• School Mathematics
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• v.15 no.4
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• pp.847-866
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• 2013

The purpose of this study was to analyze students' various solution methods revealed in the lessons of finding out the area of plane figures, and to explore instructional implications on how to draw meaningful formalization out of such multiple methods. The teacher in this study tended to select a few solution methods that were easy for students to understand and to induce formalization. An analysis of students' solution methods and the process of formalization showed that students need to understand what parts of the length of the given plane figure they should know, and to identify the base, height, and diagonal line of the figure. The analysis also showed that it was effective to choose the solution methods that were used by many students and that could be easily transformed into a concise formula. Based on these results, this paper provides instructional suggestions for a teacher to orchestrate classroom discussion toward formalization based on students' multiple solution methods.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2002.05a
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• pp.59-64
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• 2002

인지심리학 및 인지언어학 분야에서 시도한 어휘 표상, 특히 움직임과 관련된 동사의 인지도식에 관한 연구들을 비교해보고자 한다. 인간의 언어학적인 지식을 도식적으로 표상 하고자 하는 노력은 언어의 통사적인 외형에만 치중하는 연구에서는 언어의 의미구조를 파악하기 힘들다고 판단하고 의미적인 범주화를 중요시하게 되었다. 본 연구에서는 시각적 이미지 도식을 중점적으로 살펴보기로 한다. 이미지 도식은 공간적 위치 관계, 이동, 형상 등에 관한 지각과 결부되어 있다. 이미지로 나타낸 표상은 근본적으로 세상의 인식과 세상에 대한 행동방법을 사용하게 하는 유추적이고 은유적인 원칙에 기초하고 있다. 이러한 점에 있어서, 언술을 발화한 화자는 어느 정도 주관적인 행동의 능력과 그가 인식한 개념화에서부터 문자화시킨 표상을 구성한다. 인지 원칙에 입각한 의미 표상에 중점을 둔 도식으로는, Langacker, Lakoff, Talmy의 도식이 있다. 프랑스에서 톰 R. Thom과 같은 수학자들은 질적인 현상에 관심을 가져 형역학(morphodynamique)이론을 확립하였는데, 이 이론은 요즘의 인지 연구에 수학적 기초를 제공하였다. R. Thom, J. Petitot-Cocorda의 도식 및 구조 의미론의 창시자라고 불리는 B.Pottier의 도식이 여기에 속한다 J.-P. Descles가 제시한 인지연산문법(Grammaire Applicative et Cognitive)은 다른 인지문법과는 달리 정보 자동처리과정에서 사용할 수 있는 연산자와 피연산자의 관계에 기초한 수학적 연산작용을 발전시켰다. 동사의 의미는 의미-인지 도식으로 설명되는데, 이것은 서로 다른 연산자와 피연산자로 구성된 형식화된 표현이다. 인간의 인지 기능은 언어로 표현되며, 언어는 인간의 의사소통, 사고 행위 및 인지학습의 핵심적 기능을 담당한다. 인간의 언어정보처리 메카니즘은 매우 복잡한 과정이기 때문에 언어정보처리와 관련된 언어심리학, 인지언어학, 형식언어학, 신경해부학 및 인공지능학 등의 관련된 분야의 학제적 연구가 필요하다.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Journal of the Korean BIBLIA Society for library and Information Science
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• v.17 no.1
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• pp.285-303
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• 2006

This study suggests the method of converting thesauri to SKOS step by step and it is formalized in three stages of the conversion process. The study develops output and guidelines for each stage. The converting stages are: (1) Collecting and analyzing thesauri for understanding about structure of terms and semantics of relation. (2) Defining the conversion method and creating ontology of the thesauri. (3) Examining the preservation of forms and various semantic relations between the thesauri and then creating SKOS ontology. This method can be applied to the thesauruses with complicated relations in concepts. In the future, it is needed to have an embodiment of conversion after making the algorithm of conversion by stage with the method suggested in this research.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.4
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• pp.475-496
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• 2018

Although the multiplication of decimal fractions is expected to be easy for students to understand because of the similarity to natural numbers multiplication in computing methods, students show many errors in the multiplication of decimal fractions. This is a result of the instruction focused more on skill mastery than conceptual understanding. This study is a basic study for effectively developing a unit of multiplication of decimal fractions. For this purpose, we analyzed the curriculums' performance standards, significance in teaching-learning and evaluation, contents and methods for teaching multiplication of decimal fractions from the 7th curriculum to the revised curriculum of 2015 and the textbooks' activities and lessons. Further, we analyzed preceding studies and introductory books to suggest effective directions for developing teaching unit. As a result of the analysis, three implications were obtained: First, a meaningful instruction for estimation is needed. Second, it is necessary to present a visual model suitable for understanding the meaning of decimal multiplication. Third, the process of formalizing an algorithms for multiplying decimal fractions needs to be diversified.

• School Mathematics
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• v.7 no.2
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• pp.139-168
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• 2005

The purpose of this study is to investigate children's informal knowledge of the fractional multiplication and to develop a teaching material connecting the informal and the formal knowledge. Six lessons of the pre-teaching material are developed based on literature reviews and administered to the 7 students of the 4th grade in an elementary school. It is shown in these teaching experiments that children's informal knowledge of the fractional multiplication are the direct modeling of using diagram, mathematical thought by informal language, and the representation with operational expression. Further, teaching and learning methods of formalizing children's informal knowledge are obtained as follows. First, the informal knowledge of the repeated sum of the same numbers might be used in (fractional number)$\times$((natural number) and the repeated sum could be expressed simply as in the multiplication of the natural numbers. Second, the semantic meaning of multiplication operator should be understood in (natural number)$\times$((fractional number). Third, the repartitioned units by multiplier have to be recognized as a new units in (unit fractional number)$\times$((unit fractional number). Fourth, the partitioned units should be reconceptualized and the case of disjoint between the denominator in multiplier and the numerator in multiplicand have to be formalized first in (proper fractional number)$\times$(proper fractional number). The above teaching and learning methods are melted in the teaching meterial which is made with corrections and revisions of the pre-teaching meterial.

• Tunnel and Underground Space
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• v.15 no.1 s.54
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• pp.28-38
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• 2005

According to the recent development of measurement system utilizing one or a set of boreholes, visualization of the explored underground became to be a major issue. It induced even the introduction of monitoring apparatuses on the borehole wall with multi-function tool, but the usage of these was often limited by where is unfavorable rock condition and a few of engineers can approach. And so, a portable type of borehole camera with only the essential function has been investigated and a few of commercial models about this is recently being applied into the field condition. This paper was based on the monitoring results obtained using a commercial model by Dr. Nakagawa. Discontinuities in rock mass were the topic for the visualization, and it was studied how can visualize their three dimensional distribution and what a numerical formulation is needed and how to understand the visualization result. The numerical formulation was based on the geometric correlation between the dip direction / dip of discontinuous plane and the trend / plunge of borehole, a set of the equation of a plane was induced. As field application of this into two places, it is found that the above visualization methodology will be especially an useful geotechlical tool for analyzing the local distribution of discontinuities.

• Annual Conference on Human and Language Technology
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• 1996.10a
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• pp.386-392
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• 1996

대용어(anaphor)는 한 문장이나 문장과 문장간에 같은 요소가 되풀이될 때 언어 사용의 경제성(language economy)을 위하여 잉여적 표현을 제거하는 방법으로, 좀 더 간략한 언어 표현으로 대치하여 쓰는 현상이다. 따라서 본 논문에서는 중심어 주도의 단방향 활성 차트 파싱을 이용하여 한국어 문장내에서 야기되는 문맥 대용어의 해결 방안에 대해 제안한다. 이는 자연어를 입력으로 하는 실용목적의 자연어처리 시스템 구축에 있어 필수적으로 요구되는 부분이다. 대용어 해결을 위해 먼저 전산학적인 대용어 정의를 내리고, 대용어와 선행어사이의 의미 분류 및 대용어 해결 과정에 필요한 처리 조건등을 설정하였다 또한 파서내에 대용어 처리를 위해 사전내 자질구조로 ANAPMAJ, ANAPMIN, PERSON, NUM, INDEX자질을 추가하였고, 대용어 해결을 위한 알고리즘을 제안하였으며, 기존에 개발된 HPSG 파서가 처리하는 모든 문장에서 야기된 문맥 대용을 해결하여 파서이후의 응용 시스템에서 이용할 수 있는 내적 표현을 보다 분명하게 형식화하였다.

• Korean Journal of Logic
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• v.22 no.1
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• pp.43-86
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• 2019

If 1st order ZFC is consistent(has a model($M_1$)) it has a transitive denumerable model($M_2$). This leads to a paradoxical situation called 'Skolem paradox'. This can be easily resolved by Skolem's typical resolution. but In the process, we must accept the model theoretic relativity for the concept of set. This relativity can generate a situation where the meaning of the set concept, for example, is given differently depending on the two models. The problem is next. because the sentence '¬denu(PN)' which indicate that PN is not denumerable is equally true in two models, A indistinguishability problem that the concept <¬denu> is not formally indistinguishable in ZFC arise. First, I will give a detail analysis of what the nature of this problem is. And I will provide three ways of responding to this problem from the standpoint of supporting ZFC. First, I will argue that <¬denu> concept, which can be relative to the different models, can be 'almost' distinguished in ZFC by using the formalization of model theory in ZFC. Second, I will show that <¬denu> can change its meaning intrinsically or naturally, by its contextual dependency from the semantic considerations about quantifier that plays a key role in the relativity of <¬denu>. Thus, I will show the model-relative meaning change of <¬denu> concept is a natural phenomenon external to the language, not a matter of responsible for ZFC.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.2
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• pp.285-304
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• 2009

The operations of fractions are the main contents of number and operations in the elementary mathematics curriculum. They are also difficult for students to understand conceptually. Nevertheless, there has been little study on the addition and subtraction of fractions. Given this, this paper explored the connection between the national mathematics curriculum and its concomitant textbooks, the adequacy of when to teach, and the method of constructing each unit to teach addition and subtraction of fractions. This paper then analyzed elementary mathematics textbooks and workbooks by three parts aligned with the general instructional flow: 'introduction', 'activity', and, 'exercise'. First, it was analyzed with regard to the introduction part whether the word problems of textbooks might reflect on students' daily lives as intended, how different meanings of operations would be expected to be taught, and how the subsequent activities were connected with the original word problems. Second, the main analysis of activity part of the textbooks dealt with how to use concrete or iconic models to promote students' conceptual understanding of operations and how to formalize the calculation methods and principles with regard to addition and subtraction of fractions. Third, the analysis of the part of exercise in the textbooks and workbooks was conducted with regard to problem types and meanings of operations. It is expected that the issues and suggestions stemming from this analysis of current textbooks and workbooks are informative in developing new instructional materials aligned to the recently revised mathematics curriculum.