• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.3
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• pp.27-42
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• 1984

The complexity and expensiveness of water resources projects have made optimum operation and design by computer-based techniques of increasing interest in recent years. Water resources problems in real world need many decisions under numerous constraints. In addition there are nonlinearities in the state and return function. This mathematical and technical troublesome must be overcome so that the optimum operation polices are determined. Then traditional dynamic optimization method encountered two major-cruxes: variable discretization and appearance of constraints. Even several recent methods which based on the Differential Dynamic Programming(DDP) have some difficulties in handling of constraints. This paper has presented New DDP which is applicable to multi-reservoir control. It is intended that the method suggested here is superior to abailable alternatives. This belief is supported by analysis and experiments(New DDT does not suffer course of dimensionality and requires no discretization and is able to handle easily all constraints nonlinearity).

• Journal of KIISE:Databases
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• v.28 no.3
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• pp.315-323
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• 2001

The concept of vertical partitioning has been discussed so far in an objective of improving the performance of query execution and system throughput. It can be applied to the areas where the match between data and queries affects performance, which includes partitioning of individual files in centralized environments, data distribution in distributed databases, dividing data among different levels of memory hierarchies, and so on. In general, a vertical partitioning algorithm should support n-ary partitioning as well as a globally optimal solution for the generation of all meaningful fragments. Most previous methods, however, have some limitations to support both of them efficiently. Because the vertical partitioning problem basically includes the fuzziness property, the proper management is required for the fuzziness problem. In this paper we propose an efficient vertical $\alpha$-partitioning algorithm which is based on the fuzzy theory. The method can not only generate all meaningful fragments but also support n-ary partitioning without any complex mathematical computations.

• Journal of Digital Convergence
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• v.19 no.10
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• pp.253-263
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• 2021

Machine learning is the process of constructing a cost function using learning data used for learning and an artificial neural network to predict the data, and finding parameters that minimize the cost function. Parameters are changed by using the gradient-based method of the cost function. The more complex the digital signal and the more complex the problem to be learned, the more complex and deeper the structure of the artificial neural network. Such a complex and deep neural network structure can cause over-fitting problems. In order to avoid over-fitting, a weight decay regularization method of parameters is used. We additionally use the value of the cost function in this method. In this way, the accuracy of machine learning is improved, and the superiority is confirmed through numerical experiments. These results derive accurate values for a wide range of artificial intelligence data through machine learning.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.571-598
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• 2015

This study aimed to assess the spatial cognition strategies and roles taken by students in the process of solving spatial tasks. For the analysis, this study developed two spatial tests based on the mental rotation test, which were taken by 63 students in their final year in elementary schools. The results of this study showed that in terms of the method of approaching the tasks, students took the comprehensive approach and the partial approach. When solving the tasks, the students were shown to use the imagery thinking or analytic thinking method. In terms of perspective, the students rotated the object or change their perspectives. A comparison of the methods used by the students revealed that when approaching the tasks, the group of students who chose the partial approach had higher scores. In terms of solving the tasks the analytic thinking method, and in terms of perspective, changing perspectives were shown to be more effective. Such effective methods were used more frequently in discrimination tasks than in recognition tasks, and in more complicated items, than in less complicated items. In conclusion, the results of this study suggested that the partial, analytic approach and the change of perspectives are useful strategies in solving tasks which require high cognitive effort.

• Communications of Mathematical Education
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• v.27 no.4
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• pp.357-367
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• 2013

It is important to make students do research for oneself. But the practice of inquiry activity is not easy in the mathematics education field. Intellectual curiosities of students are unpredictable. It is important to meet intellectual curiosities of students. We could get a sequence in the process solving a problem. This sequence was expressed in a form of the recurrence relation $a_n=a_{n-1}+a_{n-3}$ ($n{\geq}4$), $a_1=a_2=a_3=1$. We tried to look for the general terms of this sequence. This sequence is similar to Fibonacci sequence, but the process finding the general terms is never similar to Fibonacci sequence. We can get two general terms expressed in different form after our a great deal of effort. We hope that this study will give the spot of education energy.

• Education of Primary School Mathematics
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• v.21 no.1
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• pp.55-73
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• 2018

The purpose of this study is to investigate the effects of cognitive activity on cognitive activities that students imagine and cope with continuously changing quantitative changes in functional tasks represented by linguistic expressions, table of value, and geometric patterns, We identified covariational reasoning levels and investigated the characteristics of students' reasoning process according to the levels of covariational reasoning in the elementary quantitative problem situations. Participants were seven 4th grade elementary students using the questionnaires. The selected students were given study materials. We observed the students' activity sheets and conducted in-depth interviews. As a result of the study, the students' covariational reasoning level for two quantities that are continuously covaried was found to be five, and different reasoning process was shown in quantitative problem situations according to students' covariational reasoning levels. In particular, students with low covariational level had difficulty in grasping the two variables and solved the problem mainly by using the table of value, while the students with the level of chunky and smooth continuous covariation were different from those who considered the flow of time variables. Based on the results of the study, we suggested that various problems related with continuous covariation should be provided and the meanings of the tasks should be analyzed by the teachers.

• Journal of Gifted/Talented Education
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• v.17 no.2
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• pp.307-337
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• 2007

The purpose of this study is to verify the validity of a creativity measurement tool and to discover the creativity characteristics of creative gifted students by assessing the difference in the creativity characteristics of creative gifted students, who were selected from gifted students in elementary and middle schools through the Torrance Test of Creative Thinking(TTCT), according to school level and the type of the students (gifted student in mathematics, gifted student in science). To this research purpose, creative gifted students were selected by the Torrance Test of Creative Thinking(TTCT) on 594 students, who had applied for super gifted education, from 17 gifted students institutes under the jurisdiction of Jeollabukdo office of education, Then, t-tests and multiple regression analysis were performed to analyze the creativity factors between elementary students and middle school students and between mathematics-gifted students and science-gifted students. From the research, the following results were obtained. Although TTCT is effective in distinguishing gifted students with and without creativity, correlation coefficient values between creativity factors(the correlation coefficients between 'fluency' and 'originality' and between 'fluency' and 'elaboration' were .78 and .50 respectively) suggested the possibility of low uniqueness of creativity factors. In addition, compared with elementary students, middle school students showed significantly lower fluency (circles), elaboration(picture construction, picture completion), and the abstractness of titles(picture structure). In the meantime, science-gifted students displayed significantly higher originality(picture construction), and elaboration(picture construction, picture completion, circles) than mathematics-gifted students. Therefore, continuous study is required to enhance the validity of the test for the selection of creativity gifted students. Besides, efforts should be made to find ways to enhance the creativity of gifted students and to resolve the problem of decreasing creativity with student academic level increasing.

• The Mathematical Education
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• v.63 no.3
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• pp.393-409
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• 2024

The number line model, which intuitively marks numerical magnitudes in space, is widely utilized to help in understanding the magnitudes that fractions and decimals represent. The study analyzed 6^th graders' understanding of fractions and decimals, their problem solving strategies, and whether individual differences in the flexibility of various strategy uses are associated with the accuracy of numerical representation, calculation fluency, and overall mathematical achievement. As a result of the study, students showed relatively lower accuracy in representing fractions and decimals on a number line compared to natural numbers, especially for fractions with odd denominators compared to even denominators, and for two-digit decimals compared to three-digit decimals. Regarding strategy use, students primarily used benchmark, segmentation, and approximation strategies for fractions, and benchmark, rounding, and transformation strategies for decimals sequentially. Lastly, as students used various representation strategies for fractions, their accuracy in representing fractions and their overall mathematical achievement scores showed significantly better outcomes. Taken together, we suggest the need for careful instruction on different interpretations of fractions, the place value of decimals, and the meaning of zero in decimal places. Moreover, we discuss instructional methods that integrate the number line model and its diverse representation strategies to enhance students' understanding of fractions and decimals.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.253-261
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• 2004

Game theory is mathematical analysis developed to study involved in making decisions. In 1928, Von Neumann proved that every two-person, zero-sum game with finitely many pure strategies for each player is deterministic. As well, in the early 50's, Nash presented another concept as the basis for a generalization of Von Neumann's theorem. Another central achievement of game theory is the introduction of evolutionary game theory, by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith. Keeping pace with these game theoretical studies, the first computer simulation of co-evolution was tried out by Hillis in 1991. Moreover, Kauffman proposed NK model to analyze co-evolutionary dynamics between different species. He showed how co-evolutionary phenomenon reaches static states and that these states are Nash equilibrium or ESS introduced in game theory. Since the studies about co-evolutionary phenomenon were started, however many other researchers have developed co-evolutionary algorithms, in this paper we propose Game theory based Co-Evolutionary Algorithm (GCEA) and confirm that this algorithm can be a solution of evolutionary problems by searching the ESS.To evaluate newly designed GCEA approach, we solve several test Multi-objective Optimization Problems (MOPs). From the results of these evaluations, we confirm that evolutionary game can be embodied by co-evolutionary algorithm and analyze optimization performance of GCEA by comparing experimental results using GCEA with the results using other evolutionary optimization algorithms.