• 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.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.19-38
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• 2021

The purpose of this study is to examine pre-service teachers' noticing when evaluating peers' mathematical problem posing tasks. To this end, 46 secondary pre-service teachers were asked to create real-world problems related to permutation and combination and randomly assigned to evaluate peers' problems. As a result, the pre-service teachers were most likely to notice the difficulty of their peers' mathematics problems. In particular, the pre-service teachers tended to notice particular conditions in order to increase the difficulty of a problem. In addition, the pre-service teachers noticed the clarity of a question and its solution, novelty of the problem, the natural connection between real-world contexts and mathematical concepts, and the convergence between mathematical concepts.

• Journal of the Korean School Mathematics Society
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• v.25 no.3
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• pp.279-306
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• 2022

The purpose of this case study is to get an implication on elementary pre-service teacher education programs by exploring how a pre-service teacher's noticing changes within a learning community. The pre-service teacher participated in a learning community with researchers. Data includes recordings and transcription of actual class and pre- and post discussion in the learning community, the pre-service teacher's reflection essays, field notes, and students' worksheets. Results are as follows. First, the pre-service teacher's attending moved from the result of tasks to students' mathematical thinking. Second, the pre-service teacher's interpretation changed from a lack of diversity and specificity of evidence to diversity and specificity. Third, the pre-service teacher's decision-makings changed from unproductive deciding to productive deciding.

• 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.

• 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.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.1-18
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• 2024

Teachers' ability to notice is a crucial indicator of their instructional expertise. Despite the significance of this ability, research in mathematics teacher education has predominantly focused on the noticing of preservice teachers, with limited exploration into the noticing abilities of experienced in-service teachers. This study addresses this gap by examining the noticing characteristics of in-service elementary teachers actively developing their competency in elementary mathematics education. For this purpose, 23 elementary school teachers were asked to complete an analysis sheet while viewing the mathematics lesson video depicting on the concept of (fraction)÷(natural number), allowing us to scrutinize their attending, interpreting, and responding skills in detail. The study's results revealed that teachers demonstrated a tendency to attend mathematically significant aspects related to the teaching of fraction division. They interpreted the observed phenomena through the lens of fraction division's instructional principles, proposing specific pedagogical alternatives. These findings offer valuable insights for mathematics teacher education research.

• The Mathematical Education
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• v.61 no.2
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• pp.339-357
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• 2022

This study explores pre-service secondary mathematics teachers (PSTs)' noticing competency. 17 PSTs participated in this study as a part of the mathematics teaching method class. Individual PST's essays regarding the question 'what effective mathematics teaching would be?' that they discussed and wrote at the beginning of the course were collected as the first data. PSTs' written analysis of an expert teacher's teaching video, colleague PSTs' demo-teaching video, and own demo-teaching video were also collected and analyzed. Findings showed that most PSTs' noticing level improved as the class progressed and showed a pattern of focusing on each key aspect in terms of the Teaching for Robust Understanding of Mathematics (TRU Math) framework, but their reasoning strategies were somewhat varied. This suggests that the TRU Math framework can support PSTs to improve the competency of 'what to attend' among the noticing components. In addition, the instructional reasoning strategies imply that PSTs' noticing reasoning strategy was mostly related to their interpretation of noticing components, which should be also emphasized in the teacher education program.

• Journal of The Korean Association For Science Education
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• v.37 no.4
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• pp.553-564
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• 2017

This study investigated the change of pre-service elementary teachers' professional visions through video-based reflection on science teaching with focus on their attention and pedagogical reasoning about student learning. Specifically, we compared two reflection cycles before and after pre-service elementary teachers went through the collaborative video-based reflection process in a professional learning community. The primary data were collected from eight pre-service elementary teachers and included their science lesson plans, videotaped lessons, video-reflection papers, and transcripts from the interviews. Pre-service elementary teachers' attention was categorized in five aspects: classroom management & control, teacher's instruction, students' thinking & learning, subject knowledge, and assessment. The level of their pedagogical reasoning about student thinking and learning was determined with six levels based on the number of evidence, evidence area, and evidence type. The findings revealed that 1) individual reflection is not enough - collaborative reflection is essential to change their attention toward students learning and thinking 2) pedagogical reasoning levels increase gradually throughout the individual and collaborative video-based reflection processes. The participants not only attributed student learning solely to the characteristics of students but also connected it with their own instruction or science content knowledge and used different types of evidences as they went through two reflection cycles. Implications for using video in the teacher education program were discussed.

• Journal of the Korean School Mathematics Society
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• v.22 no.4
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• pp.415-438
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• 2019

The purpose of this study is to examine what aspects of mathematical activities in elementary school mathematics textbooks pre-service school teachers pay attention to in the process of didactic transposition. To do this, the third grade students of the College of Education were asked to analyze the activities of the elementary mathematics textbooks and then select a lesson activities as needed to modify or supplement the activities. As a result of the study, in the process of revising textbook activities for mathematics lessons, pre-service teachers pay attention to whether the textbook activities provide concrete activities, whether they induce student motivation, and whether there is overlap between classes activities. For the didactic transposition of textbook activities for mathematics lessons, pre-service teachers were able to comprehensively utilize relevant curriculum documents such as national curriculum and teachers' manual for checking the goals and achievement standards and lesson objectives.

• The Mathematical Education
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• v.60 no.3
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• pp.297-319
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• 2021

The present study explored a relationship between mathematical understandings of teachers and ways in which their knowledge transferred in designing lessons for hypothetical students from Gess-Newsome (1999)'s transformative perspective of pedagogical content knowledge. To this end, we conducted clinical interviews with four secondary mathematics teachers of their solving and teaching of equation writing. After analyzing the teacher participants' attention to Key Developmental Understandings (Simon, 2007) in solving equation writing, we sought to understand the relationship between their mathematical knowledge of the problems and mathematical knowledge in teaching the problems to hypothetical students. Two of the four teachers who attended the key developmental understandings solved the problems more successfully than those who did not. The other two teachers had trouble representing and explaining the problems, which involved reasoning with improper fractions or reciprocal relationships between quantities. The key developmental understandings of all four teachers were reflected in their pedagogical actions for teaching the equation writing problems. The findings contribute to teacher education by providing empirical data on the relationship between teachers' mathematical knowledge and their knowledge for teaching particular mathematics.