• Research in Mathematical Education
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• v.23 no.1
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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.

• The Mathematical Education
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• v.52 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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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.

• Journal of The Korean Association of Information Education
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• v.11 no.1
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• pp.107-116
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• 2007

To produce accurate editing results, the ambiguity of editing scopes related to marked correction signs should be solved. Proofreading the web document modifies the document structures, and the modified structures should be robustly valid for the defined DTD. This paper presents a pen-based proof-reading interface in the XML document. In the proposed interface, correction signs are free-drawn, and the editing scopes are recognized and revised based on the contexts of the document to minimize the ambiguity of the editing scopes. The proposed interface provides both implicit and explicit modification methods for document structures. As a result, the editing scopes processed in the proposed interface are more accurate, and the document structures are maintained valid for DTD after the editing.

• East Asian mathematical journal
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• v.32 no.4
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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.

• The Mathematical Education
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• v.46 no.2 s.117
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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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• v.23 no.12
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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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.2
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• pp.161-166
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• 2014

Using and increasing the smart devices got many changes for social environment. Especially, many researchers have studied application using smart devices for improving the learning performance in education. However, Liberal Arts of Humanities has very difficult to apply to information and communication technology cause of traditional study pattern and unit characteristic. In this paper, we suggest a method to apply the Liberal Arts of Humanities to digital broadcasting and to improve learning performance. For this study, we propose a method to making smart contents and connecting them for Liberal Arts of Humanities. And also, we propose a method for applying them to digital broadcasting in order to proof the learning performance increasing by questionary, and shows the application possibility.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.257-273
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• 2018

In this paper, we deal with the isoprimetric problem of polygons from the point of view of learning materials for elementary gifted students. The isoperimetric problem of the polygon of odd degree can be solved by E-transformation(see Figure III-1) and M-transformation(see Figure III-3). But in the case of even degree's polygon, it is quite difficult to solve the problem because of the connected components of diagonals (here we consider the diagonals forming triangle with two adjacent sides of polygon). The primary purpose of this paper is to give an idea to solve the isoperimetric problem of polygons of even degree using the properties of ellipse. This idea is derived from the programs of the Institute of Science Education for Gifted Students in the Jeju National University.

• East Asian mathematical journal
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• v.24 no.5
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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.