• 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.

• 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.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.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.

• 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.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.

• 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.

• 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.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.