• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• Journal of Elementary Mathematics Education in Korea
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• v.5 no.1
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• pp.99-120
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• 2001

The purpose of this thesis is to find the guiding direction of mathematical communication in lower grade students of elementary school and to present a new direction about the effect of using concrete material in communication. It is expected that mathematical communication increases when concrete material is used for the students of the lower grades, who are in concrete operational period. Therefore, this study ai s to investigate what characteristics there are in mathematical communication of second grade students and what effect concrete materials have on mathematical communication and learning. The analysis of the teaching record shows that the second grade students use alternative terms in the process of communication since they are not familiar with mathematical symbols or terms, which is a characteristic of communication in a mathematics class in which concrete material is used. In the process of teaming the students apply their living experiences to their teaming. Since a small number of students lead class, the interaction between students is also led by them. The direction of communication in a small group is not centered around solution of a problem, and most students show a more interest in finding answers than in the process of learning. The effect that concrete material has on communication plays an important role in promoting students' speaking activity; it allows students to identify and correct their errors more easily. It also makes students' activities more predictable, and it increases a small group activities through the medium of concrete material. However, it was also noticed that students' listening activities are not appropriately developed since they do not pay attention to a teacher who uses concrete material. The effects that concrete material has on mathematics class can be summarized as follows. Concrete material promotes students' participation in class by triggering their interest of learning of mathematics and helps them to understand the course of learning. It also helps the teaming and formation of concepts for children of low academic performance. And it makes a phased learning possible according to students' ability to use concrete material and to solve a problem. Based upon the results above mentioned, the use of concrete material is absolutely needed in mathematics classes of lower grade elementary school students since it increases communication and gives much influence on mathematics learning. Therefore, teachers need to develop teaching or learning method which can help increase communication, considering the characteristics of students' communication.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.1-19
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• 2016

This study investigated the mathematical notation used today in terms of skip ping the parenthesis. At first we have studied the elementary and secondary curriculum content related to omitted rules. As a result, it is difficult to find explicit evidence to answer that question 'What is the calculation of the $48{\div}2(9+3)$?'. In order to inquire the notation fundamentally, we checked the characteristics on prefix, infix and postfix, and looked into the advantages and disadvantages on infix. At the same time we illuminated the development of mathematical notation from the point of view of skipping the parenthesis. From this investigation, we could check that this interpretation was smooth in the point of view that skipping the parentheses are the image of the function. Through this we proposed some teaching methods including 'teaching mathematical notation based on historic genetic principle', 'reproduction of efforts to overcome the disadvantages of infix and understand the context to choose infix', 'finding the omitted parentheses to identify the fundamental formula' and 'specifying the viewpoint that skipping the multiplication notation can be considered as an image of the function'.

• Journal of the Korean Society for Library and Information Science
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• v.51 no.2
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• pp.5-22
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• 2017

The purpose of this study is to analyze the teaching and learning strategies included in the inquiry tasks of elementary moral textbooks with multiple intelligences (M.I), and to propose educational information services of teacher librarians. It was found that the tasks were mainly designed by the linguistic intelligence, logical & mathematical intelligence and spatial intelligence. In terms of the information literacy process, linguistic intelligence and spatial intelligence are mainly applied to the analysis-understanding stage. Logical & mathematical intelligence is applied to the stage of comprehensive-application and linguistic intelligence is applied to expression-delivery step. In order to cultivate the insufficient M.I in inquiry activities, teacher librarians should improve room and teaching materials of their school library and provide workbooks using the graphic organizer after analyzing the linkage of the inquiry tasks between the subjects.

• School Mathematics
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• v.19 no.2
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• pp.319-343
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• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.

• 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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.2
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• pp.1092-1100
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• 2015

This thesis is a part of a case study conducted in order to understand the trends of the 16th~17th century Cheongju region bigwigs, and has examined the life and academic stream of Seogye Deuk-Yoon LEE (1553-1630) focused on the previous study, "The Great Family Genealogy of Ikjaegong of the Gyeongju LEE Family". Seogye Deuk-Yoon LEE learned from his father Seomgye Jam LEE, and GiSEO, Ji-Hwa PARK from an early age, and based the basic orientation of his studies on one's moral and religious self one's moral and religious self'. This is how he became to emphasize "Sohak" (an introductory book of Confucianism for children), and he made an effort to realize the world of Neo-Confucianism by distributing the 'YEO's Hyangyak(Lue-shih-hsiang-yueeh : autonomic regulations of the district areas)' published on "Sohak". Furthermore, he made great effort in education of the Cheongju by regarding it as his own mission to teach young scholars, continuing on the footsteps of his father. Considering this, Seogye was not only a Confucian scholar that devoted himself to 'Sugi(moral training of himself', but was also a practical scholar that committed his sense of social responsibility in ' teaching' and 'governing the people, who greatly affected the academic world of the regional bigwigs of the Cheongju during the 17th century. Furthermore, Deuk-Yoon LEE was a member of the 'Nangseongpalhyeon(eight wise men of the Cheongju region) together with his disciple Deok-soo LEE, who performed a core role in establishing the 'Gihohakpa(Capital and Chungcheong province School)' and 'Hoseosarim(forest of scholars in Chungcheong province)' of the Cheongju region. As a main figure in establishing the Sinhang Confucian academy, he prepared the socio-economic basis for the 'Gihohakpa' to take place in the Cheongju, and by academically associating with Sagye Jang-Seng Kim without regarding their conflicting parties, he became the bridge in allowing his disciple, Deok-Soo LEE to associate with the academic stream and the 'Gihohakpa'. Through such roles, he allowed the relatively easy establishment of the 'Gihohakpa' and 'Hoseosarim', which continued to Jang-Seng KIM and Si-Yeol SONG, in order to prepare the basis and establish the strength of its basis in the Cheongju region from the late 17th century.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.55-68
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• 2008

In this paper, we investigated difficulties that middle school students face in the teaming process of proof, and then inquired how does learning of proof using GSP ease students' difficulties. Throughout the inspection, we identified that students have difficulties in understanding process of premise and conclusion, use of notation, process of reasoning. And we identified, throughout learning process of proof using GSP, students can be feedbacked for their guess or reasoning, generalize the special case to general properties and have attitude checking ideas needed in proof by themselves.

• Journal of Korea Multimedia Society
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• v.15 no.7
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• pp.951-961
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• 2012

E-books produced in the country provide limited audio service for reading disables. The reason is that those books cannot translate the mathematical expressions and symbols in the context. In this paper, the 'Math Expression Reader' was implemented that can translate the expressions and symbols in the document into Korean speech for those who have reading disabilities. The math to speech generated by this program has been tested to both the public and reading disables and the results of this test has been compared whether they can exactly understand the speech and evaluated the reading rules.

• East Asian mathematical journal
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• v.24 no.5
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• pp.547-564
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• 2008

The purpose of this study was to investigate 5th graders' performance for mixed operational problem. For this purpose. two kinds of studies were conducted: a descriptive study by pencil and paper tests(32 problems) and a clinical study by interviews. The conclusions drawn from the results obtained in this study were as follows: First, students were highly scored in pencil and paper tests(M=85.25%). But that score is not up to scratch. Because the problem was composed of simple calculations and if students calculate problems from only let side, they gel 75% right answer, etc. Second, most of students solved mixed operational problems by text-based way, but some students solved flexibly. There are several error types. The main error type is students' following the wrong order of calculations. Some students have obstacles to express their thought with numerical expressions. So they make errors. Third, students solve mixed operational problems with various strategies. For examples, they solve problems by describing calculation procedures, drawing lines to indicate the order of calculations, carrying out two numerical expressions, etc.