• 한국수학교육학회지시리즈C:초등수학교육
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• 제3권1호
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• pp.1-36
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• 1999

The case of four classrooms analyzed in this study point to many commonalities in the challenges of reforming mathematics teaching in Korea and the U. S. In both national contexts we have seen the need fur a clear distinction between implementing new student-centered social practices in the classroom, and providing significant new loaming opportunities for students. In particular, there is an important need to distinguish between attending to the social practices of the classroom and attending to students conceptual development within those social practices. In both countries, teachers in the less successful student-centered classes tended to abdicate responsibility fur sense making to the students. They were more inclined to attend to the literal statements of their students without analyzing their conceptual understanding (Episodes KA5 and UP 2). This is easy to do when the rhetoric of reform emphasizes student-centered social practices without sufficient attention to psychological correlates of those social practices. The more successful teachers tended to monitor the understanding of the students and to take proactive measures to ensure the development of that understanding (Episodes KO5 and UN3). This suggests the usefulness of constructivism as a model (or successful student-centered instruction. As Simon(1995) observed, constructivist teachers envision a hypothetical learning trajectory that constitutes their plan and expectation for students learning from the particular if the trajectory is being followed. If not, the teacher adjusts or supplements the task to obtain a more satisfactory result, or reconsider her or his assumptions concerning the hypothetical learning trajectory. In this way, the teacher acts proactively to try to ensure that students are progressing in their understanding in particular ways. Thus the more successful student-centered teacher of this study can be seen as constructivist in their orientation to student conceptual development, in comparison to the less successful student-centered teachers. It is encumbant on the authors of reform in Korea and the U. S. to make sure that reform is not trivialized, or evaluated only on the surface of classroom practices. The commonalities of the two reform endeavores suggest that Korea and the U. S. have much to share with each other in the challenges of reforming mathematics teaching for the new millennium.

• 한국수학교육학회지시리즈A:수학교육
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• 제42권5호
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• pp.637-646
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• 2003

Visual representation is very important topic in Mathematics Education since it fosters understanding of Mathematical concepts, principles and rules and helps to solve the problem. So, the purpose of this paper is to analyze and clarify the various meaning and roles about the visual representation. For this purpose, I examine the status of the visual representation. Since the visual representation has the roles of creatively mathematical activity, we emphasize the using of the visual representation in teaching and learning. Next, I examine the errors in relation to the visual representation which come from limitation of the visual representation. It suggests that students have to know conceptual meaning of the visual representation when they use the visual representation. Finally, I suggest some examples of problem solving via the visual representation. This examples clarify that the visual representation gives the clues and solution of problem solving. Students can apprehend intuitively and easily the mathematical concepts, principles and rules using the visual representation because of its properties of finiteness and concreteness. So, mathematics teachers create the various visual representations and show students them. Moreover, mathematics teachers ask students to design the visual representation and teach students to understand the conceptual meaning of the visual representation.

• 한국학교수학회논문집
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• 제15권1호
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• pp.1-25
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• 2012

본 연구는 Freudental의 수학관에 근거한 RME가 표방하는 현실 속 풍부한 맥락적 상황들로 이루어진 관점으로 초등학교 4학년 교과서를 중심으로 한국 및 미국(3종) 교과서에서 제시된 문제의 맥락성을 살펴보았다. 이를 위해 맥락성의 요소를 일상성, 다양성, 수학적 잠재성으로 도출하여 맥락문제를 분류하여 분류된 문제를 비교 분석하였다. 그 결과 한국 교과서는 미국 교과서에 비해, 맥락문제가 차지하는 비율 뿐 아니라, 과정별 맥락성이 모두 낮게 나타났다. 또한 각 요소별 성향을 잘 나타내고 있는 문항을 분석, 기술함으로써 추후 교과서 개발 뿐 아니라, 문항 개발에 의미 있는 자료를 제공할 것으로 기대한다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.205-215
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• 2006

One of the most important concepts in the 7th curriculum of Korea is the student-centered education. Since educational evaluation has significant influence on the whole curriculum, if we realize the importance of the student-center education on the curriculum we should establish the student-centered educational evaluation system. Educational evaluation is defined by the theory of information to permit information users to identify, to measure, to manipulate and to communicate useful educational information concerning an educational curriculum for making decisions. If we accept the above definitions, the demands of information users are significant in the light of conceptual framework of educational evaluation. The purpose of this study is to analyze the conceptual framework of educational evaluation from information users' perspectives and to investigate the qualitative characteristics which satisfy information users' need for making decisions. We also show that students aren't provided sufficient evaluation results information to decide for their study plans by analyzing an evaluation study of the 7th primary curriculum. Finally, this study suggests how to improve an evaluation system for students in mathematics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권3호
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• pp.201-225
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• 2022

This paper details case study vignettes that focus on enhancing the teaching and learning of geometry and measurement in the elementary grades with attention to pedagogical practices for teaching through problem solving with rigor and centering equitable teaching practices. Rigor is a matter of equity and opportunity (Dana Center, 2019). Rigor matters for each and every student and yet research indicates historically disadvantaged and underserved groups have more of an opportunity gap when it comes to rigorous mathematics instruction (NCTM, 2020). Along with providing a conceptual framework that focuses on the importance of equitable instruction, our study unpacks ways teachers can leverage their deep understanding of geometry and measurement learning trajectories to amplify the mathematics through rigorous problems using multiple approaches including learning by doing, challenged-based and mathematical modeling instruction. Through these vignettes, we provide examples of tasks taught through rigorous problem solving approaches that support conceptual teaching and learning of geometry and measurement. Specifically, each of the three vignettes presented includes a task that was implemented in an elementary classroom and a vertically articulated task that engaged teachers in a professional learning workshop. By beginning with elementary tasks to more sophisticated concepts in higher grades, we demonstrate how vertically articulating a deeper understanding of the learning trajectory in geometric thinking can add to the rigor of the mathematics.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권2호
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• pp.197-219
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• 2008

Unlike ordinary situations, deifinitions play a very important role in mathematics education in schools. Mathematical concepts have been mainly acquired by given definitions. However, according to didactical intentions, mathematics education in schools has employed mathematical concepts and definitions with less strict forms than those in pure mathematics. This research mainly discusses definitions used in geometry (promising) course in primary schools to cope with possibilities of creating misconception due to this didactical transformation. After analyzing problems with potential misconceptions, a survey was conducted $\underline{with}$ 80 primary school teachers in Jeju to investigate their recognitions in meaning of mathematical concepts in geometry and attitudes toward teaching. Most of the respondents answered they taught their students while they knew well about mathematical definitions in geometry but the respondents sometimes confused mathematical concepts of polygons and circles. Also, they were aware of problems in current mathematics textbooks which have explained figures in small topics (classes). Here, several suggestions are proposed as follows from analyzing teachers' recognitions and researches in mathematical viewpoints of definitions (promising) in geometric figures which have been adopted by current mathematics textbooks in primary schools from the seventh educational curriculum. First, when primary school students in their detailed operational stage studying figures, they tend to experience $\underline{a}$ collision between concept images acquired from activities to find out promising and concept images formed through promising. Therefore, a teaching method is required to lessen possibility of misconceptions. That is, there should be a communication method between defining conceptual definitions and Images. Second, we need to consider how geometric figures and their elements in primary school textbooks are connected with fundamental terminologies laying the foundation for geometrical definitions and more logical approaches should be adopted. Third, the consistency with studying geometric figures should be considered. Fourth, sorting activities about problems in coined words related to figures and way and time of their introductions should be emphasized. In primary schools mathematics curriculum, geometry has played a crucial role in increasing mathematical ways of thoughts. Hence, being introduced by parts from viewpoints of relational understanding should be emphasized more in textbooks and teachers should teach students after restructuring this. Mathematics teachers should help their students not only learn conceptual definitions of geometric figures in their courses well but also advance to rigid mathematical definitions. Therefore, that's why mathematics teachers should know meanings of concepts clearly and accurately.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제8권2호
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• pp.81-93
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• 2004

This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

• 대한수학교육학회지:수학교육학연구
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• 제16권2호
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• pp.157-177
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• 2006

비와 비례 개념은 독립적으로 발달하는 것이 아니다. 오히려 이런 개념은 곱셈적 개념 장의 일부분으로 서로 관련을 가지면서 발달하게 된다. 곱셈적 개념 장에는 곱셈, 나눗셈, 분수, 비, 유리수와 같은 개념을 포함한다. 본 연구에서는 이런 개념의 발달 과정이 어떻게 시작하는가를 알아보기 위한 목적으로, 한 초등학교 4학년 아동을 대상으로 비례추론 과제를 해결하는 실험 수업을 실행하였다. 연구를 통해 이 아동이 비형식적 전략을 전개하면서 어떤 도전에 직면하였는지 그리고 비와 비례 개념을 전개하면서 어떤 수학적 지식이 유용하였는지를 분석할 수 있었다. 이러한 연구 결과는 비와 비례 개념의 발달은 곱셈적 개념 장의 발달과 깊은 관계가 있다는 기존의 입장을 지지하는 것으로 나타났다.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.83-98
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• 2014

We reformulate an interpolation-based unique decoding algorithm of AG codes, using the theory of Gr$\ddot{o}$bner bases of modules on the coordinate ring of the base curve. The conceptual description of the reformulated algorithm lets us better understand the majority voting procedure, which is central in the interpolation-based unique decoding. Moreover the smaller Gr$\ddot{o}$bner bases imply smaller space and time complexity of the algorithm.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제2권1호
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• pp.5-12
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• 1998

The COM curriculum provides first a core of mathematics for all students, and then offers opportunities for students to enter different streams of mathematics studies. The flexible curriculum (COM) is certainly welcome as it focuses on a transition from concrete to conceptual mathematics and on sequentially learning the power of mathematical language and symbols from simple to complex. This approach emphasizes the use of computers in mathematics education in the upper secondary grades. In Mathematics A, one unit is developed to computer operation, flow charts and programming, and computation using the computer. In mathematics B, a chapter addresses algorithms and the computer where students learn the functions of computers, as well as programs of various algorithms. Mathematics C allots a chapter for numerical computation in which approximating solutions for equations, numerical integration, mensuration by parts, and approximation of integrals. But, unfortunately, they do not have any plan for the cooperation study.