• Communications of Mathematical Education
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• v.22 no.2
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• pp.137-164
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• 2008

Given the importance of early experience in algebraic thinking, we designed six consecutive lessons in which $4^{th}$ graders were encouraged to recognize patterns in the process of finding the relationships between two quantities and to represent a given problem with various mathematical models. The results showed that students were able to recognize patterns through concrete activities with manipulative materials and employ various mathematical models to represent a given problem situation. While students were able to represent a problem situation with algebraic expressions, they had difficulties in using the equal sign and letters for the unknown value while they attempted to generalize a pattern. This paper concludes with some implications on how to connect algebraic thinking with students' arithmetic or informal thinking in a meaningful way, and how to approach algebra at the elementary school level.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.111-130
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• 2018

In this study, I compared and analyzed the contents of Korean, Japanese, Singapore, American, and Finnish textbooks about fraction which is one of the important and difficult concepts in elementary school mathematics. This is aimed to get the implications for meaningful fractional teaching and learning by analyzing the advantages and disadvantages of the methods and time of introducing the concept because fraction has the diversity of the sub-concepts and the introducing methods or process. As a result of the analysis, the fraction was introduced as part-whole(area) in all five countries' textbooks, but the use of number line, conversion between improper fraction and mixed number, whether to deal with part-whole(set) model. Furthermore, there are differences in the methods in obtaining of the equivalent fraction and the order of arrangement in comparison of fraction. Through this analysis, we discussed the reconsideration of the introducing contexts of fractions, the use of number line when introducing fractions, and the problem of segmentation and classification of contents.

• School Mathematics
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• v.5 no.3
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• pp.361-384
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• 2003

The purpose of this study was to investigate students' problem solving process based on the model of IDEAL if they learn to solve word problems of simultaneous linear equations through structure-representation instruction. The problem solving model of IDEAL is followed by stages; identifying problems(I), defining problems(D), exploring alternative approaches(E), acting on a plan(A). 160 second-grade students of middle schools participated in a study was classified into those of (a) a control group receiving no explicit instruction of structure-representation in word problem solving, and (b) a group receiving structure-representation instruction followed by IDEAL. As a result of this study, a structure-representation instruction improved word-problem solving performance and the students taught by the structure-representation approach discriminate more sharply equivalent problem, isomorphic problem and similar problem than the students of a control group. Also, students of the group instructed by structure-representation approach have less errors in understanding contexts and using data, in transferring mathematical symbol from internal learning relation of word problem and in setting up an equation than the students of a control group. Especially, this study shows that the model of direct transformation and the model of structure-schema in students' problem solving process of I and D stages.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.479-491
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• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.371-381
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• 1993

When the multicollinearity presents in the standard linear regression model, ridge regression might be used to mitigate the effects of collinearity. As the prediction-oriented criterion, the integrated mean sqare error criterion $J_w(k)$ was introduced by Lim, Choi & Park(1980). By noting the equivalent relationship between the $C_k$ criterion and $J_w(k)$ with a special choice of weight function $W(x)$, we propose a more reasonable selection rule of k w.r.t. the $C_k$ criterion than that given in Myers(1986). Next, to find the $\beta(k)$ which behaves reasonably well w.r.t. competing criteria, we adopt the minimax principle in the sense of maximizing the worst relative efficiency of k among competing criteria.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.49-65
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• 2010

The purpose of this study is to encourage the role of domain to consider the teaching of the concept of functions in modeling real situations. To do this, it is analyzed that how to introduce the concept of functions and linear functions in textbooks treated in the 1st grade and the 2nd grade of middle school. This study also reviewed the role of domain in representational activities for modeling real situations using linear functions. In these reviews, it found that many textbooks do not consider the domain in the equations of functions and these graphs and several text books used linear functions for modeling real situations which are not represented by linear functions contextually. It is concluded that the domain of function is an important concept that will be considered any representational activities for functions.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.1
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• pp.77-86
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• 2005

Related-Cipher attack was introduced by Hongjun Wu in 2002. We can consider related ciphers as block ciphers with the same round function but different round number and their key schedules do not depend on the total round number. This attack can be applied to block ciphers when one uses some semi-equivalent keys in related ciphers. In this paper we introduce differential related-cipher attacks on block ciphers, which combine related-cipher attacks with differential cryptanalysis. We apply this attack to the block cipher ARIA and SC2000. Furthermore, related-cipher attack can be combined with other block cipher attacks such as linear cryptanalysis, higher-order differential cryptanalysis, and so on. In this point of view we also analyze some other block ciphers which use flexible number of rounds, SAFER++ and CAST-128.

• Journal of Internet Computing and Services
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• v.23 no.3
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• pp.125-135
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• 2022

This study aims to explore variables using machine learning and provide analysis techniques suitable for predicting pharmacy sales whether government statistical indicators built to create an industrial ecosystem based on data, network, and artificial intelligence affect pharmacy sales. Therefore, this study explored predictive variables and performance through machine learning techniques such as Random Forest, XGBoost, LightGBM, and CatBoost using analysis data from January 2016 to December 2021 for 28 government statistical indicators and pharmacies in the retail sector. As a result of the analysis, economic sentiment index, economic accompanying index circulation change, and consumer sentiment index, which are economic indicators, were found to be important variables affecting pharmacy sales. As a result of examining the indicators MAE, MSE, and RMSE for regression performance, random forests showed the best performance than XGBoost, LightGBM, and CatBoost. Therefore, this study presented variables and optimal machine learning techniques that affect pharmacy sales based on machine learning results, and proposed several implications and follow-up studies.

• Current Research on Agriculture and Life Sciences
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• v.4
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• pp.141-153
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• 1986

This study intends to document the existing cyclical fluctuations of garic and onion price at farm gate level during the period of 1966-1986 in Korea. The existing patterns of such cyclical fluctuations were estimated systematically by removing the seasonal fluctuation and irregular movement as well as secular trend from the original price through the moving average method. It was found that the cyclical fluctuations of garic and onion prices repeated six and seven times respectively during the same period, also the amplitude coefficient of cyclical fluctuations showed speed up in recent years. It was noticed that the cyclical fluctuations of price in onion was higher than that of in garic.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.