• 한국학교수학회논문집
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• 제11권1호
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• pp.69-96
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• 2008

본 논문은 현행 중등수학에서 기하교육의 문제점을 인식하고 Freudenthal의 학습이론에 토대를 둔 수학화 활동에 적합한 학습자료의 개발 및 교수-학습활동에 따른 수학화 과정을 분석하는데 그 목적이 있다. 이를 위해 중학교 수학 8-나 단계 기하영역을 중심으로 Freudenthal의 학습 이론과 관련된 활동 중심의 학습자료와 van Hiele의 학습 단계 이론을 토대로 교수-학습 모형을 개발하여 수업에 적용한 후 수학화 활동의 효과를 분석한다.

• 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.

• 아동학회지
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• 제32권2호
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• pp.71-85
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• 2011

This study was carried out in order to better understand how cooperative learning effects the geometric understanding of young children. The geometry tasks used in the study included the geometric relationship between two dimensional shapes and three dimensional shapes, coordination, symmetry and transformation visualization and spacial reasoning. The subjects were composed of children aged five years and were taken from two kindergartens in a relatively new city close to Seoul. The experimental group of children the comparative learning in geometry. The comparative group of children were enrolled in a kindergarten that uses an the intergrated curriculum. The results indicated that cooperative learning impacted positively on the children's understanding of geometry. The specific results are as follows : The scores that the experimental acquired were higher in terms of p < .001 level. than the scores of the comparative group studying the geometric relationships between two dimensional shapes and three dimensional shapes, coordination, symmetry and transformation visualization & spacial reasoning.

• 과학교육연구지
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• 제47권3호
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• pp.263-272
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• 2023

예비교사가 비유클리드 기하학에서 수학적 정의를 이용한 이차곡선의 학습으로 유클리드 기하학의 다양한 개념을 어떻게 이해하고 활용할 수 있는지를 살펴본다. 본 연구에서는 D 대학교 수학교육과 3학년 수업에서 수학적 정의를 이용하여 택시기하, 민코프스키 거리공간과 같은 비유클리드 공간의 이차곡선 학습이 예비교사들에게 새로운 기하학적 개념을 습득하고 수용하는 능력 향상에 도움을 줄 수 있음을 보였다. 이러한 결과로부터 택시기하와 민코프스키 거리공간에서의 정의를 활용한 이차곡선 학습이 창의적이고 유연한 사고를 유도하여, 예비교사들의 유클리드 기하학 교육 전문성 향상에 기여할 것으로 기대된다.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.375-384
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• 2007

As teachings that use the ICT are more popular, many studies on the dynamic geometry environment(DGE) are under way. An important factor emphasized in the studies is to practical use learning activities of learners. In this study, we first define the learning history data in DGE. Second we develop a prototype of the DGE that is able to collect and analyze the learning history data automatically. The environment enables not only to grasp leaning history but also to create and manage new learning objects.

• 대한수학교육학회지:학교수학
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• 제4권2호
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• pp.283-296
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• 2002

In this study we tried to find the method of using the tangrams and the mosaic puzzles together for learning the elementary geometry in the Korean primary schools. The tangram and the mosaic puzzle activity-panels were developed and the activity-cards for them also were designed. The criteria to be used for the analyses of contents of the activity-cards were developed. We surveyed and analyzed the students' responses, A previous research had insisted that solely using the tangrams were not useful in learning about an obtuse-angled triangle in the elementary geometry (Welchman, 1999), but the combinative uses of the tangrams and the mosaic puzzles were found to extend the limits of the previous study in investigating the figures of the plain diagrams. Actually, the tangrams and the mosaic puzzles helped the students to learn the concepts of several elements of the plain diagrams such as 'angles', 'sides', and 'angular points', with students'operational comparison of the diagrams developed with them. They also provided useful clues in learning the relationship between the 'length' and the 'area' of the Plain diagrams. The students participated in the class with much activities, using the operational learning materials. They also comprehended the concepts and the principles of the elementary geometry more thoroughly, expressing their ideas in spoken or written languages through interactive communication. In conclusion, the tangram and mosaic puzzles can be used for learning the elementary geometry of the primary school level as motivative learning materials, helping students enhance diverse mathematical thinking and discover mathematical principles.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권2호
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• pp.177-186
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• 2004

In this paper, we introduce new functional definitions for school geometry based on DGS (dynamic geometry system) teaching-learning environment. For the vertices forming a geometric figure, we first consider the relationship between the independent vertices and dependent vertices, and using this relationship and educational considerations in DGS, we introduce functional definitions for the geometric figures in terms of its independent vertices. For this purpose, we design a new DGS called JavaMAL MicroWorld. Based on the needs of new definitions in DGS environment for the student's construction activities in learning geometry, we also design a new DGS based geometry curriculum in which the definitions of the school geometry are newly defined and reconnected in a new way. Using these funct onal definitions, we have taught the new geometry contents emphasizing the sequential expressions for the student's geometric activities.

• 한국초등수학교육학회지
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• 제14권2호
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• pp.401-420
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• 2010

본 연구는 공간추론활동을 통한 기하학습이 수학적 문제해결력과 수학적 태도에 미치는 효과를 알아보는데 목적이 있다. 이러한 연구 목적을 규명하기 위하여 서울특별시 소재의 초등학교 6학년 2개 반을 연구대상으로 선정하여 실험집단에는 공간추론활동을 통한 기하학습을, 비교집단에는 일반적인 기하학습을 실시하였다. 학습내용은 6학년 1, 2학기 단원에서 선정하였으며 이를 바탕으로 실험집단과 비교집단에 적용할 지도안, 활동지를 작성하여 4주 동안 11차시를 적용하였다. 그 결과, 공간추론활동을 통한 기하학습을 한 실험집단과 일반적인 기하학습을 한 비교집단의 사후 수학적 문제해결력에서 통계적으로 유의미한 차이가 존재하였다. 수학적 태도에서는 유의미한 차이는 보이지 않았지만 실험 집단 내에서는 실험 전에 비하여 실험 처치 후에 수학적 태도가 유의미하게 향상되었음을 알 수 있었다. 이와 같은 결과로부터, 공간추론활동을 통한 기하학습은 학생들의 분석력, 공간감각능력, 논리력을 향상시켜 이를 종합적으로 발휘해야 해결할 수 있는 수학적 문제해결력을 신장시키고 수학적 태도에 긍정적인 영향을 미친다는 것을 알 수 있었다.

• 한국컴퓨터그래픽스학회논문지
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• 제23권1호
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• pp.57-65
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• 2017

본 논문에서는 포인트 클라우드로 구성된 모델 내의 오류를 줄이고, 기하학적 형태를 복원하기 위한 사전 학습 방법을 제시한다. 이를 위해, 대상 모델과 유사한 형태 특징을 갖는 모델로부터 3차원 특징 정보를 추출하여 사전을 구성하고, 이를 통해 기하 복원을 수행한다. 본 연구에서 제시한 방법은 다음과 같이 세 단계로 구성된다. 첫째, 유사 모델로부터 기하 패치를 구성하는 단계, 둘째, 획득한 패치의 3차원 형태 특징을 학습하는 단계, 셋째, 학습된 사전을 이용하여 기하를 복원하는 단계이며, 최종적으로 원본 모델과 복원 결과의 오차를 계산하며, 복원 결과의 정확도를 확인한다.

• 한국학교수학회논문집
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• 제5권2호
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• pp.101-109
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• 2002

Among interactive dynamic geometry softwares, Cinderella has some merits on the accuracy of algorithms and compatibility with internet. In this paper we compare dynamic geometry softwares such as GSP, Cabri II, Cinderella briefly and we design a web based interactive learning materials using the exercise editor of Cinderella and some Java applets, and we propose a web based interactive teaching and learning model in which achievement test can be given by the clickings on the help icon.