• 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.

• Research in Mathematical Education
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• v.25 no.1
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• pp.91-97
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• 2022

Competent mathematics teachers need to implement the responsive teaching strategy to use student thinking to make instructional decisions. However, the responsive teaching strategy is difficult to implement, and limited research has been conducted in traditional classroom settings. Therefore, we need a better understanding of responsive teaching practices to support mathematics teachers adopting and implementing them in their classrooms. Responsive teaching strategy is connected with teachers' noticing practice because mathematics teachers' ability to notice classroom events and student thinking is connected with their interaction with students. In this regard, this review introduced and examined a study of the relationship between mathematics teachers' noticing and responsive teaching: In the context of teaching for all students' mathematical thinking conducted by Kim et al. (2017).

• Research in Mathematical Education
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• v.23 no.2
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• pp.93-111
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• 2020

The purpose of this study was to examine mathematics teachers' perceptions of multicultural education. To achieve this goal, the study explored how 10 elementary mathematics teachers noticed multicultural content in a mathematics textbook. Building upon noticing framework (Jacobs, Lamb, & Philipp, 2010), we first examined teachers' attention toward multicultural content in a mathematics textbook. Then, we examined teachers' interpretation of the content. We employed a content analysis approach to examine the collected data. The results indicated that most mathematics teachers held a content integration perspective. Their view was that "multicultural education" referred to learning about the diverse cultures of different countries. Moreover, although they noticed some multicultural content in the textbook, they wanted to discuss them in superficially descriptive ways and avoid talking about social justice issues. Additionally, some teachers believed that mathematics is a culture-free subject. They argued that multicultural content should not be presented in mathematics textbooks. We also discussed uncommon themes, which were reported by only a few mathematics teachers.

• Education of Primary School Mathematics
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• v.24 no.2
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• pp.83-102
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• 2021

Curricular noticing is about how teachers understand the content and pedagogical opportunities inherent in curriculum materials. Since the enacted curriculum differs depending on which aspect of the curriculum material is paid attention to and how to interpret it, it is necessary to focus on Curricular Attending and Curricular Interpreting in Curricular Noticing for enhancing the teaching expertise of preservice teachers. First, this study categorized the objects that preservice elementary mathematics teachers attended when planning the lesson for rate. Second, in order to find out the reason for paying attention to those objects, it was analyzed what factors were related to interpret. By discussing the results, implications were drawn on how to use Curricular Noticing in preservice teacher education to enhance the pedagogical design competency of preservice elementary mathematics teachers.

• Research in Mathematical Education
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• v.26 no.2
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• pp.105-120
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• 2023

With the rapid advancement of educational technology, recent studies have connected teachers' professional noticing with the use of digital resources in mathematical instructions. In this study, I examined elementary mathematics preservice teachers' attending and interpreting a mathematical software, ST Math, in the exploring and implementing phases. The findings indicate that preservice teachers paid attention to visual representations and manipulation prior to interactions with children and further took into consideration on task structures and situated context after interactions. They interpreted the events based on connected mathematical knowledge of prior interactions and further reflected on the progression of problem-solving strategies and sequence of tasks. In addition, four distinctive profiles of transitioning of evaluation on ST Math activities were identified with illustrations. Implications for noticing and teacher education were discussed.

• 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.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.

• Research in Mathematical Education
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• v.23 no.4
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• pp.181-217
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• 2020

This study explores how pre-service teachers (PSTs) view, interpret, and utilize non-textual elements (NTEs) in mathematics curriculum. Fifty-two PSTs, who enrolled in a mathematics methods course at a Midwestern university in the U.S., engaged in a three-part task that consisted of evaluations and modifications of NTEs in the sample mathematics curriculum materials. We ascertain what PSTs consider to be the strengths and weaknesses of NTEs, how they define the primary goals of NTEs, and how they would work to modify or adapt existing NTEs with effective teaching in mind. By using the Curricular Noticing Framework, we can better understand how PSTs recognize opportunities within mathematics curriculum and gain a deeper understanding regarding how PSTs' prior experiences may affect their curricular-attending habits, which has consequences for their future teaching. Findings indicate that PSTs understand NTEs to be simply a support for traditional mathematics curriculum, rather than tools on their own. Also, they tend to prefer NTEs that are familiar to them. From our findings, we draw implications for teacher educators who support PSTs' interpretation and utilization of NTEs.

• 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 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.