• 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.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.193-204
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• 2017

The purpose of the study was to investigate and develop a practical approach to integrating student-driven mathematical problems posing in mathematics instruction. A problem posing activity was performed during regular mathematics instruction. A total of 540 mathematical problems generated by students were recorded and analysed using systemic procedures and criteria. Of the problems, 81% were mathematically solvable problem and 18% were classified as error type problems. The Mathematically solvable problem were analysed and categorized according to the complexity level; 13% were of a high-level, 30% mid-level and 57% low-level. The error-type problem were classified as such within three categories: non-mathematical problem, statement or mathematically unsolvable problem. The error-type problem category was distributed variously according to the leaning theme and accomplishment level. The study has important implications in that it used systemic procedures and criteria to analyse problem generated by students and provided the way for integrating mathematical instruction and problem posing activity.

• Communications of Mathematical Education
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• v.16
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• pp.345-365
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• 2003

우리 나라 수학경시대회의 운영은 선발에 초점이 맞추어져 있어, 지속적인 교육 및 피드백이 결여되어 있고 단순히 경시대회성 기출문제만을 반복하여 출제하고 있는 실정이다. 그러므로 영재의 특성을 고려하고, 영재성을 키워주기 위해서는 무엇보다도 수학 창의적 문제해결력을 신장시켜줄 수 있는 학습 자료의 개발이 시급하다. 따라서 본 논문에서는 초등수학경시대회 기출문제와 시중에 출판되어 있는 경시대회 준비를 위한 학습자료를 분석하여, 일선 초등학교 현장에서 실시되고 있는 영재교육을 활성화시킬 수 있는 방안을 연구하는 데 목적이 있다.

• 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.

• Education of Primary School Mathematics
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• v.19 no.2
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• pp.143-160
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• 2016

Despite the recent increasing interest in classroom expertise of teachers for gifted there has been lack of research on exploring or analyzing the components of classes for gifted tailored to the characteristics of each subject matter Given this, this study looked for the components of performance domain of classes for gifted in mathematics and then analyzed one teacher's 12 lessons in terms of the components. The features of the lessons included the establishment of classroom atmosphere by considering the characteristics of mathematically gifted students, the introduction of or expansion to mathematically enriched tasks, promotion to mathematically higher thinking, and emphasis of mathematical pattern, connections, and utility. This study is expected for researchers to provide a practical case on how to analyze elementary classes for gifted in mathematics. It also helps teachers who teach gifted students to develop professional vision of mathematics instruction and to increase their classroom expertise.

• School Mathematics
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• v.10 no.2
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• pp.259-277
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• 2008

Conventional assessments only provide a single summary score that indicates the overall performance level or achievement level of a student in a single learning area. For assessments to be more effective, test should provide useful diagnostic information in addition to single overall scores. Cognitive diagnosis modeling provides useful information by estimating individual knowledge states by assessing whether an examinee has mastered specific attributes measured by the test(Embretson, 1990; DiBello, Stout, & Rousses, 1995; Tatsuoka, 1995). Attributes are skills or cognitive processes that are required to perform correctly on a particular item. By the results of this study, students, parents, and teachers would be able to see where a student stands with respect to mastering the attributes. Such information could be used to guide the learner and teacher toward areas requiring more study. By being able to assess where they stand in regard to the attributes that compose an item, students can plan a more effective learning path to be desired proficiency levels. It would be very helpful to the examinee if score reports can provide the scale scores as well as the skill profiles. While the scale scores are believed to provide students' math ability by reporting only one score point, the skill profiles can offer a skill level of strong, weak or mixed for each student for each skill.

• The Mathematical Education
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• v.63 no.1
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• pp.63-83
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• 2024

The purpose of this study is to analyze the mathematical connection components of the tasks included in the trigonometric ratio unit of 3rd grade middle school textbook based on the 2015 revised mathematics curriculum and investigate teachers' perceptions and practical measures regarding these components. To this end, we analyzed the characteristics of mathematical connection tasks included in the trigonometric ratio units in nine types of 3rd grade middle school mathematics textbooks, and we conducted a questionnaire survey and interviews with one in-service math teachers in pre interview and with two in-service math teachers in this interview to investigate their perceptions and practical measures. As a result of the study, the number of tasks with external connection in the trigonometric ratio unit were less than those of internal connection. In addition, in terms of teachers' perceptions and practical measures, the perspective of analyzing tasks with mathematical connections varied depending on the teacher's perspective, and the practical measures varied accordingly. These findings are significant in that they reveal the relationship between mathematical tasks, teacher perceptions and measures to foster effectively students' mathematical connections.

• School Mathematics
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• v.18 no.2
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• pp.397-423
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• 2016

Mathematics learning motivation is an important variable which is not only the primary goal of learning mathematics but also mediates the effects of the mathematics learning. Nevertheless, the present learning environment is full of impeding factors which reduce learners' motivation to learn mathematics and mathematical self-regulatory efficacy. The purpose of this study is to offer various suggestions for program to enhance and forster mathematics learning motivation based on empirical findings and theories on motivation, self-regulatory learning, regulatory focus, reducing academic stress and math anxiety. The concrete and practical ideas are suggested in terms of mathematical self-regulatory efficacy, learners' characteristics, learning task. The analysis of the effects revealed a positive effect on mathematical self-regulatory learning.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.295-322
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• 2021

This study was conducted for one semester through one group pretest-posttest design with 49 first-year middle school students to explore the effects of mathematics-centered STEAM class experiences on students' mathematical modeling abilities. The main results of this study are as follows: First, the results of the pre and post-mathematical modeling ability tests showed that the average score of posttest was improved compared to the pretest, and that the experiences of mathematics-centered STEAM classes provided in this study had a positive effect on improving the mathematical modeling ability of first-year middle school students. Second, STEAM classes were more effective in solving mathematical modeling problems that require students' creative and divergent thinking. Third, the content analysis of student responses for each subquestion showed that STEAM classes were especially more helpful in activating students' mathematical model construction and validating steps.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.3
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• pp.461-483
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• 2017

The ability to think mathematically and to reason inductively are basics of logical reasoning and the most important skill which students need to acquire through their Math curriculum in elementary school. For these reasons, we need to conduct an analysis in their procedure in inductive reasoning and find difficulties thereof. Therefore, through this study, I found parts which covered inductive reasoning in their Math curriculum and analyzed the abilities and characteristics of students in solving a problem through inductive reasoning.