• Research in Mathematical Education
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• v.25 no.3
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• pp.171-173
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• 2022

• Research in Mathematical Education
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• v.2 no.1
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• pp.163-181
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• 1998

The paper deals with some aspects of early childhood geometry in the Czech Republic. Children's first geometrical experiences come from real life. In our opinion, there exist four types of geometrical experience which can be called the partition of space, the filling of space motion in space and the dimension of space. We distinguish three levels of the mathematical learning process: a spontaneous level, an operational level and a theoretical level.

• Research in Mathematical Education
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• v.1 no.2
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• pp.163-181
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• 1997

The paper deals with some aspects of early childhood geometry in the Czech Republic. Children's first geometrical experiences come from real life. In our opinion, there exist four types of geometrical experience which can be called the partition of space, the filling of space motion in space and the dimension of space. We distinguish three levels of the mathematical learning process: a spontaneous level, an operational level and a theoretical level.

• Bulletin of the Korean Chemical Society
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• v.11 no.6
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• pp.511-515
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• 1990

Ab initio calculations with MP3 and CISD method were performed for the FCO and $FCO^+$. The equilibrium geometry of FCO shows the reasonable agreement with experimental values. $FCO^+$ has a linear geometry with $R_{CF}=1.213\;and\;R_{CO}=1.118{\AA}$. The quadratic force constants of $FCO^+$ are 23.21 md ${\AA}^{-1}$ for CO stretch and 12.38 md ${\AA}^{-1}$ for CF stretch. The cubic force constants and the other molecular constants are also calculated.

• The Mathematical Education
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• v.44 no.2 s.109
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• pp.159-167
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• 2005

As the 7th mathematics curriculum reform in Korea was implemented with its goal based on Freudenthal's perspectives on mathematization theory, the research on the effect of mathematization has been become more significant. The purpose of this thesis is not only to find whether this foreign theory would be also applied effectively into our educational practice in Korea, but also to investigate how much important role teachers should play in their teaching students, in order that students accomplish the process of mathematization more effectively. Two case studies were carried out with two groups of middle-school students using qualitative-research method with the research instrument designed by the researcher. It was found that we could get the possibility of being able to apply effectively this theory even to our educational practice since the students engaged in their mathematization using the horizontal mathematization and the vertical mathematization in geometry. Also, it was mentioned that teachers' role was so important in guiding students' processes of mathematization, although mathematization is the teaching-learning theory, stimulating students' activities. Since the Freudenthal's mathematization applied in the thesis is so meaningful in our educational practice, we need more various research about this theory that helps students develope their mathematical thinking.

• The Mathematical Education
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• v.52 no.2
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• pp.149-161
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• 2013

This study was to focus on analyzing about the composition of storytelling in the first graders' math textbooks of the middle school, which were recently implemented. The textbooks published by three well known publishing companies were chosen and three graduate students had scored the frequency of the problems according to three types of storytelling. As the results, in areas of mathematics, Number & Operation(44.23%), Letters & Formula(44.53%), Function(46.53%), Probability(41.67%), Geometry(46.23%) showed to have storytelling in balance. The type of 'explosion of mathematical history(EMH)' was shown in geometry most, the type of 'connection to daily life(CDL)' in statistics most, and the type of integration of disciplines(ID)' in geometry most in 5 math areas. Among three types of storytelling, the type of EMH was shown fewer that other 2 types. If we develop more problems in this type, students would study mathematics in-depth according to Freudenthal's principle of historical reinvention.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2022.06a
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• pp.253-256
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• 2022

실사 영상 기반의 메타버스 환경을 구축하기 위한 다수의 카메라를 통한 영상 취득 및 부호화, 전송 기술이 활발히 연구되고 있고, 이를 위해 영상 압축 표준화 단체인 moving picture experts group (MPEG) 에서는 MPEG immersive video (MIV) 표준을 개발하였다. 하지만, 현재 널리 사용되는 가상 현실 영상을 스트리밍 가능한 장비의 연산 능력으로는 MIV 기반 몰입형 영상을 스트리밍 시 복호기 동기화 문제가 발생할 수 있다. 따라서 본 논문은 저사양 및 고사양 장비에서 적응적으로 복호기 개수를 조절 가능한 geometry packing 기법을 MIV 의 참조 소프트웨어인 test model for immersive video (TMIV)에서 구현한다. 제안하는 패킹 기법은 지오메트리 영상을 패킹하여 텍스쳐 영상과 같은 높이를 가지도록 한 후 각각 단일 서브픽쳐 (subpicture) 로 부호화한다. 이후 부호화된 서브픽쳐들에 적응적으로 비트스트림 병합이 적용되어 장비의 복호기 사양에 대응한다.

• The Mathematical Education
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• v.46 no.3
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.211-218
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• 2009

We investigate the multiple solutions for a suspending beam equation with jumping nonlinearity crossing three eigenvalues, with Dirichlet boundary condition and periodic condition. We show the existence of at least six nontrivial periodic solutions for the equation by using the finite dimensional reduction method and the geometry of the mapping.