• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.327-344
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• 2006

This study examined the proof levels and understanding of constituents of proving by three mathematically gifted 6th grade korean students, who belonged to the highest 1% in elementary school, through observation and interviews on the problem-solving process in relation to constructing a rectangle of which area equals the sum of two other rectangles. We assigned the students with Clairaut's geometric problems and analyzed their proof levels and their difficulties in thinking related to the understanding of constituents of proving. Analysis of data was made based on the proof level suggested by Waring (2000) and the constituents of proving presented by Galbraith(1981), Dreyfus & Hadas(1987), Seo(1999). As a result, we found out that the students recognized the meaning and necessity of proof, and they peformed some geometric proofs if only they had teacher's proper intervention.

• Proceedings of the Korea Multimedia Society Conference
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• 2000.11a
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• pp.428-431
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• 2000

웹 기반 교육은 웹을 수단으로 하여 지식을 생성·조직·전파하는 새로운 교육 방식으로 웹이 제공하는 상호작용성을 교육에 활용한다면 기존의 면대면 교육에서 부족했던 점을 보완할 수 있다. 본 논문에서는 웹을 수단으로 하는 웹 기반 교육의 학생 교수간 상호작용성을 활용하여 중학교 기하영역을 위한 웹 기반 코스웨어를 설계·구현하였다. 설계된 코스웨어는 기존의 독립형 컴퓨터를 기반으로 하는 멀티미디어 코스웨어의 한계성을 극복하고 학습자 중심의 능동적 참여 및 개별화 학습을 유도할 수 있는 장점을 지니며 중학 수학 교과 과정중 논증기하의 교수-학습효과를 극대화 할 수 있는 방안으로 평가된다.

• School Mathematics
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• v.15 no.2
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• pp.389-404
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• 2013

Researchers have suggested that students should be experienced in progress of geometric thinking set out in naive and intuitive level and deduced throughout gradual formalization rather than completed mathematics are conveyed to students for students' understanding. This study examined naive and intuitive thinking of students by investigating students' geometric problem solving without diagrams. The students showed these naive thinking: lack of recognition of relation between problem and conditions, use of intuitive judgement depending on diagrams, lacking in understanding of role of specific case, and use of unjustified assumption. This study suggests implication for instruction in geometry.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.431-450
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• 2007

A polygon is one of the main subjects of the geometry curriculum that is handled widely from the second-grade elementary school to middle school. In this research, we analyze second-grade middle school students' conceptions of the polygon that are revealed in the process of seeking the definition and the area of it given in a lattice worksheet.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.51-62
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• 2008

In the 7th-curriculum, only basic arithmetics of complex numbers have been taught. They are taught formally like literal manipulations. This paper analyzes mathematically essential relations between algebra of complex numbers and plane geometry. Historical analysis is also performed to find effective methods of teaching complex numbers in school mathematics. As a result, we can integrates this analysis with school mathematics by help of Viete's operations on right triangles. We conclude that teaching geometric interpretation of complex numbers is possible in school mathematics.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.435-452
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• 2016

This study was designed to explore students' instrumentalization in relation to the van Hiele's teaching method within a technology environment using GeoGebra. To carry out the study, a total of 4 lesson units was developed based on van Hiele teaching method for two slow learners in Gyeonggi province, Korea. The results of study were as follows. Instrumentalization of students was actualized from preparation, to adaptation, and to application stages. In preparation, and adaptation stages, depending on visualization, students used a trial-and-error method a lot, however in application stage the role of GeoGebra was just to check the solution of what they conjectured. Therefore, a teacher should prepare geometric tasks according to the processes of instrumentalization based on geometric teaching method. During instrumentalization and instrumentation of users, usage scheme(US) and instrumented action scheme(IAS) should be concrete.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.101-114
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• 2006

The content and method of geometry taught in secondary school is rooted in 'Elements' by Euclid. On the other hand, however, there are differences between the content and structure of the current textbook and the 'Elements'. The gaps are resulted from attempts to develop the geometry education. Specially, the content and method for the proportional relations of geometric figures has been varied. In this study, we reviewed the changes of the proportional relations of geometric figures with pedagogical point of view. The conclusion that we came to is that the proportional relations in incommensurable case Is omitted in secondary school. Teacher's understanding about the proportional relations of geometric figures is needed for meaningful geometry education.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.455-467
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• 2008

We need to reflect the establishment of meaning and level of 'proof and argumentation in middle school mathematics'. It should be considered as human activity through communication in community. Thus, we should design instruction from this standpoint. From this point of view, we had been operated 'Geometry Inquiry Class' aimed at middle school students in eighth grade for two years to improve current geometry class in middle school. In this study, we will observe how individual students' original proof schemes are developed and accepted to the class through the process of mutual negotiation between the teacher and students. The episode with four phases begins with the initial proof schemes students have offered. Through the negotiation of class participants, it gives birth to the proof scheme unique to the current geometry classroom. Why do we pay attention to the process? It is because we think that the value of this type of instruction lies in the process of communication and mutual understanding and mutual reference, not in the completeness of the final product. This is the very appropriate proof in the middle school mathematics classroom.

• Communications of Mathematical Education
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• v.12
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• pp.57-66
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• 2001

우리는 공간적인 패턴, 모양, 그리고 움직임의 세계-즉, 기하의 세계-에 살고 있다. 아동들은 그들의 환경에 자연스럽게 매혹되고, 보고, 듣고, 움직임으로써 계속해서 정보를 받아들이므로, 그들의 공간적인 능력은 일반적으로 수(數)기능을 능가하기도 한다. 이러한 차원에서 볼 때, 우리나라의 수학과 7차 교육과정에 공간 감각을 기르기 위한 내용이 새로이 추가되었다는 것은 아주 고무적인 일이라고 생각하며, 이와 관련하여 문헌 연구를 통해서 공간감각에 대한 개념을 살펴보고, 교육과정 및 교과서를 분석하여 공간감각을 길러줄 수 있는 내용을 체계화하며, 공간감각을 증진시킬 수 있는 교구 활용 방안을 제시하고자한다.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.359-370
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• 2004

제7차 교육과정에서 중요하게 여기는 자기주도적 학습을 이루기 위한 첫 걸음은 동기유발에 있다고 할 수 있다. 또한 지식기반 정보화 사회에서의 주된 화두는 창의력의 증진에 있다. 이러한 관점에서, 본 논문은 칠교판을 활용하는 수업모형을 제시하여 기하영역의 학습에서 동기유발의 소재로 삼고 이를 통하여 창의력의 증진을 도모하였다.