• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.35-43
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• 2003

The randomization of scalar multiplication in ECC is one of the fundamental concepts in defense methods against side-channel attacks. This paper proposes a countermeasure against simple and differential power analysis attacks through randomizing the transformed m-ary method based on a random m-ary receding algorithm. The proposed method requires an additional computational load compared to the standard m-ary method, yet the power consumption is independent of the secret key. Accordingly, since computational tracks using random window width can resist against SPA and DPA, the proposed countermeasure can improve the security for smart cards.

• 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 Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.237-255
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• 2014

The purpose of this study is to investigate elementary school students' understanding the concept and operations of decimal fraction. The survey research was performed for this study. This survey was done by selecting 156 students. Questionnaire were made in five areas with reference to the 2007 revised mathematics curriculum. Five areas were the concept of decimal fraction, the addition, the subtraction, the multiplication and the division of decimal fraction. The results of such analysis are as follow: The analyzed result of understanding about concepts and operation of decimal fraction showed a high rate of correct answer, more than 85%. Students thought that multiplication and division of decimal fraction is more difficult than addition, subtraction, concept of decimal fraction. As the learning about concepts and operation of decimal fraction progress, the learning gap is bigger. Effort to reduce the learning deficits are needed in the lower grades. Mathematics is the study of the hierarchical. Learning deficits in low-level interfere with the learning in next-level. Therefore systematic supplementary guidance for a natural number and decimal fraction in low-level is needed. And understanding concepts and principles of calculations should be taught first.

• Journal of The Korean Association For Science Education
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• v.34 no.4
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• pp.335-347
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• 2014

Size/scale is a central idea in the science curriculum, providing explanations for various phenomena. However, few studies have been conducted to explore student understanding of this concept and to suggest instructional approaches in scientific contexts. In contrast, there have been more studies in mathematics, regarding the use of number lines to relate the nature of numbers to operation and representation of magnitude. In order to better understand variations in student conceptions of size/scale in scientific contexts and explain learning difficulties including alternative conceptions, this study suggests an approach that links mathematics with the analysis of student conceptions of size/scale, i.e. the analysis of mathematical structure and reasoning for a number line. In addition, data ranging from high school to college students facilitate the interpretation of conceptual complexity in terms of mathematical development of a number line. In this sense, findings from this study better explain the following by mathematical reasoning: (1) varied student conceptions, (2) key aspects of each conception, and (3) potential cognitive dimensions interpreting the size/scale concepts. Results of this study help us to understand the troublesomeness of learning size/scale and provide a direction for developing curriculum and instruction for better understanding.

• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• Education of Primary School Mathematics
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• v.15 no.3
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• pp.219-233
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• 2012

Practicality and value of mathematics can be verified when different problems that we face in life are resolved through mathematical knowledge. This study intends to identify whether the fraction teaching is being taught and learned at current elementary schools for students to recognize practicality and value of mathematical knowledge and to have the ability to apply the concept when solving problems in the real world. Accordingly, contextual problems and noncontextual problems are proposed around fractional arithmetic area, and compared and analyze the achievement level and problem solving processes of them. Analysis showed that there was significant difference in achievement level and solving process between contextual problems and noncontextual problems. To instruct more meaningful learning for student, contextual problems including historical context or practical situation should be presented for students to experience mathematics of creating mathematical knowledge on their own.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.31-61
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• 2013

The purpose of this study is to confirm constructivists' assumption that when a little low level learners are taken in learner-centered instruction based on a constructivism they can also construct knowledge by themselves. To achieve this purpose, the researchers compare the effects of learner-centered instruction based on the constructivism and teacher-centered instruction based on the objective epistemology where second graders learn multiplication facts through the each treatment on learners' reasoning ability and achievement. Some conclusions are drawn from results as follows. First, learner-centered instruction based on a constructivism has significant effect on learners' reasoning ability. Second, learner-centered instruction has slightly positive effect on learners' deductive reasoning ability. Third, learner-centered instruction has more an positive influence on understanding concepts and principles of not-presented mathematical knowledge than teacher-centered instruction when implementing it with a little low level learners.

• School Mathematics
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• v.6 no.2
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• pp.135-151
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• 2004

This study investigated children's realistic response on problematic word problems focused on number operations. Even though word problems and problem solving should be considered in terms of realistic context, results indicates that children's responses didn't show realistic consideration in solving problems. Also, children showed their tendency of mindless or mechanical operation in solving problems and modeling problems

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.6A
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• pp.855-861
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• 2000

This paper concerns a development of LQ-servo PI controller design on the basis of time-domain approach. The motivation is because the previous design techniques developed on the frequency-domain is not well suited meet the time-domain design specifications. Our development techniques used in this paper is base on the convex optimization methods including Lagrange multiplier, dual concept, semidefinite programming.