• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• Journal of the Korean School Mathematics Society
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• v.22 no.1
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• pp.63-80
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• 2019

This study aims to investigate noticing of pre-service secondary mathematics teachers. For the purpose of this study, we analyzed journals of four pre-service mathematics teachers. Our analysis was based on a framework including three categories such as Aware, Interpret, and Response. As results, we found a tendency that pre-service secondary mathematics teachers have more general awareness of students and relatively fewer interpretations of students' mathematical thinking than other categories. In addition, in the category of Response, the pre-service secondary mathematics teachers were more likely to explain to students than to promote students' thinking through questions. Based on these results, we would like to discuss implications for pre-service secondary mathematics teacher education.

• 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.

• The Mathematical Education
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• v.60 no.2
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• pp.229-247
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• 2021

Students' mathematical thinking is represented via various forms of outcomes, such as written response and verbal expression, and teachers could infer and respond to their mathematical thinking by using them. This study analyzed 39 elementary teachers' competency to notice students' problem-solving strategies containing mathematical errors in fraction addition and subtraction with uncommon denominators problems. Participants were provided three types of students' problem-solving strategies with regard to fraction addition and subtraction problems and asked to identify and interpret students' mathematical understanding and errors represented in their artifacts. Moreover, participants were asked to design additional questions and problems to correct students' mathematical errors. The findings revealed that first, teachers' noticing competency was the highest on identifying, followed by interpreting and responding. Second, responding could be categorized according to the teachers' intentions and the types of problem, and it tended to focus on certain types of responding. For example, in giving questions responding type, checking the hypothesized error took the largest proportion, followed by checking the student's prior knowledge. Moreover, in posing problems responding type, posing problems related to student's prior knowledge with simple computation took the largest proportion. Based on these findings, we suggested implications for the teacher noticing research on students' artifacts.

• 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.

• 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.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.257-275
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• 2021

This study investigated the prospective teacher's noticing of students' mathematical thinking from the perspective of how the prospective teacher pays attention to, interprets, and responds to the student's responses related to variables. The prospective teachers were asked to infer the students' thinking from the variables related to the tasks and suggest feedback accordingly. An analysis of the responses of 26 prospective teachers showed that it was not easy for prospective teachers to pay attention to the misconception of variables and that some of them did not make proper interpretations. Most prospective teachers who did not attend and interpret were found to have failed to provide an appropriate response due to a lack of overall understanding of variables. even though prospective teachers who did proper attend and interpret were found to have failed to respond appropriately due to a lack of empirical knowledge, even with proper attention and interpretation.