• Communications of Mathematical Education
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• v.25 no.2
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• pp.451-472
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• 2011

In this paper we studied problem solving related with geometric interpretation of algebraic expressions. We analyzed algebraic expressions, related these expressions with geometric interpretation. By using geometric interpretation we could find new approaches to solving mathematical problems. We suggested new problem solving methods related with geometric interpretation of algebraic expressions.

• The Mathematical Education
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• v.42 no.4
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• pp.503-521
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• 2003

In this paper, we propose programs of geometry related courses for the department of mathematics education of teacher training universities. We suggest 4 courses, ‘Geometry I’, ‘Geometry II’, ‘Differential Geometry’, ‘Topology’ as geometry related courses in Shin et. al.(2003). Among those 4 courses, we state desirable direction of curricula on 3 courses, ‘Geometry I’, ‘Geometry II’, ‘Differential Geometry’ in this paper.

• School Mathematics
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• v.9 no.2
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• pp.197-222
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• 2007

The study aims to reflect the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands in the light of the results from recent researches in geometry education and the direction of geometry standards for school mathematics of the National Council of Teachers of Mathematics in order to induce implications for improving korean geometry curriculum and textbook series. In order to attain these purposes, the present paper reflects the history of elementary school geometry education in the Netherlands, sketches the elementary school geometry education based on the Realistic Mathematics Education in the Netherlands by reflecting general goals of the mathematics education, the core goals for geometry strand of the Netherlands, and geometry and spatial orientation strand of Dutch Pluspunt textbook series for the elementary school more concretely. Under these reflections on the documents, it is analyzed what is the characteristics of geometry strand in the Netherlands as follows: emphasis on realistic spatial phenomenon, intuitive and informal approach, progressive approach from intuitive activity to spatial reasoning, intertwinement of mathematics strands and other disciplines, emphasis on interaction of the students, cyclical repetition of experiencing phase, explaining phases, and connecting phase. Finally, discussing points for improving our elementary school geometry curriculum and textbook series development are described as follows: introducing spatial orientation and emphasizing spatial visualization and spatial reasoning with respect to the instruction contents, considering balancing between approach stressing on grasping space and approach stressing on logical structure of geometry, intuitive approach, and integrating mathematics strands and other disciplines with respect to the instruction method.

• Proceedings of the Korea Information Processing Society Conference
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• 2011.04a
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• pp.1441-1444
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• 2011

본 논문에서는 초등학교 교육과정에서 교육목표로 다루고 있는 창의성이라는 주제와 학교현장에서 초등학생들에게 쉽게 접목시킬 수 있는 교육용 프로그래밍 언어인 LOGO 프로그래밍과 프랙탈 기하이론을 초등학교 컴퓨터교육에 활용하기 위한 방안을 제시한다. 향후 컴퓨터교육과정은 알고리즘과 프로그래밍 영역이 포함될 예정이며, 이러한 알고리즘과 프로그래밍 교육에는 교육용 프로그래밍 언어 사용이 필수적이며 이의 활용에 대한 연구가 시급한 상황이다. LOGO 프로그래밍과 프랙탈을 함께 지도함으로서 규칙성, 반복성, 유사성, 닮음 등 수학적 개념을 쉽게 이해하는 것이 가능하므로, 이를 활용하여 초등학교 수학과 교육과정에서 반드시 학습해야 할 도형, 측정, 규칙성과 문제 해결 영역과 연계하여 지도하면 좋은 효과를 얻을 수 있을 것으로 기대된다.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.655-678
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• 2010

In the elementary mathematics, geometric education emphasize spatial sense and understandings of figures through development of intuitions in space. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and methods in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. First, we investigate visualization methods for plane problem solving and space problem solving respectively, and analyse in diagram form how progress understanding of figures and visualization process. Next, we derive constituent factor on visualization process, and make a check errors which represented by difficulties in visualization process. Through these analysis, this paper aims at deriving an influence of visualization on geometric problem solving in the elementary mathematics.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.89-112
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• 2017

In this study we have analyzed processes of generalization in which students have geometrically solved cubic equation $x^3+ax=b$, regarding geometrical solution of cubic equation $x^3+4x=32$ as examples. The result of this research indicate that students could especially re-interpret the geometric solution of the given cubic equation via dynamically understanding the variables in dynamic geometry environment. Furthermore, participants could simultaneously re-interpret the given geometric solution and then present a different geometric solutions of $x^3+ax=b$, so that the level of generalization could be improved. In conclusion, the study could provide useful pedagogical implications in school mathematics that the dynamic geometry environment performs significant function as a means of students-centered exploration when understanding variables and enhancing the level of generalization in problem solving.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.1-23
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• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Communications of Mathematical Education
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• v.16
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• pp.67-80
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• 2003

함수적 사고는 수학적 문제 해결에 있어 기본적인 사고이다. 함수적 사고에서는 변수 사이의 종속성 파악이 그 핵심이 된다. 이는 DGS 동적 기하의 동적(변화), 종속적(구성)이라는 특성에 잘 부합한다. 이에 우리는 동적 기하 환경에서 타당한 종속성 부여를 통해 primitive한 생성자를 알아보고, 이들의 조작과 역 조작, 합성 조작하는 과정을 통해 함수적 사고에 접근하는 방법을 연구해 보려 한다. 나아가 자취 기능을 이용함으로써 시각화를 통해 종속적 관계를 표현해 보고자 한다. 이것은 MicroWorld 환경에서 학습자가 스스로 대상을 구성하는 경험을 통해 함수적 사고를 자연스럽게 형성하도록 하는 것이 바람직하다는 관점에 바탕을 두고 있다.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.715-730
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• 2016

The purpose of this study is to analyze Descartes's point of view on the mathematical connection of algebra and geometry which help comprehend the traditional frame with a new perspective in order to access to unsolved problems and provide useful pedagogical implications in school mathematics. To achieve the goal, researchers have historically reviewed the fundamental principle and development method's feature of analytic geometry, which stands on the basis of mathematical connection between algebra and geometry. In addition we have considered the significance of geometric solving of equations in terms of analytic geometry by analyzing related preceding researches and modern trends of mathematics education curriculum. These efforts could allow us to have discussed on some opportunities to get insight about mathematical connection of algebra and geometry via geometric approaches for solving equations using the intersection of curves represented on coordinates plane. Furthermore, we could finally provide the method and its pedagogical implications for interpreting geometric approaches to cubic equations utilizing intersection of conic sections in the process of inquiring, solving and reflecting stages.