• Korean Journal of Mathematics
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• v.22 no.1
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• pp.169-180
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• 2014

In this study, we consider the informal and formal definition of limit on the basis of middle and high school curriculum, and then analyze the reason of difficulties experienced when sophomores learn the formal definition(${\epsilon}-{\delta}$ procedure) of limit. We conducted teaching of the formal definition of limit with sophomores and analyzed their errors which were appeared when they applied to limits problems. In addition, we try to improve the understanding of ${\epsilon}-{\delta}$ procedure of the limit taught in analysis.

• The Mathematical Education
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• v.47 no.3
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• pp.373-386
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• 2008

In highschool probability education, this study analyzed conflicts between intuitive concept and formal definition which originates from the process of establishing the concept of statistical independence. In judging independence, completely different types of problems requiring their own approach was analyzed by dividing them into two types. By doing so, this study researched a way to view independence as an overall idea. That is purposed to suggest a solution to a conflicts between intuitive concept and formal definition and to help not to judge independence out of wrong intuition. This study also suggests that calculation process which leads to precise perception of sample space and event be provided when we prove independence by expressing events with assembly symbols.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

• Korean Institute of Interior Design Journal
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• v.15 no.4 s.57
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• pp.138-146
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• 2006

Main elements in definition of space value were physical, formal, and reasonable characteristics in the past. Howener recently, definition of space value is changing by being advanced about study concerned with human's cognition and thinking way in definition and analysis of space. As you see, cognitive psychologists have emphasized the importance of human's cognitive structure and process and studied diverse aspects of human's thinking ; consciousness, perception, memory, image, language, decision-making, inference, and so on. Therefore main elements in definition of space value are five-dimensional, psychological, symbolic, mental, emotional characteristics above physical, formal, and reasonable characteristics. As mentioned above, the conversion of thinking focused on reason to thinking focused on human's spirit and emotion is achieved in contemporary architecture and 'human's experience' in space becomes a very important factor. For that reason, the purpose of this study is consideration of human's cognitive process in space by conversion of thinking and gives a definition about experience. And, I would like to define 'experience design' whose main attribute is experience in space and establish theoretical basis of experience design through theoretical researches about experience. This study on experience design that induces users to participate in space and stimulate human's spirit is a important point in definition of space value not only contemporary interior architecture but also prospective generation.

• East Asian mathematical journal
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• v.35 no.2
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• pp.239-257
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• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.675-686
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• 2011

The aim of this paper is two fold: One of them is to introduce a formal definition of ordinals which is equivalent to Neumann's definition without assuming the axiom of regularity. The other is to introduce the weak transfinite set and show that the weak transfinite set is a transfinite limit ordinal.

• School Mathematics
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• v.4 no.4
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• pp.555-563
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• 2002

The purpose of this paper is to try formulating a working definition of connection of informal and formal mathematical knowledge. Many researchers have suggested that informal mathematical knowledge should be connected with school mathematics in the process of learning and teaching it. It is because informal mathematical knowledge might play a important role as a cognitive anchor for understanding school mathematics. To implement the connection of them we need to know what the connection means. In this paper, the connection between informal and formal mathematical knowledge refers to the making of relationship between common attributions involved with the two knowledge. To make it clear, it is discussed that informal knowledge consists of two properties of procedures and conceptions as well as formal mathematical knowledge does. Then, it is possible to make a connection of them. Now it is time to make contribution of our efforts to develop appropriate models to connect informal and formal mathematical knowledge.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• Journal of Construction Engineering and Project Management
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• v.3 no.1
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• pp.22-27
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• 2013

Inter-organizational Relationships (IORs) governance is one of the emerging research areas that have been studied in different contexts (e.g. economics, strategy, organization, and management). This view, particularly, attracted rising attention from academics and practitioners in the context of construction projects, due to the complex forms of IORs in terms of inter-firm exchanges (e.g. engineering, procurement, finance, construction, and operation) in these projects. The focus of IORs governance is to control Inter-organizational relationships among two or more cooperative parties to alleviate conflict and achieve mutual gains. One of the mechanisms that have been identified in the related literature is formal governance mechanism. Although many empirical studies have been conducted using formal governance terms and indicators, there isn't yet a consensual definition of this mechanism and its components that may cause misinterpretation of research results and also impede future research. This paper makes contribution to the concept of IORs governance by clarifying the meaning of formal governance mechanism and identifying different indicators of this mechanism that have been used and identified in previous studies. This provides an innovative and useful framework to understand formal governance mechanism and its application in construction projects.

• International conference on construction engineering and project management
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• 2013.01a
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• pp.321-327
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• 2013

Inter-organizational Relationships (IORs) governance is one of the emerging research areas that have been studied in different contexts (e.g. economics, strategy, organization, and management). This view, particularly, attracted rising attention from academics and practitioners in the context of construction projects, due to the complex forms of IORs in terms of inter-firm exchanges (e.g. engineering, procurement, finance, construction, and operation) in these projects. The focus of IORs governance is to control Inter-organizational relationships among two or more cooperative parties to alleviate conflict and achieve mutual gains. One of the mechanisms that have been identified in the related literature is formal governance mechanism. Although many empirical studies have been conducted using formal governance terms and indicators, there isn't yet a consensual definition of this mechanism and its components that may cause misinterpretation of research results and also impede future research. This paper makes contribution to the concept of IORs governance by clarifying the meaning of formal governance mechanism and identifying different indicators of this mechanism that have been used and identified in previous studies. This provides an innovative and useful framework to understand formal governance mechanism and its application in construction projects.