• KSII Transactions on Internet and Information Systems (TIIS)
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• v.3 no.1
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• pp.5-25
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• 2009

In recent years the popularity of multi-hop wireless networks has been growing. Its flexible topology and abundant routing path enables many types of applications. However, the lack of a centralized controller often makes it difficult to design a reliable service in multi-hop wireless networks. While packet routing has been the center of attention for decades, recent research focuses on data discovery such as file sharing in multi-hop wireless networks. Although there are many peer-to-peer lookup (P2P-lookup) schemes for wired networks, they have inherent limitations for multi-hop wireless networks. First, a wired P2P-lookup builds a search structure on the overlay network and disregards the underlying topology. Second, the performance guarantee often relies on specific topology models such as random graphs, which do not apply to multi-hop wireless networks. Past studies on wireless P2P-lookup either combined existing solutions with known routing algorithms or proposed tree-based routing, which is prone to traffic congestion. In this paper, we present two wireless P2P-lookup schemes that strictly build a topology-dependent structure. We first propose the Ring Interval Graph Search (RIGS) that constructs a DHT only through direct connections between the nodes. We then propose the ValleyWalk, a loosely-structured scheme that requires simple local hints for query routing. Packet-level simulations showed that RIGS can find the target with near-shortest search length and ValleyWalk can find the target with near-shortest search length when there is at least 5% object replication. We also provide an analytic bound on the search length of ValleyWalk.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.12
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• pp.30-45
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• 2014

Recently, multimedia application users who demand for ubiquitous computing environment are rapidly increasing, and wireless mesh network is receiving attention as a cost-effective key technology for next generation wireless networking. When multiple flows are transmitting data at the same time in the network, routing for path selection of each flow and link resource allocation for data transmission of each flow are one of the key factors that influence to the effectiveness of the network directly. In this paper, we consider problems for path discovery and resource allocation of links at the same time and we propose an algorithm based on mathematical modeling using a technique for cross-layer optimization design in STDMA-based wireless mesh networks that can enhance transfer performance for each flow. We show by performance analysis that the proposed algorithm can enhance the throughput performance by maximally utilizing given bandwidth resources when the number of flows increase in multi-hop wireless mesh networks.

• Journal of the Korean School Mathematics Society
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• v.4 no.1
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• pp.91-101
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• 2001

Nowadays the number of students that is losing their interest as well as learning desire in mathematics is increasing because of lack of logical thought creative power and abstract expression that present-day mathematics requires by reason of discrepancy of extreme scholastic ability by speciality of mathematics. In these conditions, we reduce the number of learning depression by bringing about learning desire or learning interest on mathematics, and students learn effective learning methods to be voluntary learning of discovery themselves that studies basic concepts, principles, rules through logical thought of students to solve difference of scholastic ability, thus we assumed that debate studies through small group activities in ability group would be one of ways to improve learning power, so the results of our research are as follows; 1. Debate studies through small group activities were very effective because of reinforcing the achivement level of students. 2. By this learning method, an individual or cooperrative learning was fostered, and lively discussions were accomplished. And learning attitudes of students were changed by the extension of cooperative learning abilities through advices or by themselves. 3. A personal opinion is payed regard by accepting an individual idea in the process of making questions. Learners can correct wrong concepts in the process of correcting wrong answers. So if we apply above-mentioned studies with easy contents from the lower grades, the effectiveness would increase as learners go to the higher grade. According to the results of various researches as follows; "The teaching-learning method oriented coopperative debate studies is effective to find solutions to mathematical problems." If small group activities are applied in the educational situation to search the course of a desirable cooperation learning through small group activities to improve scholastic abilities for a discoverable problem-solving power. I think that the teaching-learning method oriented cooperative debate studies is one of the most desirable methods to increase the problem-solving ability.

• Journal of The Korean Astronomical Society
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• v.53 no.6
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• pp.161-168
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• 2020

We report the discovery of a giant exoplanet in the microlensing event OGLE-2017-BLG-1049, with a planet-host star mass ratio of q = 9.53 ± 0.39 × 10-3 and a caustic crossing feature in Korea Microlensing Telescope Network (KMTNet) observations. The caustic crossing feature yields an angular Einstein radius of θE = 0.52 ± 0.11 mas. However, the microlens parallax is not measured because the time scale of the event, tE ≃ 29 days, is too short. Thus, we perform a Bayesian analysis to estimate physical quantities of the lens system. We find that the lens system has a star with mass Mh = 0.55+0.36-0.29 M⊙ hosting a giant planet with Mp = 5.53+3.62-2.87 MJup, at a distance of DL = 5.67+1.11-1.52 kpc. The projected star-planet separation is a⊥ = 3.92+1.10-1.32 au. This means that the planet is located beyond the snow line of the host. The relative lens-source proper motion is μrel ~ 7 mas yr-1, thus the lens and source will be separated from each other within 10 years. After this, it will be possible to measure the flux of the host star with 30 meter class telescopes and to determine its mass.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.465-489
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• 2015

The purpose of this study is to suggest implications for the development and revision of future teaching materials for mathematically gifted students by using network text analysis of secondary mathematics materials. Subjects of the analysis were learning goals of 110 teaching materials in a gifted education center in science attached to a university from 2002 to 2014. In analysing the frequency of the texts that appeared in the learning goals, key words were selected. A co-occurrence matrix of the key words was established, and a basic information of network, centrality, centralization, component, and k-core were deducted. For the analysis, KrKwic, KrTitle, and NetMiner4.0 programs were used, respectively. The results of this study were as follows. First, there was a pivot of the network formed with core hubs including 'diversity', 'understanding' 'concept' 'method', 'application', 'connection' 'problem solving', 'basic', 'real life', and 'thinking ability' in the whole network from 2002 to 2014. In addition, knowledge aspects were well reflected in teaching materials based on the centralization analysis. Second, network text analysis based on the three periods of the Mater Plan for the promotion of gifted education was conducted. As a result, a network was built up with 'understanding', and there were strong ties among 'question', 'answer', and 'problem solving' regardless of the periods. On the contrary, the centrality analysis showed that 'communication', 'discovery', and 'proof' only appeared in the first, second, and third period of Master Plan, respectively. Therefore, the results of this study suggest that affective aspects and activities with high cognitive process should be accompanied, and learning goals' mannerism and ahistoricism be prevented in developing and revising teaching materials.

• Communications of Mathematical Education
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• v.27 no.1
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• pp.1-17
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• 2013

This work started with recent students' conception on Linear Algebra. We were trying to help their understanding of Linear Algebra concepts by adding visualization tools. To accomplish this, we have developed most of needed tools for teaching of Linear Algebra class. Visualizing concepts of Linear Algebra is not only an aid for understanding but also arouses students' interest on the subject for a better comprehension, which further helps the students to play with them for self-discovery. Therefore, visualizing data should be prepared thoroughly rather than just merely understanding on static pictures as a special circumstance when we would study visual object. By doing this, we carefully selected GeoGebra which is suitable for dynamic visualizing and Sage for algebraic computations. We discovered that this combination is proper for visualizing to be embodied and gave a variety of visualizing data for undergraduate mathematics classes. We utilized GeoGebra and Sage for dynamic visualizing and tools used for algebraic calculation as creating a new kind of visual object for university math classes. We visualized important concepts of Linear Algebra as much as we can according to the order of the textbook. We offered static visual data for understanding and studied visual object and further prepared a circumstance that could create new knowledge. We found that our experience on visualizations in Linear Algebra using Sage and GeoGebra to our class can be effectively adopted to other university math classes. It is expected that this contribution has a positive effect for school math education as well as the other lectures in university.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.1
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• pp.215-241
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• 2017

This study analyzed teachers' Pedagogical Content Knowledge (PCK) regarding the pedagogical aspect of the instruction of ratio and rate in order to look into teachers' problems during the process of teaching ratio and rate. This study aims to clarify problems in teachers' PCK and promote the consideration of the materialization of an effective and practical class in teaching ratio and rate by identifying the improvements based on problems indicated in PCK. We subdivided teachers' PCK into four areas: mathematical content knowledge, teaching method and evaluation knowledge, understanding knowledge about students' learning, and class situation knowledge. The conclusion of this study based on analysis of the results is as follows. First, in the 'mathematical content knowledge' aspect of PCK, teachers need to understand the concept of ratio from the perspective of multiplicative comparison of two quantities, and the concept of rate based on understanding of two quantities that are related proportionally. Also, teachers need to introduce ratio and rate by providing students with real-life context, differentiate ratios from fractions, and teach the usefulness of percentage in real life. Second, in the 'teaching method and evaluation knowledge' aspect of PCK, teachers need to establish teaching goals about the students' comprehension of the concept of ratio and rate and need to operate performance evaluation of the students' understanding of ratio and rate. Also, teachers need to improve their teaching methods such as discovery learning, research study and activity oriented methods. Third, in the 'understanding knowledge about students' learning' aspect of PCK, teachers need to diversify their teaching methods for correcting errors by suggesting activities to explore students' own errors rather than using explanation oriented correction. Also, teachers need to reflect students' affective aspects in mathematics class. Fourth, in the 'class situation knowledge' aspect of PCK, teachers need to supplement textbook activities with independent consciousness and need to diversify the form of class groups according to the character of the activities.