mathematics teachers and explains what, when and how to support teachers to improve their classroom practice focusing on supporting all students' mathematical conceptual development.

• Journal of Korean Elementary Science Education
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• v.41 no.4
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• pp.754-770
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• 2022

For teachers, noticing refers to paying attention to something, indicating they interpret it and how they are willing to react to it in the context of their own instruction. Analysis of noticing features enables us to understand the overall characteristics of the teacher's lesson design, practice, and reflection, which are core agents in the educational design and implementation. This can also be taken to be the basis of education design for competency reinforcement for teachers. Therefore, in this study, the characteristics of noticing shown in teachers' reflections after class design and demonstration were identified. For this purpose, the self-reflection journals of 106 elementary pre-service teachers enrolled in the College of Education in Gangwon-do were analyzed. In particular, the journals were gathered that were written after the demonstration dealing with the change of gas volume by temperature in science class. After designing a noticing analysis frame consisting of the five dimensions 'agent', 'stage', 'topic', 'focus', and 'stance', the frequency and ratio of noticing by each dimension's components were derived. The frequency and ratio of noticing for the dimension of 'focus' were analyzed for the dimensions of 'stage' and 'topic'. The results of the study were as follows. For the dimension of 'agent', the frequency of teacher and student was the highest, and for the dimension of 'stage', inquiry activity was the highest. For the 'topic' dimension, class design according to the teaching strategy appeared most frequently, and in the 'focus' dimension, the cases that did not specify the goal of the class and the competencies to be achieved by the students appeared most frequently. In the 'stance' dimension, description showed the highest frequency. From the analysis of how the 'focus' changes according to the 'stage' and 'topic', it was found that a characteristic focus appeared for each component of the dimension. From these results, the implications of the noticing characteristics of pre-service teachers for the design and implementation of teacher education were discussed.