• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.205-225
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• 2014

This study analyzed how two sixth graders recognized, generalized, and represented functional relationships in exploring geometric growing patterns. The results showed that at first the students had a tendency to solve the given problem using the picture in it, but later attempted to generalize the functional relationships in exploring subsequent items. The students also represented the patterns with their own methods, which in turn had an impact on the process of generalizing and applying the patterns to a related context. Given these results, this paper includes issues and implications on how to foster functional thinking ability at the elementary school.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.565-584
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• 2012

This study investigates how the GSP helps gifted and talented students understand geometric principles and concepts during the inquiry process in the generalization of the internal triangle, and how the students logically proceeded to visualize the content during the process of generalization. Four mathematically gifted students were chosen for the study. They investigated the pattern between the area of the original triangle and the area of the internal triangle with the ratio of each sides on m:n respectively. Digital audio, video and written data were collected and analyzed. From the analysis the researcher found four results. First, the visualization used the GSP helps the students to understand the geometric principles and concepts intuitively. Second, the GSP helps the students to develop their inductive reasoning skills by proving the various cases. Third, the lessons used GSP increases interest in apathetic students and improves their mathematical communication and self-efficiency.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.167-170
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• 2005

In the mobile environments for the vector map services, a map simplification work through the map generalization steps helps improve the readability of the map on a large scale. The generalization operations are various such as selection, aggregation, simplification, displacement, and so on, the formal operation algorithms have not been built yet. Because the algorithms require deep special knowledge and heuristic, which make it hard to automate the processes. This thesis proposes some map generalization algorithms specialized in mobile vector map services, based on previous works. We will show the detail to adapt the approaches on the mobile environment, to display complex spatial objects efficiently on the mobile devices which have restriction on the resources

• Journal of Korea Spatial Information System Society
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• v.4 no.1 s.7
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• pp.5-14
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• 2002

The generalization of geospatial data is an important way in deriving a new database from an original one. The generalization of a geospatial object changes not only its geometric and aspatial attributes but also results in propagation to other objects along their relationship. We call it generalization propagation of geospatial databases. Without proper handling of the propagation, it brings about an inconsistent database or loss of semantics. Nevertheless, previous studies in the generalization have focused on the derivation of an object by isolating it from others. And they have proposed a set of generalization operators, which were intended to change the geometric and aspatial attributes of an object. In this paper we extend the definition of generalization operators to cover the propagation from an object to others. In order to capture the propagation, we discover a set of rules or constraints that must be taken into account during generalization procedure. Each generalization operator with constraints is expressed in relational algebra and it can be converted to SQL statements with ease. A prototype system was developed to verify the correctness of extended operators.

• Korean Journal of Optics and Photonics
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• v.7 no.4
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• pp.305-313
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• 1996

Lens design method by using equivalent lenses was already introduced, but the method has a limitaion that all lenses should be in the air. Therefore, we often get improper solution in designing cemented lenses. In this study, the lens conversion from thick lens to equivalent lens and its reversal was generalized without any preconditions, and the third order aberration fomulrae were derived for the generalized equivalent lens system. The generalized equivalent lens conversion were applied to typical cemented doublet and triplet, and they show that the third order aberrations of the generalized equivalent lenses have better agreements with their corresponding thick lenses than the previous conversion method.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.158-160
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• 1998

지도 제작에 있어서, 기존의 구축된 대축척의 원천 데이터로부터 소축척의 목적 데이터를 추출해 냄으로 데이터 구축을 중복되지 않고 효율적으로 할 수 있게 하는 것을 지도 일반화라고 한다. 초기의 선을 단순화하는 알고리즘 개발과 향상에 대한 연구로부터, 최근에는 자동화를 위한 지식 기반 일반화 및 데이터 품질에 대한 많은 관심과 연구가 진행되고 있다. 최근에 지리 정보 시스템의 발전으로 다양한 공간 분석이 필요하고, 그 성능 향상을 위하여 위상 정보를 구축하게 된다. 그러므로, 본 논문에서는 위상 정보를 가진 원천 데이터 베이스에서, 일반화 연산자가 적용됨으로 발생하게 되는 위상 데이터의 손실과 불일치를 해결하기 위하여 일반화 연산자들이 위상 정보에 미치는 영향과 이를 해결하기 위한 규칙들을 제시한다. 그리고, 지도 일반화 과정에서 위상 정보의 일관성을 유지한 목적 데이터 베이스를 구축하는 시스템을 구현하는 것이 본 논문의 목적이다.

• Journal of the Korea Computer Graphics Society
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• v.4 no.2
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• pp.47-55
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• 1998

본 논문은 일반화된 원통(generalized cylinder)의 모양을 상호작용을 통해 조절할 수 있도록 하는 직접 제어 방법을 제시한다. 이 연구에서는 일반화된 원통을 단면을 이루는 B-스플라인 곡선이 B-스플라인 동작에 의해서 움직여 지나간 스윕(sweep) 곡면으로 해석한다. 만들어진 곡면은 주어진 단연 곡선들을 골격 곡선을 따라서 보간하는 NURBS 곡면으로 나타내어진다. 사용자가 일반화된 원통 곡면 위의한 점을 움직일 때, 단면의 모양과 해당하는 동작을 수정하여 일반화된 원통의 곡면이 사용자에 의해 움직여진 위치를 지나도록 변형시킨다. 곡면의 변형은 목표 추적 과정을 거쳐 이루어진다. 이 방법에 의해 구현된 시스템을 이용하여 실시간으로 일반화된 원통을 직접 제어를 통해 디자인 할 수 있다.

• Journal of the Korean Geographical Society
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• v.39 no.4
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• pp.633-642
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• 2004

This study tries to generalize the stream network by constructing rule-based modelling. A study on the map generalization tends to be concentrated on development of algorithms for modification of linear features and evaluations to the limited cartographic elements. Rule-based modelling can help to improve previous algorithms by application of generalization process with the results that analyzing mapping principles and spatial distribution patterns of geographical phenomena. Rule-based modelling can be applied to generalize various cartographic elements, and make an effective on multi-scaling mapping in the digital environments. In this research, nile-based modelling for stream network is composed of generalization rule, algorithm for centerline extraction and linear features. Before generalization, drainage pattern was analyzed by the connectivity with lake to minimize logical errors. As a result, 17 streams with centerline are extracted from 108 double-lined streams. Total length of stream networks is reduced as 17% in 1:25,000 scale, and as 29% in 1:50,000. Simoo algorithm, which is developed to generalize linear features, is compared to Douglas-Peucker(D-P) algorithm. D-P made linear features rough due to the increase of data point distance and widening of external angle. But in Simoo, linear features are smoothed with the decrease of scale.

• School Mathematics
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• v.10 no.1
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• pp.23-42
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• 2008

The purpose of this study was to describe characteristics of thinking in elementary gifted students' solutions to algebraic tasks. Especially, this paper was focused on the students' strategies to develop generalization while problem solving, the justifications on the generalization and metacognitive thinking emerged in stildents' problem solving process. To find these issues, a case study was conducted. The subjects of this study were four 6th graders in elementary school-they were all receiving education for the gifted in an academy for the gifted attached to a university. Major findings of this study are as follows: First, during the process of the task solving, the students varied in their use of generalization strategies and utilized more than one generalization strategy, and the students also moved from one strategy toward other strategies, trying to reach generalization. In addition, there are some differences of appling the same type of strategy between students. In a case of reaching a generalization, students were asked to justify their generalization. Students' justification types were different in level. However, there were some potential abilities that lead to higher level although students' justification level was in empirical step. Second, the students utilized their various knowledges to solve the challengeable and difficult tasks. Some knowledges helped students, on the contrary some knowledges made students struggled. Specially, metacognitive knowledges of task were noticeably. Metacognitive skills; 'monitoring', 'evaluating', 'control' were emerged at any time. These metacognitive skills played a key role in their task solving process, led to students justify their generalization, made students keep their task solving process by changing and adjusting their strategies.