• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.469-482
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• 2008

This study analysed difficult points on the understanding of infinity when the concept is considered as actual infinity or as potential infinity. And I consider examples that the concept of actual infinity is used in texts of elementary and middle school mathematics. For understanding of modem mathematics, the concept of actual infinity is required necessarily, and the intuition of potential infinity is an epistemological obstacle to get over. Even so, it might be an excessive requirement to make such epistemological rupture from the early school mathematics, since the concept of actual infinity is not intuitive, derives many paradoxes, and cannot offer any proper metaphor.

• 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 Korean Institute of Industrial Engineers
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• v.29 no.2
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• pp.126-134
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• 2003

Among a variety of models proposed by so far to calculate the real options value when the investment decision about the underlying project may be delayed, the Black-Scholes and the binomial lattice models have been widely used and discussed by academics and practitioners. However these two models do not provide us with intuition into how it is constructed and what it does really mean. In this paper, we will therefore explore its components and practically more intuitive meaning. With the components explored, we developed the mathematical model to calculate the real options value and thus strategic net present value, based on the opportunity cost concept, for which the investment decision about the underlying project is postponed by one year. We will finally present a short illustrative example for readers better understanding on the model proposed in the paper.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.355-372
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• 2020

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

• Journal of the Korean housing association
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• v.17 no.4
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• pp.145-153
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• 2006

Ubiquitous space can be described as a combined space of physical space and digital space. Ubiquitous space possesses new possibilities by combining the two. The concept of ubiquitous home will bring new changes in residential space design. First of all, it makes possible for more convenient and secure home. It has to be developed along with city and town level changes as ubiquitous environment. Secondly, concept of extended space as an extension of living space becomes possible by linking with outside spaces. Thirdly, as consumer requirements for residential spaces will become more versatile by social changes, ubiquitous home can be a good means to meet these versatile consumer requirements by accommodating concept of multi-functional space and flexible space. It is quite important to predict user requirements in rapidly changing social environment and versatile personal inclinations. Instead of POE methodology which can analyze and evaluate in exiting types of designs, storytelling methodology can be used to predict and direct for future requirements of living. The methodology makes scenarios of space usage for future living and extracts design requirements for the living. The concept of intelligent space has to be introduced. It is different from digital home that only accomodate digital devices in space. In intelligent space, space itself has to be recognized as an identity that interacts human directly. Intelligent space recognize human requirements and control digital devices as a response. Multi-functional space is closely related with intelligent space that can changes for business, entertainments as well as for rests by user requirements instantly. Flexible space that also intends to meet requirements of mobility and versatility can be attained through the integration of digital technology into current physical mobile systems. Interaction design becomes integral part for ubiquitous space design along with physical design. For the residential space design, digital illiteracy has to be considered for interaction design. Instead of the concept of passive existence, space itself has to be recognized as active subsistence that reacts with human. Intuitive and natural interaction for human will be a key design element for space-human interface design.

• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.247-265
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• 2003

The purpose of this study is to analyze the essence of ratio concept from educational viewpoint. For this purpose, it was tried to examine contents and organizations of the recent teaching of ratio concept in elementary school text of Korea from ‘Syllabus Period’ to ‘the 7th Curriculum Period’ In these text most ratio problems were numerically and algorithmically approached. So the Wiskobas programme was introduced, in which the focal point was not on mathematics as a closed system but on the activity, on the process of mathematization and the subject ‘ratio’ was assigned an important place. There are some educational implications of this study which needs to be mentioned. First, the programme for developing proportional reasoning should be introduced early Many students have a substantial amount of prior knowledge of proportional reasoning. Second, conventional symbol and algorithmic method should be introduced after students have had the opportunity to go through many experiences in intuitive and conceptual way. Third, context problems and real-life situations should be required both to constitute and to apply ratio concept. While working on contort problems the students can develop proportional reasoning and understanding. Fourth, In order to assist student's learning process of ratio concept, visual models have to recommend to use.

• Journal of The Korean Association For Science Education
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• v.16 no.4
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• pp.340-350
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• 1996

Knowledge is composed through the interaction between the concept structure already held by students and their experience, and learning can be said to be the active process of solving the cognitive conflict caused by this interaction. Therefore, this study consists in showing the effective learning method and finding out the elements which the teacher has to own, through examining several forms of pre-conception or mis-conception of the inertia, the force-equilibrium, the action and reaction, the heat, and the electric current, and then finding out their solution and studying student's change in science concepts. For this study, the types of concept on the five above-mentioned materials which students have were examined through the concept-classifying question paper, and the classes to which the class mode for the change of concepts applied, were practised in each different classroom by each different instructor - a professor, a scientist, a teacher, and two students, respectively. And the effect of the teaching strategy based on these classes, and each different instructor' influence on the change of concept in students. were examined. The result of my study is as follows; 1. Students have various types of pre-conception which are different from science concept, and these types of pre-conception tend to last even after learning in class. 2. The thoughts on the correct science concept of the high school third-grade students who learned the physics in the traditional teaching method, and the second grade students who don't learn the physics yet, were nearly equal those of the second grade students by receiving the physics class through the cognitive conflict course were greatly changed especially that students showed the distinct change on mechanics and electric current. 3. Students didn't show the remarkable change of the science concept on the five materials in the four kinds of experimental classes by each different instructor but in the part of mechanics, there was the distinct change between the class by professor and those by the students. This was due to the difference of the authority and the attitude of the concept demonstrator. 1) The authority, the kind attitude, and the responsibility of the expert played an important role in the correct concept-formation of mechanics part - especially in the case of the mis-conception caused by the intuitive belief. 2) In the class by instructor with the democratic teaching method, the change of concept took place more easily, because in his class students could discuss the subject freely, so that they might experience the thought course to give them the confidence on the science concept.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.63-78
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• 2011

The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.4
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• pp.205-215
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• 2006

Pen-input displays, such as LCD tablets and tablet PCs, are already popular for its usability in CAD design, in particular. in concept design phase. We propose an intuitive B-Spline modification scheme that can be used for the CAD systems targeting for such devices. Differently from the control point based modification schemes for the B-splines, our scheme relates user pen marking to determining the final shape of the target curve and surface. This, eventually, reduces time for interacting with the shape parameters (i.e., by control points or direct manipulators), which has been regarded as an unavoidable routine tasks for design. To prove its usability, we made an experiments with selected subjects who have been working for industrial design.

• Proceedings of the IEEK Conference
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• 2000.11a
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• pp.217-220
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• 2000

This paper studies a real-time VBR traffic characterization. There are two big approaches to determine traffic. One is a statistic approach and the other is a deterministic approach. This paper proposes a new constraint function, what we called “Sub-Sum Constraint Function”(SSCF). This function is mainly based on a deterministic approach and uses a statistic approach. It predicts and calculates the next rate with a present information about the stream. SSCF captures the intuitive bounded by a rate lower than its peak rate and closer to its long-term average rate. This model makes a order of the constraint function much less than any other works (O(n)). It can also be mapped on a token bucket algorithm which consists of r (token rate) and b (token depth). We use a concept, EB(effective bandwidth) for a utility of our function and comparing with other techniques such as CBR, average VBR. We simulated 21 multimedia sources for verifying the utility of our function.