• The Mathematical Education
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• v.62 no.1
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• pp.35-55
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• 2023

The purpose of this study is to examine not only students' cognition in the mathematical error-finding activity of the concept of irrational numbers, but also the students' learning stance regarding the use of errors and a teacher's questioning strategies that lead to changes in the level of mathematical discourse. To this end, error-finding individual activities, group activities, and additional interviews were conducted with 133 middle school students, and students' cognition and the teacher's questioning strategies for changes in students' learning stance and levels of mathematical discourse were analyzed. As a result of the study, students' cognition focuses on the symbolic representation of irrational numbers and the representation of decimal numbers, and they recognize the existence of irrational numbers on a number line, but tend to have difficulty expressing a number line using figures. In addition, the importance of the teacher's leading and exploring questioning strategy was observed to promote changes in students' learning stance and levels of mathematical discourse. This study is valuable in that it specified the method of using errors in mathematics teaching and learning and elaborated the teacher's questioning strategies in finding mathematical errors.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.251-268
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• 1996

In this paper, a higher-order feedforward neural network called ridge polynomial network (RPN) which shows good approximation capability for nonlnear continuous functions defined on compact subsets in multi-dimensional Euclidean spaces, is presented. This network provides more efficient and regular structure as compared to ordinary higher-order feedforward networks based on Gabor-Kolmogrov polynomial expansions, while maintating their fast learning property. the ridge polynomial network is a generalization of the pi-sigma network (PSN) and uses a specialform of ridge polynomials. It is shown that any multivariate polynomial can be exactly represented in this form, and thus realized by a RPN. The approximation capability of the RPNs for arbitrary continuous functions is shown by this representation theorem and the classical weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental function approximation based on learning algorithm of the PSN. Simulation results on several applications such as multivariate function approximation and pattern classification assert nonlinear approximation capability of the RPN.

• Research in Mathematical Education
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• v.18 no.4
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• pp.273-288
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• 2014

In recent years, coding education has been globally emphasized and the Free Semester System will be executed to the public schools in Korea from 2016. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this research aims to design 'learning environment' in which learners can design and construct mathematical objects through computers and print them out through 3D printers. Furthermore, it will design learning mathematics by constructing the figurate number patterns from 'soma cubes' in the playing context and connecting those to algebraic and combinatorial patterns, which will allow students to experience mathematical connectivity. It is expected that the activities of designing figurate number patterns suggested in this research will not only strengthen CT capacity in relation to mathematical thinking but also serve as a meaningful program for the Free Semester System in terms of career experience as 3D printers can be widely used.

• Journal of Educational Research in Mathematics
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• v.11 no.1
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• pp.113-121
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• 2001

The purpose of this paper is to investigate the significance and the role of intuitive model and the example of its development. Intuitive model is the tools of intuition in mathematics and the sources for the creative learning mathematics. It consists of the analogical model, paradigmatic model and diagrammatic model. Intuitive model must have a number features in order to be really useful as heuristic devices. It must present a high degree of natural, consistent and structural correspondence with the original. It must also correspond to human information processing characteristics and enjoy a relative autonomy with respect to the original. Sometimes, the difficulty in teaming mathematics stems from the abstractive characteristics of mathematics. So, we have to assist students' learning using the intuitive model that reveals the concrete representation and various changes of mathematical concepts, rules and principles.

• Korean Institute of Interior Design Journal
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• v.19 no.6
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• pp.20-29
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• 2010

Art historians and critics have defined the style as common features appeared in a class of objects. Abstract common features from a set of objects have been used as a bench mark for date and location of original works. Commonalities in shapes are identified by relationships as well as physical properties from shape descriptions. This paper will focus on how the computer and human can recognize common shape properties from a class of shape objects to learn design knowledge. Shape representation using schema theory has been explored and possible inductive generalization from shape descriptions has been investigated. Also learned shape knowledge can be used. for new design process as design concept. Several design process such as parametric design, replacement design, analogy design etc. are used for these design processes. Works of Mario Botta and Louis Kahn are analyzed for explicitly clarifying the process from conceptual ideas to final designs. In this paper, theories of computer science, artificial intelligence, cognitive science and linguistics are employed as important bases.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.3
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• pp.52-63
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• 1995

A neuro-fuzzy algorithm is presented for nuclear reactor power control in a pressurized water reactor. Automatic reacotr power control is complicated by the use of control rods because of highly nonlinear dynamics in the axial power shape. Thus, manual shaped controls are usually employed even for the limited capability during the power maneuvers. In an attempt to achieve automatic shape control, a neuro-fuzzy approach is considered because fuzzy algorithms are good at various aspects of operator's knowledge representation while neural networks are efficinet structures capable of learning from experience and adaptation to a changing nuclear core state. In the proposed neuro-fuzzy control scheme, the rule base is formulated based ona multi-input multi-output system and the dynamic back-propagation is used for learning. The neuro-fuzzy powere control algorithm has been tested using simulation fesponses of a Korean standard pressurized water reactor. The results illustrate that the proposed control algorithm would be a parctical strategy for automatic nuclear reactor power control.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.157-160
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• 1995

Neural networks potentially offer a general framework for modeling and control of nonlinear systems. The conventional neural network models are a parody of biological neural structures, and have very slow learning. In order to emulate some, dynamic functions, such as learning and adaption, and to better reflect the dynamics of biological neurons, M.M.Gupta and D.H.Rao have developed a 'dynamic neural model'(DNU). Proposed neural unit model is to introduce some dynamics to the neuron transfer function, such that the neuron activity depends on internal states. Numerical examples are presented for a model system. Those case studies showed that the proposed DNU is so useful in practical sense.

• Research in Mathematical Education
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• v.15 no.1
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• pp.45-57
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• 2011

Mathematical thinking is a core element in mathematics education and classroom learning. This paper wish to investigate how primary four (grade 4) students develop their mathematical thinking through working on tasks in multiplication where greatest products of multiplication are required. The tasks include the format of many digit times one digit, 2 digits times 2 digits up to 3 digits times 3 digits. It is found that the process of mathematical thinking of students depends on their own representation in obtaining the product. And the solution is obtained through a pattern/analogy and "pattern plus analogy" process. This specific learning process provides data for understanding structure and mapping in problem solving. The result shows that analogy allows successful extension of solution structure in the tasks.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.449-450
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• 2007

Evolvable hardware(EHW) is a dynamic field that brings together reconfigurable hardware, artificial intelligence, fault tolerance and autonomous systems. This paper gives an introduction to the field. The features that can be used to identify and classify evolvable hardware are the evolutionary algorithm, the implementation and the genotype representation. Evolvable hardware (EHW) is hardware that can change its own circuit structure by genetic learning to achieve maximum adaptation to the environment. In conventional EHW, the learning is executed by software on a computer.

• Journal of Educational Research in Mathematics
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• v.10 no.1
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• pp.139-159
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• 2000

The experimental software such as Cabri II, The Geometer's Sketchpad, etc. provides dynamic environment which construct and explore geometric objects interactively and inductively. It has the effects on mathematics itself differently from other technologies that are used in instruction. What is its characteristics\ulcorner What are the educational implication of it for the learning of geometry\ulcorner How is mental reasoning of geometric problems changed by transformation of the means of representation and the environment to manipulate them\ulcorner In this study, we answer these questions through the review of the related literatures and the analysis of textbooks, teaching materials using it and curricular materials. Also, we identify implications about how the criteria for choosing geometic content and the ways of constructing context, for orchestrating the students' exploration with the secondary geometry curriculum, can be changed.