• 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.

• 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.

• 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.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.

• School Mathematics
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• v.14 no.4
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• pp.495-516
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• 2012

This study distinguished thinking related to statistical variability into six components - the noticing of variability, the explanation of variability, the control of variability, the modeling of variability, the understanding of samples, and the understanding of sampling distribution and investigated the relationships among the thinking components. This study found that this distinction of thinking components related to statistical variability is reasonable. The results showed that each correlation coefficient of the modeling of variability, the understanding of samples, and the understanding of sampling distribution with regard to the noticing of variability, the explanation of variability, and the control of variability is similar. Based on this results, new variable, the understanding of sampling, has been drawn. The results also showed that while the noticing of variability and the control of variability influence the understanding of sampling, the explanation of variability does not influence it.

• 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.

• 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.

• The Journal of the Korea Contents Association
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• v.22 no.10
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• pp.426-436
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• 2022

This study aimed to explore the role of models and reformulations as feedback to English writing in L2 learners' noticing and their writing. 92 participants were placed into three groups; a models group (MG), a reformulations group (RG), a control group (CG), involved in a three-stage writing task. In stage 1, they were asked to perform a 1st draft of writing, while taking notes on the problems they experienced. In stage 2, the MG was asked to compare their writing with a model text and the RG with a reformulated version of it. They were instructed to write down whatever they noticed in their comparison. The CG was asked to just read their writing. In stage 3, all the participants attempted subsequent revisions. The results indicated that all the participants noticed problematic linguistic features the most in a lexical category, and models and reformulations led to higher rate of noticing the problematic linguistic features reported in stage 1 and contributed to subsequent revisions. It was also revealed that the MG and RG significantly improved with their writings of MG and RG on the post-writing test. The findings imply that models and reformulations result in better performance in L2 writing and should be promoted in an English writing class.

• Child Health Nursing Research
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• v.21 no.2
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• pp.160-167
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• 2015

Purpose: This study was done to evaluate the Lasater Clinical Judgement Rubric for use with Korean nursing students. Methods: A methodological study was used to validate the rubric developed by Lasater to assess clinical judgment during nursing simulation. Participants were 34 nursing students at K University in Seoul. Between February and May, 2012, analysis was done of 91 video clips recording performance during simulation. Results: Findings showed reliability and validity of the rubric. For internal consistency, Cronbach's ${\alpha}$ score was .884 and intraclass correlation coefficient was .839, which established reliability. The rubric was validated using the exploratory factor analysis and content validity. The content validity score was 83%, establishing the appropriateness and readiness of the tool. Factor analysis showed that noticing, responding, and reflecting domains had Eigen values of 2.669, 1.991, and 2.912, respectively and were bound, but unlike the original tool in which four factors noticing, interpretation, responding, and reflecting domains were bound. Conclusion: Results of the study indicate that the rubric shows acceptable reliability and validity in Korean nursing students. This evaluation tool for nursing simulation allows nursing faculty to objectively evaluate students' clinical judgment as well as students to reflect on their clinical judgment process during simulation.

• 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.