• 대한수학교육학회지:학교수학
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• 제9권2호
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• pp.197-222
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• 2007

본 연구는 최근 기하 교육 동향과 전미수학교사협의회에서 2000년대의 수학교육의 방향과 관련해서 제시한 기하 교육의 규준에 비추어 현실적 수학교육에 기초한 네덜란드의 초등학교 기하 교육과정에 대해 알아보고, 우리나라의 초등학교 도형 영역 지도를 위한 시사점을 제시하는 데 그 목적이 있다. 이런 목적을 달성하기 위해 네덜란드의 초등학교 기하 교육의 역사를 살펴보고, 네덜란드의 초등학교 기하 교육과정에 중요한 영향을 미치는 요소인 일반 목표와 기하 영역의 핵심 목표, RME에 기초한 네덜란드의 초등학교 수학 교과서의 지도 내용과 지도 방법의 특징을 살펴보았다. 그 결과 우리나라 도형 영역의 교육과정과 교과서 개발을 위해 논의할 문제로 지도 내용의 측면에서 공간 방향의 도입, 공간 시각화와 공간 추론의 강화, 지도방법의 측면에서 공간적 접근과 도형적 접근의 균형, 직관적 접근의 중시, 통합적 접근의 고려 등을 제안하였다.

• 대한수학교육학회지:수학교육학연구
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• 제26권1호
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• pp.47-62
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• 2016

수학적 창의성을 함양하는 것은 최근 개정된 수학과 교육과정들에서 계속 강조해온 목표중의 하나이다. 그러나 일반 학생들을 대상으로 수학적 창의성을 함양하는 것에 관련된 연구는 아직 충분하지 않은 실정이다. 창의적인 인간의 육성을 표방하는 현실적 수학교육 이론은 일반 학생들을 대상으로 하는 수학적 창의성 교육에 시사점을 제공할 수 있음에도, 이에 대한 구체적인 논의가 이루어지지 않았다. 이 글에서는 수학적 창의성 교육의 관점에서 현실적 수학교육 이론을 재음미하여 공교육을 통한 수학적 창의성 교육의 방안을 모색하는 것에 목표를 둔다. 연구 결과는 다음과 같다. 첫째, 수학화를 통해 수학적 창조를 경험하도록 할 수 있으며, 이 때 확실성을 추구하고 확실성을 창조하도록 기회를 제공할 필요가 있다. 둘째, 학생들이 상상에 의하여 현실이라고 느끼는 맥락에서 출발해야 수학적 창조의 기회를 제공할 수 있다. 셋째, 학생들이 모델링에 의하여 현실 맥락과 결합된 수학을 창조하도록 할 수 있다. 넷째, 모델링은 주어진 모델이 왜 모델인가를 이해하는 것, 곧 주어진 모델의 의미를 창조하는 것에서 출발한다. 다섯째, 사고실험에 의하여 국소적인 교수이론을 개발하고, 이를 적용한 후 개선하는 것이 수학적 창의성 교육의 연구방법으로 적합하다. 결론적으로, 수학적 창의성의 함양을 보통의 수학수업에서 일반 학생들을 대상으로 구현하는 데에 현실적 수학교육 이론에서 제안하는 모델은 적절하고 유용한 방안이 될 수 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제6권2호
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• pp.159-170
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• 2002

The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing developmental research effort to adapt the instructional design perspective of Realistic Mathematics Education (RME) to the teaching and learning of differential equations at Ewha Womans University. The RME theory based on the design heuristic using context problems and modeling was developed for primary school mathematics. However, the analysis of this study indicates that a RME design for a differential equations course can be successfully adapted to the university level.

• 한국수학교육학회지시리즈A:수학교육
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• 제44권3호
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• pp.375-396
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• 2005

This paper reports on the main results of 3 study that compared students' beliefs, skills, and understandings in an innovative approach to differential equations to more conventional approaches. The innovative approach, referred to as the Realistic Mathematics Education Based Differential Equations (IODE) project, capitalizes on advances within the discipline of mathematics and on advances within the discipline of mathematics education, both at the K-12 and tertiary levels. Given the integrated leveraging of developments both within mathematics and mathematics education, the IODE project is paradigmatic of an approach to innovation in undergraduate mathematics, potentially sewing as a model for other undergraduate course reforms. The effect of the IODE projection maintaining desirable mathematical views and in developing students' skills and relational understandings as judged by the three assessment instruments was largely positive. These findings support our conjecture that, when coupled with careful attention to developments within mathematics itself, theoretical advances that initially grew out research in elementary school classrooms can be profitably leveraged and adapted to the university setting. As such, our work in differential equations may serve as a model for others interested in exploring the prospects and possibilities of improving undergraduate mathematics education in ways that connect with innovations at the K-12 level

• 대한수학교육학회지:수학교육학연구
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• 제9권1호
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• pp.81-109
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• 1999

This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권1호
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• pp.49-59
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• 2008

In this paper, we discuss two representations of a curve. One is a static representation as set of points, the other is a dynamic representation using time parameter. And we suggest needs of designing a computer microword where we can represent a curve both statically and dynamically. We also emphasize the importance of translation activity from a static representation to a dynamic representation. For this purpose, we first consider constructionism and 'computers and mathematics education' as a theoretical backgrounds. We focus the curve of a parabola in this paper since this is common in mathematics curriculum and is related to realistic situation such as throwing ball. And we survey the mathematics curriculum about parabola representation. And we introduce JavaMAL microworld that is integrated microworld between LOGO and DGS. In this microworld, we represent a parabola using a dynamic action, and connect this dynamic parabola action to recursive patterns. Finally, we remake a parabola for a realistic situation using this dynamic representation. And we discuss the educational meaning of dynamic representation and its computer microworld.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제15권4호
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• pp.341-355
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• 2011

A research group consisting of some mathematics education scholars and school teachers has been formed to build a website which intended to combine both theories and practices of mathematical teaching since 2002. There were three working stages: video-tapping realistic math teaching, developing video discs of different themes, and designing e-Learning. The group members learned knowledge of teaching by actual participating. On the other hand, the products enabled the audience to get professional development in knowledge of both mathematics and teaching. Management process of this group and effects upon the participants and users will be presented and discussed in this paper. A research group consisting of some mathematics education scholars and school teachers has been formed to build a website which intended to combine both theories and practices of mathematical teaching since 2002. There were three working stages: video-tapping realistic math teaching, developing video discs of different themes, and designing e-Learning. The group members learned knowledge of teaching by actual participating. On the other hand, the products enabled the audience to get professional development in knowledge of both mathematics and teaching. Management process of this group and effects upon the participants and users will be presented and discussed in this paper.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2006년도 제36회 전국수학교육연구대회 프로시딩
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• pp.129-146
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• 2006

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제19권4호
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• pp.733-767
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• 2005

During the past decades, there has been a fundamental change in the objectives and nature of mathematics education, as well as a shift in research paradigms. The changes in mathematics education emphasize learning mathematics from realistic situations, students' invention or construction solution procedures, and interaction with other students of the teacher. This shifted perspective has many similarities with the theoretical . perspective of Realistic Mathematics Education (RME) developed by Freudental. The RME theory focused the guide reinvention through mathematizing and takes into account students' informal solution strategies and interpretation through experientially real context problems. The heart of this reinvention process involves mathematizing activities in problem situations that are experientially real to students. It is important to note that reinvention in a collective, as well as individual activity, in which whole-class discussions centering on conjecture, explanation, and justification play a crucial role. The overall purpose of this study is to examine the developmental research efforts to adpat the instructional design perspective of RME to the teaching and learning of differential equation is collegiate mathematics education. Informed by the instructional design theory of RME and capitalizes on the potential technology to incorporate qualitative and numerical approaches, this study offers as approach for conceptualizing the learning and teaching of differential equation that is different from the traditional approach. Data were collected through participatory observation in a differential equations course at a university through a fall semester in 2003. All class sessions were video recorded and transcribed for later detailed analysis. Interviews were conducted systematically to probe the students' conceptual understanding and problem solving of differential equations. All the interviews were video recorded. In addition, students' works such as exams, journals and worksheets were collected for supplement the analysis of data from class observation and interview. Informed by the instructional design theory of RME, theoretical perspectives on emerging analyses of student thinking, this paper outlines an approach for conceptualizing inquiry-oriented differential equations that is different from traditional approaches and current reform efforts. One way of the wars in which thus approach complements current reform-oriented approaches 10 differential equations centers on a particular principled approach to mathematization. The findings of this research will provide insights into the role of the mathematics teacher, instructional materials, and technology, which will provide mathematics educators and instructional designers with new ways of thinking about their educational practice and new ways to foster students' mathematical justifications and ultimately improvement of educational practice in mathematics classes.

• 한국초등수학교육학회지
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• 제11권2호
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• pp.99-115
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• 2007

본 연구의 목적은 현실적 맥락을 활용한 수학화 학습을 실제 현장에 적용하여 이러한 학습이 아동의 수학적 사고에 어떠한 효과를 나타내는지 알아보는 데에 있다. 이러한 연구 목적을 위해 서울시 D초등학교 5학년 2개 학급을 연구 대상으로 6주간 17차시에 걸쳐 실험이 이루어졌고, 실험 설계는 전후 검사 통제집단 설계를 하였다. 또한 1학기말 수학 학업 성취도 평가 결과를 기준으로 선정된 실험 집단의 상(30%), 하(30%) 집단 학생들을 대상으로 하여 시기별(전기-중기-후기)로 관찰, 질문지, 녹음, 활동지와 형성평가지 분석의 방법을 사용하여 현실적 맥락을 활용한 수학화 학습을 통해 나타난 아동의 수학화 과정이 어떠한지를 각 과정별로 분석하여 살펴보았다. 그 결과 현실적 맥락을 활용한 수학화 학습을 실시한 실험집단의 경우 수학의 방법 및 내용적 측면에서 나타난 수학적 사고에서 평균 점수가 비교 집단보다 향상되었고 통계적으로도 유의미한 차이가 나타났다. 또한 현실적 맥락을 활용한 수학화 학습을 실시한 수학 집단에서 수학화 과정의 4단계인 직관적 탐구, 수평적 수학화, 수직적 수학화, 응용적 수학화 각각의 과정에서 상 하위 집단별 학생들은 수업이 전기-중기-후기로 진행되어 갈수록 각 과정의 수학화가 더욱 활발히 일어났음을 알 수 있었다.