• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.45-61
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• 2009

The powerful role of analogical reasoning in discovering mathematics is well substantiated in the history of mathematics. Mathematically gifted students, thus, are encouraged to learn via in-depth exploration on their own based on analogical reasoning. In this study, 57 gifted students (31in the 7th and 26 8th grade) were asked to formulate or clarify analogy. Students produced fruitful constructs led by analogical reasoning. Participants in this study appeared to experience the deep thinking that is necessary to solve problems made with analogies, a process equivalent to the one that mathematicians undertake. The subjects had to reflect on prior knowledge and develop new concepts such as an orthogonal projection and a point of intersection of perpendicular lines based on analogical reasoning. All subjects were found adept at making meaningful analogues of a triangle since they all made use of meta-cognition when searching relations for analogies. In the future, methodologies including the development of tasks and teaching settings, measures to evaluate the depth of mathematic exploration through analogy, and research on how to promote education related to analogy for gifted students will enhance gifted student mathematics education.

• Journal of the Korea Institute of Military Science and Technology
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• v.2 no.1
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• pp.90-100
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• 1999

유전자 알고리즘은 전통적인 등반 알고리즘을 이용하여 구하기 어려웠던 최적화 문제를 해결하기 위한 강인한(Robust) 탐색 기법이다. 특히 목적함수가 (1)여러 개의 국부 최대치를 가지는 경우, (2)수학적으로 표현이 불가능하거나 어려운 경우, (3)목적함수에 교란 항(disturbance term)이 섞여 있을 경우도 우수한 탐색 능력을 갖는 것으로 알려져 있다. 본 논문에서는 유전자 알고리즘을 이용하여 나타나는 다양한 해집합을 형성하는 개체군을 군집성 분석(cluster analysis)을 이용하여 군집화하고, 각 군집에 부여된 군집 적합도에 따라서 최적해를 구함으로써 단순 유전자 알고리즘에 의한 최적화보다 훨씬 향상된 탐색 알고리즘을 제안하였다. 반응표면의 형태가 정형화한 테스트 함수의 형태로 나타난다고 가정한 경우에 대하여 몬테 칼로 시뮬레이션을 통하여 본 알고리즘을 적용하여 평가하고 분석하였다.

• Proceedings of the Korean Society of Computer Information Conference
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• 2011.06a
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• pp.225-228
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• 2011

창의성이 강조되는 시대에 영재 교육의 중요성은 점차 높아지고 있다. 그러나 정보 영재를 위한 연구는 수학이나 과학 영재에 비해 미미한 수준이며, 특히 초등 정보영재를 위한 프로그래밍 교육은 창의적 알고리즘을 개발하는 능력을 기르는 것보다 학습자의 수준에 맞지 않는 특정 프로그래밍 언어의 사용법이나 문법 위주의 교육에 치중하고 있다는 우려의 목소리가 높았다. 이에 본 논문에서는 초등 정보영재의 알고리즘적 사고력을 향상시키기 위한 실생활 중심의 컨텐츠를 제안하고자 한다. 초등학생의 생활과 밀접하게 연관된 주제를 선정하여 학습 동기를 유발하고, Polya의 문제해결모형을 토대로 스스로 이야기를 만들고 그 안에서 알고리즘을 찾아가는 과정을 통해 알고리즘적 사고력을 향상시킬 수 있도록 컨텐츠를 설계하였다.

• Proceedings of the Korea Information Processing Society Conference
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• 2012.04a
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• pp.1406-1409
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• 2012

최근 학문간 융합을 통한 STEAM 융합인재교육에 관한 연구가 활발하게 진행되고 있다. STEAM 교육은 과학, 기술, 공학, 예술 그리고 수학의 학문 영역을 유기적으로 융합하여 차세대 학습자들이 미래 사회에 필요한 핵심역량을 높일 수 있도록 하는 교육방식이다. 국가적인 차원에서 창의적인 융합인재를 위한 미래형 과학기술 교육을 중요하게 여기고 있으며, 과학기술 교육 패러다임에 변화를 기대하고 있다. 따라서 본 연구에서는 융합형 인재양성을 위한 집단지성 기반의 STEAM 교육 방안을 연구하고, 학습자의 과학기술에 대한 흥미와 이해를 높이고 융합적 사고와 문제해결 능력을 배양하기 위한 지능로봇 교육과정을 제시한다. 또한 집단 학습자들 간의 교육 적용 사례를 소개하고, 학습자의 만족도 분석을 통하여 검증하였다. 향후 본 연구의 결과로 집단 학습자의 학습 성취도를 향상시키고, 융합형 과학기술 인재양성 교육방안으로 발전하기를 기대한다.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.571-598
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• 2015

This study aimed to assess the spatial cognition strategies and roles taken by students in the process of solving spatial tasks. For the analysis, this study developed two spatial tests based on the mental rotation test, which were taken by 63 students in their final year in elementary schools. The results of this study showed that in terms of the method of approaching the tasks, students took the comprehensive approach and the partial approach. When solving the tasks, the students were shown to use the imagery thinking or analytic thinking method. In terms of perspective, the students rotated the object or change their perspectives. A comparison of the methods used by the students revealed that when approaching the tasks, the group of students who chose the partial approach had higher scores. In terms of solving the tasks the analytic thinking method, and in terms of perspective, changing perspectives were shown to be more effective. Such effective methods were used more frequently in discrimination tasks than in recognition tasks, and in more complicated items, than in less complicated items. In conclusion, the results of this study suggested that the partial, analytic approach and the change of perspectives are useful strategies in solving tasks which require high cognitive effort.

• Journal of the Korean School Mathematics Society
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• v.4 no.2
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• pp.115-123
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• 2001

In its seventh revision to start in 2001, mathematics will have a new emphasis in the middle school curriculum. Mathematics subject is now composed of practical things in the use of mathematics. Also, the future of new generation, which has been known as the information age, places much focus on problem-solving in order to collect, analyze, synthesize, and judge various kinds informations. This demand of problem-solving ability is not only related with mathematical education but, along the entire educational process, its related to actual life. With this change of social structure, the importance of school education is increasing rapidly. Therefore, in order to grow abilities and create new knowledge, adapted this new method of self-oriented learning in groups to middle school 2nd graders for one year, the results were as follows : 1. Students developed their ability of the use of mathematical terms and signs correctly. 2. Students' mathematical knowledge and problem-solving ability improved as they had increased interest in mathematics. 3. Students' peership was enhanced through their communication and cooperative activities in groups during the class. 4. Students themselves were more willing to volunteer and participate during the class.

• 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.33 no.1
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• pp.1-19
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• 2019

This study deals with the case of student-centered discrete mathematics class with cyber lab. First, we provided lecture notes and cyber labs we developed. In particular, discrete mathematics is a course that covers the principles of algorithms. The purpose of this study is to provide students with basic mathematics, aiming to actively participate in the learning process, to improve their abilities and to reach the ultimate goal of student success with confidence. Second, based on interactions, students were able to prepare for the lectures, review, question, answer, and discussion through an usual learning management system of the school. Third, all the students generated materials through one semester, which were reported, submitted, presented and evaluated. It was possible to improve the learning effectiveness through the discussions and implementation of using some easy open source programming language and codes. Our discrete math laboratory could be practiced without any special knowledge of coding. These lecture models allow students to develop critical thinking skills while describing and presenting their learning and problem-solving processes. We share our experience and our materials including lecture note and cyber lab as well as a possible model of student-centered mathematics class that does not give too much of work load for instructors. This study shares a model that demonstrates that any professor will be able to have an individualized, customized, and creative discrete education without spending much of extra time and assistant, unlike previous research.

• Journal of the Korean earth science society
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• v.22 no.6
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• pp.469-479
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• 2001

This study investigated the trends in the number of applicants and mean score and applicants’ responses on the test items of Earth Science in the College Scholastic Ability Test (CSAT) implemented for 3 years (1999-2001). The percentage of applicants of science track were 43.14% in 1995, but reduced through 29.5% in 2001 to 26.92% in 2002 CSAT For elective subject, about 22% of science track students applied to Earth Science II which ranked third to Biology II and Chemistry II. In 1999, test items were developed to have the expected difficulty 40 ${\sim}$ 59% (6 items) to 60 ${\sim}$ 79% (10 items). But in 2001 every 16 items were developed to have difficulty 60 ${\sim}$ 79%, which was caused by the policy of so called ‘easy CSAT’. Thus the mean score of ‘Earth Science II’ was increased from 50.26 in 1999 through 64.47 in 2000, to 67.58 in 2001. Applicants were generally very good at solving test items focusing on process skills only and familar items but poor at solving test items related to the motion of the earth and planets and sea wave, especially items calling two or more concepts. Thus special measures to cope with the decrease in applicants of science track should be provided. And it is recommended to develop test items with wider range of difficulty and to reduce test items calling process skills only. And special consideration should be given to teaching the content area with poor achievement and high actual difficulty compared to the expected.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.1
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• pp.49-57
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• 2022

Recently, various uses of artificial intelligence have been made possible through the deep artificial neural network structure of machine learning, demonstrating human-like capabilities. Unfortunately, the deep structure of the artificial neural network has not yet been accurately interpreted. This part is acting as anxiety and rejection of artificial intelligence. Among these problems, we solve the capability part of artificial neural networks. Calculate the size of the artificial neural network structure and calculate the size of data that the artificial neural network can process. The calculation method uses the group method used in mathematics to calculate the size of data and artificial neural networks using an order that can know the structure and size of the group. Through this, it is possible to know the capabilities of artificial neural networks, and to relieve anxiety about artificial intelligence. The size of the data and the deep artificial neural network are calculated and verified through numerical experiments.