• 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.

• 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.

• Communications of Mathematical Education
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• v.38 no.1
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• pp.69-92
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• 2024

This study analyzed students' mathematical noticing in high school sequence classes based on students' two perceptions of sequence. Specifically, mathematical noticing was analyzed in four aspects: center of focus, focusing interaction, task features, and nature of mathematics activities, and the following results were obtained. First of all, the change pattern of central of focus could not be uniquely described by any one component among 'focusing interaction', 'task features', and 'the nature of mathematical activities'. Next, the interactions between the components of mathematical noticing were identified, and the teacher's individual feedback during small group activities influenced the formation of the center of focus. Finally, students showed two different modes of reasoning even within the same classroom, that is, focusing interaction, task features, and nature of mathematics activities that resulted in the same focus. It is hoped that this study will serve as a catalyst for more active research on students' understanding of sequence.

• 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.

• Journal of the Korean School Mathematics Society
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• v.25 no.4
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• pp.423-446
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• 2022

This study explores and compares Korean and U.S. elementary preservice teachers' analytic approaches of students' addition and subtraction computational strategies. Twenty-six Korean and twenty U.S. elementary preservice teachers participated in the study. Participants were asked to analyze mathematical approaches and errors from students' addition and subtraction operations. Preservice teachers' written documents were analyzed by applying open coding and inductive coding based on the grounded theory. As a result, the pattern of error analysis and interpretation of students' addition computations were similar for both Korean and U.S. preservice teachers whereas there were some differences in the analysis of students' subtraction computations. Both Korean and U.S. preservice teachers had difficulties identifying students' strategies and errors for a complicated and unconventional computational approach. Results also indicated that preservice teachers' noticing and interpretation of students' strategies and errors were influenced by their K-12 mathematics curriculum and teacher education program. This study suggests implications and future directions for teacher education, more contextualized teacher preparation programs and balanced connection to the K-12 curriculum.

• Journal of The Korean Association For Science Education
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• v.43 no.2
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• pp.167-180
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• 2023

Teacher interventions in science classrooms are important because they can have a major impact on students' practices. This study qualitatively analyzed what kinds of utterances teachers used to intervene in students' practices of constructing scientific explanations. Two elementary school teachers, L and K, participated in the study, and their lessons in the sixth-grade science unit, 'Structure and Function of Plants' were reorganized for students to engage in the scientific practice of constructing explanations. In each lesson, the two teachers were asked to support students' practices as part of responsive teaching. The results of the study showed that the two teachers mainly utilized empathetic and disciplinary utterances, respectively, which were used to support emotional, processual, and conceptual aspects of students' scientific practices. The empathetic utterances were employed to support students' practices in the order of noticing, actively accepting, and offering alternatives. By contrast, the disciplinary utterances were used in the order of finding deficiencies, evaluating, and urging to improve students' practices. The reasons the teachers made use of empathetic and disciplinary utterances, respectively, were discussed, and implications for science education were suggested.

• Proceedings of the KSPS conference
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• 1997.07a
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• pp.228-229
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• 1997

1 Intonation is important. It cannot be ignored. To convince students of the importance of intonation, we can use sentences with two very different interpretations according to intonation. Example: "I thought it would rain" with a fallon "rain" means it did not rain, but with a fall on "thought" and a rise on "rain" it means that it did rain. 2 Although complex, intonation is structured. For both teacher and student, the big job of tackling intonation is made simpler by remembering that intonation can be analysed into systems and units. There are three main systems in English intonation: Tonality (division into phrases) Tonicity (selection of accented syllables) Tone (the choice of pitch movements) Examples: Tonality: My brother who lives in London is a doctor. Tonicity: Hello. How ARE you. Hello. How are YOU. Tone: Ways to say "Thank you" 3 In deciding what to teach, we must distinguish what is universal from what is specifically English. This is where contrastive studies of intonation are very valuable. Usually, for instance, division into phrases (tonality) works in broadly similar ways across languages. Some uses of pitch are also similar across languages - for example, very high pitch may signal excitement or urgency. 4 Although most people think that intonation is mainly about pitch (the tone system), actually accent placement (tonicity) is probably the single most important aspect of English intonation. This is because it is connected with information focus, and the effects on interpretation are very clear-cut. Example: They asked for coffee, so I made them coffee. (The second occurrence of "coffee" must not be accented). 5 Ear-training is the beginning of intonation training in the VeL approach. First, students learn to identify fall vs rise vs fall-rise. To begin with, single words are used, then phrases and sentences. When learning tones, the fIrst words used should have unstressed syllables after the stressed syllable (Saturday) to make the pitch movement clearer. 6 In production drills, the fIrst thing is to establish simple neutral patterns. There should be no drama or really special meanings. Simple drills can be used to teach important patterns: Example: A: Peter likes football B: Yes JOHN likes football TOO A: Mary rides a bike B: Yes JENny rides a bike TOO 7 The teacher must be systematic and let learners KNOW what they are learning. It is no good using new patterns and hoping that students will "pick them up" without noticing. 8 Visual feedback of fundamental frequency with a computer display can help students learn correct patterns. The teacher can use the display to demonstrate patterns, or students can practise by themselves, imitating recorded models.

• Journal of The Korean Association For Science Education
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• v.35 no.6
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• pp.1031-1038
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• 2015

The list of words and the semantic structure that connects them have been important to the areas of psychology, psychoanalysis, linguistics, and education. Some researchers in constructivist perspectives of science education also have interests in the structure of science concepts expressed by science terminologies. The purpose of this paper was to investigate the test environment factors influencing the word association test as a method to identify students' semantic structures for science terminologies. We set up four variables that are possibly considered in recognizing a word as having scientific meaning. The four variables include: noticing whether stimulus words are science terminologies or not, presenting science terminologies and everyday words alternately, whether presider is science teacher or not, and whether students have learned the concepts or not. In comparing the test results of the experimental group and the control group, we have checked whether each variable influences the test result or not. Stimulus words included nine science terminologies containing both ordinary and scientific meanings, and subjects included 282 middle school students. The degree of recognizing science terminology as having scientific meaning was found to increase only when stimulus words were noticed as science terminologies. In the case of the remaining variables, there was no difference between the control group and the experimental group.