• 한국수학교육학회지시리즈D:수학교육연구
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• 제23권1호
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• pp.1-12
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• 2020

In this case study, a professor was observed to investigate use of instructional examples when teaching the Intermediate Value Theorem in a calculus course. Video-recorded lessons were analyzed with constant comparison to video-stimulated recall interviews and field notes. The professor employed multiple instructional examples, which was initiated by students and modified by the professor. The professor asked students to build non-existing examples as an informal proof of the Intermediate Value Theorem and assessment of students' previous knowledge. Use of incorrect examples on instructional purpose can be an appropriate way for formative assessment as well as a bridge between informal and formal proofs in college mathematics.

• 한국수학교육학회지시리즈A:수학교육
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• 제52권1호
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• pp.83-95
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• 2013

The purpose of this paper is to explain and reinterprets Apollonius' Symptoms on conic sections based on the current secondary curriculum of mathematics, present the historical background of Apollonius' Symptoms to teachers and students and introduce visualization proof of Apollonius' symptoms on a parabola, a hyperbola and an ellipse by a new method using dynamic geometry software(GSP) respectively.

• 대한수학회보
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• 제46권1호
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• pp.135-146
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• 2009

In the present note we study the properties of weak Armendariz rings, and the connections among weak Armendariz rings, Armendariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a finite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is infinite dimensional, from given any semi prime ring. We next find more examples of weak Armendariz rings.

• 정보교육학회논문지
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• 제11권1호
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• pp.107-116
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• 2007

전자펜을 이용한 문서교정 시스템에서 정확한 교정결과를 보장하기 위해서는 문서 교정자가 드로잉한 교정부호와 문서내용간의 영역 모호성(ambiguity)을 해결하여야 한다. 한편 교정의 대상이 되는 전자문서가 HTML/XML과 같은 경우 교정된 문서구조가 반드시 기 정의된 DTD를 위배하지 않아야 한다. 본 논문에서는 펜 기반의 교정시스템에서 교정부호(마킹)와 대상문서간의 모호성 문제를 최소화하기 위한 기법을 제안한다. 제안 인터페이스에서는 모호성 문제를 최소화하기 위하여 교정부호와 문서간의 컨텍스트(Context)를 반영하였으며 동시에 대상문서의 문서 구조를 유지하기 위한 방법을 제공한다. 그 결과 본 논문에서 제안한 교정 인터페이스는 기존 교정시스템에 비하여 보다 정확한 영역정보를 포함할 수 있으며, 교정부호 입력에 따른 구조문서 변경시에도 원본문서의 DTD에 따르는 문서구조를 유지할 수 있다.

• East Asian mathematical journal
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• 제32권4호
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권2호
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• pp.173-192
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• 2007

We define mathematical learning as a process of overcoming framing difference of teachers and students, two main subjects in a mathematics class. We have reached this definition to the effect that we can grasp a mathematical classroom per so and understand students' mathematical learning in the context. We could clearly understand the process in which the framing differences are overcome by analyzing mutual negotiation of informants in specific cultural models, both in its form as well as in its meaning. We review both of the direct and indirect forms of negotiation while keeping track of 'evolution of subject' in terms of content of negotiation. More specifically, we discuss direct negotiation briefly and review indirect negotiation from three distinct themes of (1) argument structure, (2) revoicing, and (3) development patterns and narrative structure of proof. In addition, we describe the content of negotiation under the title of 'Evolution of Subject.' We found that major modes of mutual negotiation are inter-reference and appropriation while the product of continued negotiation is inter-resemblance.

• International Journal of Computer Science & Network Security
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• 제23권12호
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• pp.167-174
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• 2023

Electronic educational environments in the conditions of quarantine restrictions of COVID-19 have become a common phenomenon for the organization of distance educational activities. Under the conditions of Russian aggression, Ukrainian proof of their use is unique. The purpose of the article is to analyze the role of electronic educational environments in the process of training applicants for higher education in Ukraine in the realities of a large-scale war. General scientific methods (analysis, synthesis, deduction, and induction) and special pedagogical prognostic methods, modeling, and SWOT analysis methods were used. In the results, the general properties of the Internet educational platforms common in Ukraine, the peculiarities of using the Moodle and Prometheus platforms, and an approximate model of the electronic learning environment were discussed. The reasons for the popularity of Moodle among Ukrainian universities are analyzed, but vulnerable elements related to security are emphasized. It was also determined that the high cost of Prometheus software and less functionality made this learning environment less relevant. The conclusions state that the military actions drew the attention of universities in Ukraine to the formation of their own educational platforms. This is especially relevant for technical and military institutions of higher education.

• 한국인터넷방송통신학회논문지
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• 제14권2호
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• pp.161-166
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• 2014

스마트 기기 사용의 증가는 많은 사회적 변화를 가져왔다. 특히 교육에서는 보다 높은 학습효과를 위하여 스마트 기기 적용을 연구하여 왔다. 그러나 인문교양은 전통적인 교육 패턴 뿐만 아니라 과목이 가지는 특성 때문에 정보통신에 적용하기가 매우 어려운 분야였다. 본 연구에서는 인문교양 과목을 디지털 방송에 적용하고 그 효과를 증대시키기 위한 방안을 제시하려 한다. 이를 위하여 인문교양의 스마트 콘텐츠 제작 및 연계 방안을 제시하고, 그 실효성을 위하여 디지털 방송에 적용하는 방안에 대한 설문을 통해 적용 가능성을 제시하고자 한다.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제32권3호
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• pp.257-273
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• 2018

이 논문에서는, 영재학생들을 위한 학습 자료의 관점에서, 선행연구(최근배, 2009, 2011; 이재운, 최근배, 2015)에서 미비한 점이 있는 짝수 각형의 등주문제를 해결하는 과정을 Geometer's Sketchpad로 추론하고 정당화하는 아이디어를 논의하고 있으며, 주된 아이디어는 두 가지의 변형([그림 III-1]과 [그림 III-3])을 사용하는데 나타나는 수학화의 과정이다. 여기에 사용된 아이디어는 제주대학교 영재교육원 수학반 심화과정 프로그램 (등주문제 또는 디도여왕의 문제, 2004년부터 현재까지) 운영 중에 도출된 것이다.

• East Asian mathematical journal
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• 제24권5호
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• pp.527-545
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• 2008

One of the education purpose of the section "Figures" in the eighth grade is to develop students' deductive reasoning ability, which is basic and essential for living in a democratic society. However, most or middle school students feel much more difficulty or even frustration in the study of formal arguments for geometric situations than any other mathematical fields. It is owing to the big gap between inductive reasoning in elementary school education and deductive reasoning, which is not intuitive, in middle school education. Also, it is very burden for students to describe geometric statements exactly by using various appropriate symbols. Moreover, Usage of the same symbols for angle and angle measurement or segments and segments measurement makes students more confused. Since geometric relations is mainly determined by the measurements of geometric objects, students should be able to interpret the geometric properties to the algebraic properties, and vice verse. In this paper, we first compare and contrast inductive and deductive reasoning approaches to justify geometric facts and relations in school curricula. Convincing arguments are based on experiment and experience, then are developed from inductive reasoning to deductive proofs. We introduce teaching methods to help students's understanding for deductive reasoning in the textbook by using stepwise visualization materials. It is desirable that an effective proof instruction should be able to provide teaching methods and visual materials suitable for students' intellectual level and their own intuition.